Sex, Age, and Urban Context: Modeling Social and Demographic Drivers of Mumps Transmission in Chengdu, China (2008–2019)

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Methods A sex- and age-specific Susceptible – Exposed – Pre-symptomatic – Symptomatic Infected – Asymptomatic Infected – Recovered (SEPIAR) model, adjusted for seasonal variations, was employed to categorize the population and analyze transmission dynamics. Results Over the study period, 40,087 mumps cases were reported in Chengdu, with an annual incidence of 21.72 per 100,000, peaking in 2011 at 40.83 per 100,000. Incidence rates were highest among male students aged 5–14, with significant seasonal peaks in May-July and November-December. District-wise, Wenjiang and Jinniu had the highest rates (45.45 and 43.25 per 100,000), while Jianyang city had the lowest (3.26 per 100,000). The SEPIAR model demonstrated robust fitting across demographics ( R ² = 0.13–0.73, P < 0.001). Notably, females aged 10–14 exhibited the highest transmission risk to males aged 0–14, with all mean time-varying reproduction numbers ( R t ) exceeding 1. The median R t for females aged 10–14 to males aged 5–9 was 1.18, to males aged 0–4 was 0.75, and within the same age group was 0.55. Conclusions This study underscores the critical role of sex and age in mumps transmission and validates the utility of the SEPIAR model for outbreak analysis. To mitigate transmission, we recommend: 1) targeted vaccination campaigns during seasonal peaks, 2) prioritizing booster doses for females aged 10–14, 3) strengthening surveillance in high-incidence districts, and 4) improving healthcare reporting in rural regions. These strategies are vital for achieving sustained mumps control in megacities. Mumps Sex disparities Age disparities Time-dependent reproduction number China Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Mumps is an infectious disease caused by the mumps virus (MuV) that leads to swelling of the salivary glands[ 1 ]. This disease primarily spreads through respiratory droplets[ 2 ]. Globally, over 500,000 cases of mumps are reported annually[ 3 ]. Although the incidence rate has decreased with the administration of the mumps-containing vaccine (MuCV), mumps outbreaks still occur in areas with low vaccination rates[ 4 ]. In China, mumps is a notifiable Class C infectious disease. Despite the inclusion of the Measles-Mumps-Rubella (MMR) vaccine in the national immunization program since 2008, over 250,000 cases of mumps infections are reported annually, with more than 90% occurring in children under 16 years old, particularly in the 5–9 age group[ 5 , 6 ]. Numerous studies have shown that the incidence of mumps varies by sex in different countries, with males having a significantly higher incidence than females[ 7 – 11 ]. From 2004 to 2018, China reported 2,656,766 cases in males and 1,613,180 cases in females, with a male-to-female ratio of 1.64:1[ 12 ]. In Poland in 2020, the incidence rate for males was 1.8 per 100,000, and for females, it was 1.2 per 100,000, with a male-to-female ratio of 1.5:1[ 13 ]. During 2000–2007 in the United States, the average annual incidence rate for males was 9.95 per 100,000, while for females, it was 4.88 per 100,000, with a male-to-female ratio as high as 2.04:1[ 14 ]. The clinical manifestations of mumps also differ by sex, with acute MuV infection occurring more frequently in males[ 15 , 16 ]. A cohort study showed that the overall incidence of mumps-related complications in males is 2.5 times that in females, possibly due to higher rates of meningitis and orchitis in males[ 7 ]. Another study found a male-to-female incidence ratio for meningitis of 6.67:1[ 17 ]. In the pre-vaccine era, the rate of mumps complications was higher. Among male patients, approximately 20% of cases would develop orchitis after puberty, while the incidence of oophoritis and mastitis in female patients was significantly lower than that of orchitis in males[ 18 ]. Common symptoms in children and adolescents, regardless of sex, include salivary gland swelling, fever, and headache[ 19 ]. Although these symptoms are usually mild, some cases may develop severe complications such as meningitis and pancreatitis, potentially impacting long-term health[ 20 ]. Numerous studies, both domestically and internationally, have utilized various mathematical models to analyze the epidemic characteristics and development trends of mumps[ 21 – 24 ]. For instance, time series forecasting using the SARIMA-SVR model, the construction of the SVEILHR model with periodic transmission rates to study the relationship between seasonal fluctuations and mumps transmission, and the use of multi-groups SVEIAR models with infinite distribution delays to explore the impact of vaccination, asymptomatic infections, and population heterogeneity on mumps transmission[ 25 – 27 ]. Shi et al. employed a mixed-effects quasi-Poisson regression model to assess the impact of MMR vaccination on mumps incidence in Guangzhou, China[ 28 ]. Despite these advancements in vaccination and disease control, the transmission characteristics of mumps between sexes and their influencing factors remain scientific questions with research gaps. This study aims to investigate the transmission characteristics of mumps between different sexes and the influence of sex and age on these characteristics. Specific questions include: 1) Are there significant differences in the transmissibility of mumps among different age groups? 2) How do sex and age affect the transmission pathways and speed of mumps? 3) Are current vaccination strategies sufficiently effective for different sexes and age groups, or do they require further optimization? Addressing these questions will not only fill existing research gaps but also provide scientific evidence for developing more precise prevention and control strategies, thereby further reducing the incidence and transmission risk of mumps. Material and methods Study Design This study builds on a previously established age-specific SEPIAR model by dividing the population into males and females to construct a sex- and age-specific SEPIAR transmission model[ 29 ]. Transmission-related parameters were adjusted according to the seasonality of mumps transmission to determine the transmission characteristics and epidemic features of mumps across different sexes and age groups. Data Collection This study collected demographic data from the Chengdu Statistical Yearbook from 2008 to 2019, including annual total population numbers, birth rates, and death rates for each district, to establish a demographic database. Mumps report data from January 1, 2008, to December 31, 2019, were collected from the Chinese Disease Prevention and Control Information System (CISDCP), including sex, age, date of onset, and diagnosis date, to establish a mumps database. The diagnosis of mumps was based on the standards set by the National Health Commission of the People's Republic of China. Reviews of mumps-related natural history literature were conducted, obtaining parameters such as disease course, incubation period, infectious period, and the proportion of asymptomatic infections[ 21 , 26 , 28 – 30 ]. Model construction Sex- and Age-specific SEPIAR model Based on the epidemic characteristics and transmission patterns of mumps in Chengdu, this study explores the transmissibility of mumps among different sexes and builds a sex-specific SEPIAR model. In this model, the population is divided into six categories: Susceptible ( S ), Exposed ( E ), Pre-symptomatic ( P ), Symptomatic Infected ( I ), Asymptomatic Infected ( A ), and Recovered/Removed ( R ). The total population is further divided into eight groups by sex and age, with subscripts m and f representing males and females, and subscripts i and j representing the four age groups for males and females, respectively ( i : males − 1: 0–4 years, 2: 5–9 years, 3: 10–14 years, 4: 15 years and above; j : females − 5: 0–4 years, 6: 5–9 years, 7: 10–14 years, 8: 15 years and above). This model is based on the following assumptions: 1) N represents the total population ( N mi for the number of males, N fj for the number of females), b r is the birth rate, and d r is the natural death rate. 2) The infection rate coefficient after effective contact between S and I is β , and asymptomatic infected individuals A are infectious, with an infectiousness of k 1 (0 ≤ k 1 ≤ 1) times that of symptomatic infected individuals I and k 2 (0 ≤ k 2 ≤ 1) times that of presymptomatic individuals P . Additionally, there is transmissibility between different sexes (with β fjmi representing the coefficient for females infecting males and β mifj for males infecting females). Thus, at time t , for males, the number of new infections is β mimi S mi ( I mi + k 1 A mi + k 2 P mi ) + β fjmi S mi ( I fj + k 1 A fj + k 2 P fj ). 3) The proportion of asymptomatic infected individuals is ρ . Exposed individuals transition through a latent period (1/ ω 1 ), a non-infectious incubation period (1/ ω 2 ), and an infectious incubation period (1/ ω 3 ) to become asymptomatic infected ( A ), pre-symptomatic ( P ), and symptomatic infected ( I ) cases, respectively. At time t , for males, the numbers transitioning from E to A and P are ρω 1 E mi and (1- ρ ) ω 2 E mi , respectively, and the number transitioning from P to I is ω 3 P mi . The model assumes the incubation period of mumps equals the latent period. 4) Symptomatic and asymptomatic cases transition to the recovered/removed ( R ) class after infectious periods of 1/ γ and 1/ γ 1 , respectively. The sex- and age-specific model framework is shown in Fig. 1 , and its equations are as follows: Differential Equations for Males d ( S mi )/ dt = N mi b r - S mi \(\:\sum\:_{i=1}^{n}{\beta\:}_{mimi}\) ( I mi + k 1 A mi + k 2 P mi ) - S mi \(\:\sum\:_{j=1}^{n}{\beta\:}_{fjmi}\) ( I fj + k 1 A fj + k 2 P fj ) - d r S mi d ( E mi )/ dt = S mi \(\:\sum\:_{i=1}^{n}{\beta\:}_{mimi}\) ( I mi + k 1 A mi + k 2 P mi ) + S mi \(\:\sum\:_{j=1}^{n}{\beta\:}_{fjmi}\) ( I fj + k 1 A fj + k 2 P fj ) - ρω 1 E mi - (1 - ρ ) ω 2 E mi - d r E mi d ( A mi )/ dt = ρω 1 E mi - γA mi - d r A mi d ( P mi )/ dt = (1- ρ ) ω 2 E mi - ω 3 P mi - d r P mi d ( I mi )/ dt = ω 3 P mi - γ 1 I mi - d r I mi d ( R mi )/ dt = γA mi + γ 1 I mi - d r R mi i = 1, 2, …, n j = 1, 2, …, n Differential Equations for Females d ( S fj )/ dt = N fj b r - S fj \(\:\sum\:_{j=1}^{n}{\beta\:}_{fjfj}\) ( I fj + k 1 A fj + k 2 P fj ) - S fj \(\:\sum\:_{i=1}^{n}{\beta\:}_{mifj}\) ( I mi + k 1 A mi + k 2 P mi ) - d r S fj d ( E fj )/ dt = S fj \(\:\sum\:_{j=1}^{n}{\beta\:}_{fjfj}\) ( I fj + k 1 A fj + k 2 P fj ) + S fj \(\:\sum\:_{i=1}^{n}{\beta\:}_{mifj}\) ( I mi + k 1 A mi + k 2 P mi ) - ρω 1 E fj - (1 - ρ ) ω 2 E fj - d r E fj d ( A fj )/ dt = ρω 1 E fj - γA fj - d r A fj d ( P fj )/ dt = (1- ρ ) ω 2 E fj - ω 3 P fj - d r P fj d ( I fj )/ dt = ω 3 P fj - γ 1 I fj - d r I fj d ( R fj )/ dt = γA fj + γ 1 I fj - d r R fj i = 1, 2, …, n j = 1, 2, …, n This study considers the seasonality of mumps transmission, which is dynamic and primarily affects the infection rate coefficient ( β )[ 31 , 32 ]. In this model, the mumps transmission rates within and between different age groups ( β mimi , β fjfj , β mifj , and β fjmi ) are also influenced by seasonal variations[ 33 ]. Therefore, the following trigonometric functions were established as shown below: $$\:\beta\:={\beta\:}_{0}[1+{sin}\left(\frac{2\pi\:\left(t+\alpha\:\right)}{T}\right)]$$ In this equation, β 0 , t , α , and T represent the baseline relative transmission rate, time, a constant to adjust the time position, and the time span of the seasonal cycle, respectively. Parameter Estimation According to the model and natural history of mumps, eight parameters are involved: natural birth rate ( b r ), natural death rate ( d r ), infection rate coefficient by sex and age group ( β mifj , where subscripts m and f represent males and females, and subscripts i and j ( i ≠ j ) represent age groups 1 to 8), proportion of asymptomatic infected individuals ( ρ ), relative rate of the latent period ( ω 1 ), relative rate of the non-infectious incubation period ( ω 2 ), relative rate of the infectious period ( ω 3 ), removal rate of asymptomatic infected individuals ( γ 1 ), and removal rate of symptomatic infected individuals ( γ ). A systematic review further confirmed that the proportion of asymptomatic mumps cases ranges between 15% and 27%, suggesting ρ be set to 0.20[ 34 , 35 ]. The incubation period for mumps is 16–18 days. Since mumps patients can secrete MuV in saliva from about seven days before gland swelling to nine days after onset, the infectious and recovery periods for mumps patients are 7 days and 9 days, respectively, thus ω 3 = 1/7 and γ 1 = 1/9, with values of 0.14 and 0.11, respectively[ 36 , 37 ]. The latent and non-infectious periods of mumps, which refer to the difference between the incubation period and the infectious period, are both 9–11 days. This gives a value of 10 days, so ω 1 = ω 2 = 1/10, with a value of 0.10. Considering the actual epidemic definition of mumps in Chengdu and previous research, the course range is set to 5–25 days, with a value of 16 days, and γ = 1/16, with a value of 0.06. Additionally, the values of parameters k 1 and k 2 are set to 0.30[ 38 ]. The meanings and estimated values of each parameter, as well as the initial settings of variables, are shown in Table 1 . Table 1 Descriptions and Values of Parameters in the Sex- and Age-Specific SEPIAR Model of Mumps Parameter Descriptions Method Unit Range Value d r Birth Rate Statistical Yearbook years − 1 0–1 0.01067 b r Death Rate Statistical Yearbook years − 1 0–1 0.00773 β mimi Transmission Coefficient Between Male Age Groups Curve fitting days − 1 0–1 – β fjmi Transmission Coefficient from Females to Male Age Groups Curve fitting days − 1 0–1 – β fjfj Transmission Coefficient Between Female Age Groups Curve fitting days − 1 0–1 – β mifj Transmission Coefficient from Males to Female Age Groups Curve fitting days − 1 0–1 – k 1 Relative Transmission Rate of Asymptomatic to Symptomatic Individuals Reference 1 0–1 0.3 k 2 Relative Transmission Rate of Presymptomatic to Symptomatic Individuals Reference 1 0–1 0.3 ρ Proportion of Asymptomatic Individuals Reference 1 0.15–0.27 0.2 ω 1 Relative Rate of Latent Period Reference days − 1 0.09–0.11 0.1 ω 2 Relative Rate of Non-infectious Period Reference days − 1 0.09–0.11 0.1 ω 3 Relative Rate of Infectious Period Reference days − 1 – 0.14286 γ Recovery Rate of Asymptomatic Infected Individuals Reference days − 1 0.04–0.20 0.06250 γ 1 Recovery Rate of Symptomatic Infected Individuals Reference days − 1 0.04–0.20 0.11111 Quantitative Evaluation of Transmissibility Previous studies have shown that the transmissibility of the MuV is often quantified by the basic reproduction number ( R 0 )[ 39 – 41 ]. R 0 is an indicator of the transmissibility of an infectious disease, defined as the expected number of new cases directly generated by one infectious case during its infectious period in a fully susceptible population. The higher the R 0 value, the greater the transmissibility of the disease. When R 0 is less than 1, the disease will not cause an outbreak, and the number of cases will gradually reduce to zero, leading to disease elimination. When R 0 is greater than 1, the disease will spread. Therefore, R 0 is used as a threshold parameter to predict whether an infection will spread and to assess the potential transmissibility and spread of emerging pathogens. As the epidemic progresses, due to the implementation of government intervention policies, changes in individual behaviors (such as wearing masks, reducing travel), and the reduction in the number of susceptible individuals (due to increased infections or vaccination), the ideal model conditions for defining R 0 are no longer met. At this point, using R 0 to measure transmissibility is no longer suitable, and the effective reproduction number ( R eff ) or time-dependent reproduction number ( R t ) should be used instead. R eff is the expected number of secondary infections caused by a single individual during their entire infectious period in a susceptible population after control measures are implemented. R t refers to the expected number of secondary infections spread by a single infected individual. In this study, we first calculate R eff and then obtain the R t based on the time variations in the R eff expression ( S ( t ) , β ( t ) , ...). Therefore, we use R t to assess the relative transmissibility of mumps within and between different sexes and age groups. This study employs the next-generation matrix (NGM) method to calculate R t , using different age groups of males as an example[ 42 ]. Assuming balanced birth and death rates, we use the first type of next-generation matrix method (Van den Driessche and Watmough Approach) to calculate R eff , and then derive the time-dependent R t by substituting the real-time state function S ( t ) into the R eff expression. R 0 is also obtained by substituting the disease-free equilibrium into the R eff expression. The calculation procedure is detailed in Additional file 1. Simulation Method and Statistical Analyses This study utilized MATLAB (R2021a) and Berkeley Madonna 8.3.18 (developed by Robert Macey and George Oster of the University of California at Berkeley. Copyright©1993–2001 Robert I. Macey & George F. Oster) to fit the actual mumps incidence in Chengdu's entire population and by sexes and age groups from 2008 to 2019. The simulation method (fourth-order Runge-Kutta method with a tolerance setting of 0.001) was the same as in previous studies[ 43 – 45 ]. Data processing, analysis, and the creation of figures and tables were performed using R (Version 4.4.1, R Foundation for Statistical Computing, Vienna, Austria) and GraphPad Prism (version 9.3.0, GraphPad Software, San Diego, California, USA). Coefficient of determination ( R 2 ) values and P values were used to calculate and evaluate the goodness of fit for mumps incidence in Chengdu's entire population and by sexes and age groups, all calculated by GraphPad Prism 9.3.0. Results From 2008 to 2019, Chengdu reported a total of 40,087 mumps cases, with an annual incidence rate of 21.72 per 100,000. The lowest incidence rate was in 2016, at 10.67 per 100,000, and the highest was in 2011, at 40.83 per 100,000. According to the mumps epidemic curve in Chengdu from 2008 to 2019 (annual data) and the timing of the national immunization program (NPI), the mumps epidemic trend in Chengdu can be divided into three distinct phases: 1) Stage of Insignificant Vaccine Effect (January 2008 to December 2011): During this period, the effect of the mumps vaccine was not significant. Although free vaccinations were provided for children aged 18–24 months, the annual incidence initially decreased after 2008 but then significantly increased after 2010. The number of mumps cases decreased from 4,963 in 2008 to 3,177 in 2009, a reduction of 35.99% with an absolute incidence difference of 14.37 per 100,000. However, it then rose sharply to 5,951 cases in 2011, a 46.61% increase compared to 2009, with an absolute incidence difference of 16.14 per 100,000. 2) Stage of Significant Vaccine Effect (January 2012 to December 2016): During this period, the MMR vaccine had a significant effect. With the gradual expansion of MMR vaccine coverage, mumps was effectively controlled. The number of mumps cases decreased from 5,657 in 2012 to 1,983 in 2016, a reduction of 64.95% with an absolute incidence difference of 26.77 per 100,000. 3) Stage of Mumps Case Resurgence (January 2017 to December 2019): During this period, the number of cases rebounded. The number of mumps cases increased slightly each year, peaking at 2,709 cases in 2019, a 14.17% increase compared to 2017, with an absolute incidence difference of 1.16 per 100,000. These results are shown in Fig. 2 A. The monthly trend of mumps incidence from 2008 to 2019 shows clear periodic and seasonal trends, with epidemic peaks occurring every 4–5 years. Each year has two peak months, from May to July and from November to December, as shown in Fig. 2 B. From 2008 to 2019, mumps predominantly affected the 5–14 age group. The annual average incidence rates for males aged 5–9 and 10–14 were 7.97 per 100,000 and 4.31 per 100,000, respectively, while for females aged 5–9 and 10–14, the rates were 5.23 per 100,000 and 2.93 per 100,000, respectively. In 2012, the incidence rates peaked for all groups, with males aged 5–9 and 10–14 reaching 14.30 per 100,000 and 8.59 per 100,000, and females aged 5–9 and 10–14 reaching 9.27 per 100,000 and 5.69 per 100,000, respectively. The annual incidence trends for all age groups were generally consistent with the overall incidence trend in Chengdu, as shown in Fig. 3 A. Among all cases, the number of male cases was 23,955, with an average annual reported incidence rate of 48.25 per 100,000; the number of female cases was 16,132, with an average annual reported incidence rate of 31.08 per 100,000. The incidence ratio of males to females was 1.55:1 (Mann-Whitney U = 0, P < 0.001). There were considerable differences in mumps incidence rates between different age groups of both sexes. The median incidence rate for males aged 0–4 was 129.70 per 100,000 [IQR: (98.13–211.50) per 100,000]; for females, it was 92.99 per 100,000 [IQR: (72.52–136.60) per 100,000], with a male-to-female ratio of 1.39:1. For males aged 5–9, the median incidence rate was 267.20 per 100,000 [IQR: (191.60-469.30) per 100,000]; for females, it was 174.90 per 100,000 [IQR: (126.9-310.50) per 100,000], with a ratio of 1.53:1. For males aged 10–14, the median incidence rate was 143.40 per 100,000 [IQR: (82.97–271.30) per 100,000]; for females, it was 92.55 per 100,000 [IQR: (49.44–201.5) per 100,000], with a ratio of 1.55:1. For males aged 15 and above, the median incidence rate was 3.10 per 100,000 [IQR: (2.20–4.91) per 100,000]; for females, it was 3.61 per 100,000 [IQR: (2.21–4.92) per 100,000], with a ratio of 0.86:1. Specific data and trends are shown in Fig. 3 B. From an occupational distribution perspective, during 2008–2019, the highest cumulative number of reported cases was among students (including different age groups), totaling 20,615 cases, accounting for 51.42% of the total cases. This was followed by children in kindergartens and nursery schools and scattered children, with cumulative cases of 12,573 and 3,576, respectively, accounting for 31.36% and 8.92% of the total cases, as shown in Fig. 4 . From 2008 to 2019, Chengdu's districts and counties reported a total of 38,300 mumps cases, with an average annual incidence rate of 25.36 per 100,000 people. Looking at the cumulative number of cases by districts and counties, Jinniu District reported the most cases, with 3,791 cases (9.90%), followed by Wuhou District with 3,422 cases (8.96%). Pujiang County reported the fewest cases, with only 440 cases (1.15%). The annual incidence rates by district and county showed a trend of initial increase, followed by a decrease, and then a slight rise over the years. After 2008, the mumps epidemic gradually spread from central Chengdu to surrounding areas, peaking in 2011. From 2011 to 2015, the epidemic trend showed a decline, then a rise, and then a decline again, followed by a slight increase in subsequent years. Overall, compared to other regions, Wenjiang District and Jinniu District had relatively high average annual incidence rates of 45.45 per 100,000 and 43.25 per 100,000, respectively. Jianyang City had the lowest average annual incidence rate of 3.26 per 100,000. These results are shown in Fig. 5 . This study used a sex- and age-specific SEPIAR model to fit the actual mumps prevalence rate in Chengdu's total population and in different sexes and age groups (Table 2 ). The fitting effect for the actual incidence rate of the entire population across all ages and sexes in Chengdu was very good ( R ² = 0.73, P < 0.001), as shown in Fig. 6 A. Among all sexes and age groups, the fitting R ² ranged from 0.13 to 0.50, and all were statistically significant ( P < 0.001). The best fitting was for males aged 5–9 years ( R ² = 0.50, P < 0.001), followed by females aged 5–9 years ( R ² = 0.49, P < 0.001), as shown in Fig. 6 B. Table 2 Goodness-of-Fit Tests for the Entire Population and Different Sexes and Age Groups in Chengdu Classification Age groups R 2 P Entire Population – 0.73 < 0.001 Males 0–4 years 0.29 < 0.001 5–9 years 0.50 < 0.001 10–14 years 0.26 < 0.001 ≥ 15 years 0.13 < 0.001 Females 0–4 years 0.16 < 0.001 5–9 years 0.49 < 0.001 10–14 years 0.43 < 0.001 ≥ 15 years 0.14 < 0.001 Based on the sex- and age-specific SEPIAR model, the calculation of mumps transmissibility for the entire population and by sexes and age groups in Chengdu showed that the overall daily transmissibility trend of mumps was consistent with its incidence rate. The peak of R t always occurred 1–2 months before the incidence peak, and from 2005 to 2019, there were clear seasonal patterns and two transmission peaks each year, as shown in Fig. 7 . During the period from 2008 to 2019, the relative R t trends between sexes and age groups also showed two distinct peaks each year. Among these, the average relative transmission risk of females aged 10–14 to males aged 0–4 ( R 71 ) was 1.71, to males aged 5–9 ( R 72 ) was 2.17, to males aged 10–14 ( R 73 ) was 1.56, and to females aged 0–4 ( R 75 ) was 0.71. Additionally, the average relative transmission risk among females aged 5–9 ( R 66 ) was 0.35. For males aged 5–9, the average relative transmission risk to females aged 5–9 ( R 26 ) was 0.46, and to females aged 10–14 ( R 27 ) was 0.50. For males aged 10–14, the average relative transmission risk to females aged 5–9 ( R 36 ) was 0.25. Overall, the age group of females aged 10–14 posed a higher transmission risk to males aged 0–14 (mean of R 71 , mean of R 72 and mean of R 73 values all greater than 1), whereas the transmission risk of different male age groups to other age groups was much lower than that of females, as shown in Fig. 8 . From the calculated median and range of R t between sexes and age groups from 2005 to 2019, the top three were: relative R t of females aged 10–14 to males aged 5–9 (median = 1.18, range: 2.21×10 − 6–16.05), relative R t of females aged 10–14 to males aged 0–4 (median = 0.75, range: 5.29×10–14–13.19), and relative R t within females aged 10–14 (median = 0.55, range: 3.41×10–13–14.52), as shown in Fig. 9 . Discussion In this study, we employed a sex- and age-specific SEPIAR model to more accurately assess the transmissibility of mumps within the population, fully considering population heterogeneity factors. By accounting for the differences in MuV transmission between different sexes and age groups, this model can more accurately reflect the transmission characteristics of mumps across various sexes and age groups. The goodness-of-fit test results indicate that the model is highly effective and can accurately reflect the actual incidence of mumps in different sexes and age groups in Chengdu from 2008 to 2019. During the period from 2008 to 2019, the trend of mumps in Chengdu underwent three stages. The first was the ineffective vaccine stage (2008–2011), during which the effect of the mumps vaccine was not significant. Although free vaccination was provided for children aged 18–24 months, the number of cases initially declined (from 2008 to 2009) but then increased significantly after 2010. This indicates that the initial vaccination efforts were insufficient to maintain a low incidence rate[ 46 ]. The likely reason is that before 2008, the MMR vaccine was classified as a second-class vaccine in Chengdu, following the principles of voluntary, self-paid vaccination. However, due to irregular or inadequate vaccination practices, the vaccination coverage rate was low, resulting in a low level of mumps antibodies. As the number of susceptible individuals accumulated over the years, the chance of mumps infection increased, leading to a rise in reported cases and incidence rates. After 2008, Chengdu followed EPI requirements to provide free MMR vaccination to children aged 18–24 months. However, children born before 2008 were already beyond the recommended vaccination age and became the target group of unvaccinated children. These children were in their school-entry age and were highly susceptible to MuV infection. Therefore, vaccinating only the current 18–24 months old children did not control the incidence among high-risk groups. The second stage was the effective vaccine stage (2012–2016). With the expansion of MMR vaccine coverage, the incidence of mumps was effectively controlled. The number of cases decreased significantly from 5,657 in 2012 to 1,983 in 2016. The marked decline in incidence during this period highlighted the effectiveness of expanding MMR vaccine coverage in controlling mumps outbreaks. The final stage was the resurgence of cases (2017–2019). During this period, mumps cases increased slightly, reaching a peak of 2,709 cases in 2019. The re-emergence of cases suggests gaps in vaccine coverage, waning immunity, or changes in virus transmission dynamics. Many studies indicate that children who received one dose of the MMR vaccine are increasingly likely to contract mumps again over time. The decline in vaccine-induced immunity may be one of the reasons for the resurgence of mumps cases in Chengdu after 2017[ 47 – 49 ]. Continuous monitoring and potential booster vaccination strategies are necessary. The incidence of mumps exhibits clear seasonality, with two annual peak periods (May to July and November to December). To address this seasonal trend, it is necessary to implement targeted interventions (such as wearing masks while traveling, vaccination, etc.), particularly during identified peak seasons and high-risk transmission periods. Analyzing the population distribution of mumps in Chengdu, it primarily affects the 5–14 age group, with incidence rates in males consistently significantly higher than in females. This aligns with previous studies[ 9 , 10 , 30 ]. In terms of occupational distribution, students account for the majority of cases, followed by children in kindergartens and diaspora children. Previous research has shown that mumps outbreaks typically occur in densely populated school environments. Boys are generally more active and have more social contacts than girls, implying higher exposure and thus a greater risk of contracting the MuV[ 50 – 53 ]. Since students usually start school in March and September, susceptible populations accumulate significantly in the following 2–3 months. Once a MuV infection occurs, it can trigger a large-scale outbreak. This also explains why there are two peak months for mumps incidence each year[ 8 ]. The incidence rates of mumps across Chengdu's districts and counties vary significantly. Wenjiang District and Jinniu District have relatively high average annual incidence rates of 45.45 per 100,000 and 43.25 per 100,000, respectively. Jianyang City has the lowest average annual incidence rate, at only 3.26 per 100,000. The high number of mumps cases in Jinniu District and Wenjiang District is likely due to well-established medical facilities and surveillance systems that allow for more accurate recording and reporting of actual cases. Additionally, a large population base increases the opportunity for exposure to infection sources. Studies indicate that insufficient medical standards and a lack of awareness in epidemic reporting by primary healthcare institutions are critical reasons for the spread of mumps in less economically developed areas. Moreover, inconsistencies in MMR vaccination rates are due to differences in socioeconomic status and healthcare conditions across districts[ 22 ]. Additionally, the massive migration of people from surrounding counties to the main urban areas of Chengdu has rapidly increased the population density in the urban districts. This migration phenomenon has intensified crowding, raising the risk of infectious disease transmission[ 54 – 56 ]. The peak of R t always occurs 1–2 months before the peak in incidence, indicating that the transmissibility of mumps increases before the actual reported cases rise. This fact suggests an early intervention window. During this period, public health measures should be taken, such as increasing vaccination or conducting awareness campaigns to reduce transmission. Health authorities should time these campaigns and interventions to coincide with these periods to reduce the overall disease burden during peak seasons. Examining the relative transmissibility by specific sexes and age groups, females aged 10–14 have a higher transmission risk to males aged 0–14 ( R t > 1), while males of different age groups have a much lower transmission risk to other age groups ( R t < 1). This indicates that males have high susceptibility but low transmissibility, while females have lower susceptibility but higher transmissibility. Females have a higher transmissibility than males. There are several possible reasons for this: males and females exhibit significant differences in humoral and cell-mediated immune responses after MMR vaccination[ 57 ]. Studies show that after receiving two doses of the MMR vaccine, females have significantly higher neutralizing antibody titers than males (120.8 IU/mL vs. 98.7 IU/mL, P = 0.038), while males have higher levels of secreted MIP-1α, MIP-1β, TNFα, IL-6, IFNγ, and IL-1β. These results indicate that sex significantly influences mumps-specific humoral and cell-mediated immune responses[ 58 ]. Sex hormones such as estrogen and testosterone may account for these differences, as they can regulate immune system functions[ 56 ]. For example, estrogen is believed to enhance B-cell activity, thereby increasing antibody production. Therefore, when females are infected with the MuV, clinical manifestations such as bilateral parotitis may be less pronounced, potentially leading to delays in implementing control measures and increasing transmission risk. Research has found that males typically exhibit weaker cell-mediated immune responses to viral infections like measles, potentially leading to slower recovery post-infection or less apparent vaccine protection compared to females[ 58 , 59 ]. Studies exploring how sex affects vaccine-induced cellular immunity have found that males generally produce fewer antibodies post-MMR vaccination than females, especially after two doses[ 59 ]. This finding suggests significant differences in the immune system response mechanisms between males and females. Additionally, studies indicate that sex differences in susceptibility to mumps may be due to sex hormone environments or immune gene differences on the X chromosome[ 60 , 61 ]. These findings suggest that differences in immune system response mechanisms between males and females could influence vaccine strategy development. Although males have higher incidence and complication rates of mumps compared to females, females have higher transmissibility and are more likely to transmit the MuV to males. Therefore, in control efforts, we should focus on protecting susceptible females and controlling infected females to reduce their high transmission potential to susceptible males, thereby lowering the overall incidence of mumps in the population and achieving better intervention outcomes. In summary, we recommend prioritizing the expansion of the MuCV vaccination program to ensure comprehensive coverage, including timely catch-up vaccinations for high-risk age groups that missed the initial vaccination phase (such as children born before 2008). Strengthening public health surveillance is crucial for the early detection and monitoring of mumps cases. This involves enhancing reporting mechanisms and the ability of healthcare institutions to collect data promptly and accurately. Addressing socioeconomic disparities by implementing policies that provide free or subsidized vaccines for impoverished communities and ensuring equitable access to healthcare services is vital. Additionally, public health campaigns are recommended to raise awareness of the importance of vaccination and preventive measures, particularly in high-risk periods and areas with low vaccination rates. Practitioners should focus on targeted vaccination measures for school-aged children (especially those aged 5–14), ensuring these measures are implemented before the peak transmission seasons. It is crucial to implement preventive measures during the identified window period (1–2 months before the incidence peak), such as increasing vaccination and public health education, to strengthen early intervention strategies. Health interventions tailored to different sexes should also be considered, including customized vaccination strategies for males and females, especially females aged 10–14, involving monitoring antibody levels and post-vaccination immune responses to address differences in immune reactions. Seasonal preparedness is crucial, requiring targeted interventions such as mask-wearing campaigns and increased vaccination efforts during high-risk periods to effectively reduce mumps incidence. There are some limitations to this study. Firstly, while the study considers the impact of sex and age on mumps transmission, the specific mechanisms of vaccine-induced cell-mediated immune responses are not fully understood. Further research is needed to explore how sex hormones and genetic factors contribute to sex differences. Secondly, the study has limited monitoring time for long-term immunity and persistence of immunity against mumps. Future longitudinal studies could better determine the need and timing for booster doses. Additionally, the impact of socioeconomic factors on vaccine coverage and mumps incidence requires further analysis to develop more targeted interventions. Finally, it is necessary to evaluate the effectiveness of public health campaigns and interventions, including community engagement and behavior changes, to improve overall vaccination rates and reduce mumps transmission. Addressing these limitations can further enhance mumps control strategies. Conclusions This study validated the SEPIAR model, which, by considering sex and age differences, accurately reflects the transmission characteristics of mumps in Chengdu from 2008 to 2019. The inconsistencies in vaccination methods before 2008 indicate the need for continuous monitoring, timely catch-up, and booster vaccinations to address waning immunity. The incidence of mumps is highly seasonal, with peak periods from May to July and November to December each year. The highest incidence is among males aged 5–14, and outbreaks typically occur in densely populated school environments. Therefore, it is necessary to implement targeted interventions during these high-risk periods, such as vaccine registration before students enter school, enhanced vaccination campaigns, and public health education. It is recommended to improve the medical reporting system in less economically developed areas, enhance infrastructure, and focus on increasing the awareness and capacity of primary healthcare institutions to report cases. Females aged 10–14 pose a higher transmission risk compared to males. Therefore, public health measures should prioritize early interventions for females, focusing on protecting susceptible females and controlling infected females. Additionally, sex-specific strategies should be considered, such as prioritizing vaccinations for females upon reaching the appropriate age to improve overall mumps control levels. Abbreviations MuV Mumps virus MuCV mumps-containing vaccines MMR measles-mumps-rubella SEPIAR Susceptible – Exposed – Pre-symptomatic – Symptomatic Infected – Asymptomatic Infected – Recovered CISDCP Chinese Disease Prevention and Control Information System R 0 basic reproduction number R eff effective reproduction number R t time-dependent reproduction number NGM next-generation matrix R 2 coefficient of determination NPI national immunization program Declarations Clinical trial number Not applicable. Ethics approval and consent to participate The study was approved by the Medical Ethics Committee of Chengdu Center for Disease Control and Prevention. Only broad information (such as the date of illness onset) of the cases were collected with no identifying patient information and therefore the informed consent was waived by the ethics committee/institutional review board (IRB) of Medical Ethics Committee of Chengdu Center for Disease Control and Prevention. All methods were carried out in accordance with the relevant guidelines and regulations of the Helsinki Declaration. Availability of data and materials Data that supporting the findings of this study are available from the Chengdu Center for Disease Control and Prevention but there are restrictions on the availability of these data, which were used with permission in this study, and are therefore not publicly available. However, data may be obtained from the authors with permission from Director Liang Wang ( [email protected] ) upon reasonable request. Author Contributions TY: Conceptualization, Methodology, Software, Formal analysis, Visualization and Writing - Original Draft. XD, JL, LL and LX: Data curation and Investigation. YW: Supervision. LW: Writing- Reviewing and Editing. All authors read and approved the final manuscript. Funding This study was partly supported by the Major and Application Projects of Chengdu Science and Technology Key R&D Support Plan (2021-YF09-00061-SN). Acknowledgements The authors would like to express their sincerest gratitude to the following people, without whom the study would not have been possible: (1) study participants for providing data, and (2) field investigators for collecting the data. Conflict of interest The authors declare that they have no competing interests. References Hviid A, Rubin S, Muhlemann K. Mumps. Lancet. 2008;371(9616):932–44. Vaidya SR, Tilavat SM, Hamde VS, Bhattad DR. Outbreak of mumps virus genotype G infection in tribal individuals during 2016-17 in India. Microbiol Immunol. 2018;62(8):517–23. Marlow M, Leung J. Mumps. 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Supplementary Files Additionalfile1.pdf Cite Share Download PDF Status: Published Journal Publication published 21 Apr, 2026 Read the published version in BMC Public Health → Version 1 posted Editorial decision: Revision requested 19 Feb, 2025 Editor assigned by journal 19 Feb, 2025 Submission checks completed at journal 19 Feb, 2025 First submitted to journal 17 Feb, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6052129","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":417980489,"identity":"fcaadb31-1ee8-4bf5-8d67-72009d2c1666","order_by":0,"name":"Tianlong Yang","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Tianlong","middleName":"","lastName":"Yang","suffix":""},{"id":417980490,"identity":"5af0600d-f73a-4986-b7e7-472d5ac28ba2","order_by":1,"name":"Xunbo Du","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Xunbo","middleName":"","lastName":"Du","suffix":""},{"id":417980491,"identity":"824413d2-cd95-4254-8a31-e7b62518a3b1","order_by":2,"name":"Junfan Li","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Junfan","middleName":"","lastName":"Li","suffix":""},{"id":417980492,"identity":"d41fbc83-e8ec-43a8-979c-0d7263d8f74e","order_by":3,"name":"Lu Long","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Lu","middleName":"","lastName":"Long","suffix":""},{"id":417980493,"identity":"675f67cf-93ab-4fa5-8018-6bcd42fbe7b7","order_by":4,"name":"Li Xie","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Xie","suffix":""},{"id":417980496,"identity":"da236288-8880-4636-b654-015c9adb9c37","order_by":5,"name":"Yao Wang","email":"","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":false,"prefix":"","firstName":"Yao","middleName":"","lastName":"Wang","suffix":""},{"id":417980498,"identity":"9be9e464-fd63-415e-8f77-bf49e80d44cc","order_by":6,"name":"Liang Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYLCCBwZAgr3/wQGJHzZybOztBwhrSQBp4TnD+MCyJ82Yj+dMAhFaQISED7NBBdvhxHkSDgZ4VRscP3v4RUKBXZ58BO8xiRs8h9PbJIBG/KjYhlvLmbw0iwSD5GLD231pkjMs0nPbpBsPMPacuY1Ti9mBHDODBAPmxI1zDphJS/BY57bJHEhgZmzDo+X8G5CW+sSNMxLMpP+wMaezSQBNwKvlRo7xgwSDw4nzJXKMDSTYnBMIarG/8cYMGMjHEzfwHEt8INmTZtgGDOSD+Pwi2Z9j/OHDn+rE+e3NB0BRKS/f3n7wwY8K3FqAgE0CRBocQBI6gFUhAjB/AJHyDQSUjYJRMApGwcgFAEyiXwe92nf5AAAAAElFTkSuQmCC","orcid":"","institution":"Chengdu Center for Disease Control and Prevention","correspondingAuthor":true,"prefix":"","firstName":"Liang","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-02-18 03:23:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6052129/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6052129/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12889-026-27302-7","type":"published","date":"2026-04-21T15:58:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":77134859,"identity":"8a42015e-aa77-4149-a85f-1fa7ca7087d0","added_by":"auto","created_at":"2025-02-25 12:52:44","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":352105,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSex- and age-specific SEPIAR model framework of mumps.\u003c/strong\u003e(\u003cem\u003em\u003c/em\u003e and \u003cem\u003ef\u003c/em\u003e represent males and females; \u003cem\u003ei\u003c/em\u003e: males - 1: 0-4 years, 2: 5-9 years, 3: 10-14 years, 4: ≥15 years; \u003cem\u003ej\u003c/em\u003e: females - 5: 0-4 years, 6: 5-9 years, 7: 10-14 years, 8: ≥15 years, respectively (\u003cem\u003ei \u003c/em\u003e≠ \u003cem\u003ej\u003c/em\u003e))\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/7791ef037ae0b90869ff3ab5.jpg"},{"id":77134492,"identity":"6f3af21a-2c3b-45fc-b2ed-d504d748973b","added_by":"auto","created_at":"2025-02-25 12:44:45","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":13082631,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEpidemiological Trends of Mumps in Chengdu from 2008 to 2019. \u003c/strong\u003e(A: Annual incidence rate of mumps; B: Monthly number of cases)\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/78e9294293b650051356abba.jpg"},{"id":77134483,"identity":"18f43251-4ca4-415b-8c2d-c4c50b59f5a4","added_by":"auto","created_at":"2025-02-25 12:44:44","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4952721,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEpidemiological Trends of Mumps Among Different Sexes and Age Groups in Chengdu from 2008 to 2019. \u003c/strong\u003e(A: Prevalence rate (per 100,000 persons); B: Incidence rate (per 100,000 persons))\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/bd399e3ab88285d767e37d7c.jpg"},{"id":77134472,"identity":"da0d5072-3940-481b-964f-afbcb960deef","added_by":"auto","created_at":"2025-02-25 12:44:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1323694,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProportion of Mumps Cases Among Different Occupations in Chengdu from 2008 to 2019.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/7e8e74542737906168a13b4d.png"},{"id":77134501,"identity":"39328129-c6d5-4c8f-866c-dd2afcc1a1fa","added_by":"auto","created_at":"2025-02-25 12:44:45","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":16219848,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eChoropleth maps of Mumps in Various Districts, Counties, and County-level Cities of Chengdu from 2008 to 2019.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/cfcc814f481ddcdb08eeb718.png"},{"id":77136360,"identity":"4170f884-16b9-4d40-8bd2-b07a274a4b82","added_by":"auto","created_at":"2025-02-25 13:00:44","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":11323347,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFitting of Mumps Epidemic Curves in Chengdu from 2008 to 2019 Using the SEPIAR Model for Specific Sexes and Ages. \u003c/strong\u003e(A: Entire population; B: By Specific sexes and age groups)\u003c/p\u003e","description":"","filename":"Figure6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/c7534e846d80986236536ea0.jpg"},{"id":77136357,"identity":"3f5041fd-59dc-4691-8f1c-bbcf8b36f794","added_by":"auto","created_at":"2025-02-25 13:00:44","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1234830,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDaily trends in Incidence Rate and Transmissibility of Mumps in Chengdu from 2008 to 2019.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/f4d0fd38d7723bfee328d2b1.jpg"},{"id":77136359,"identity":"a7fa849e-fbeb-4f70-810f-4d94866aa3cb","added_by":"auto","created_at":"2025-02-25 13:00:44","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":907355,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDaily trends in Relative Transmissibility of Mumps Among Different Sexes and Age Groups in Chengdu from 2008 to 2019.\u003c/strong\u003e (1: males 0-4 years; 2: males 5-9 years; 3: males 10-14 years; 4: males ≥15 years; 5: females 0-4 years; 6: females 5-9 years; 7: females 10-14 years; 8: females ≥15 years)\u003c/p\u003e","description":"","filename":"Figure8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/29f5a06573d1b46bdfb9bc29.jpg"},{"id":77134495,"identity":"a76a607e-af79-445f-a427-00c0323c9ec4","added_by":"auto","created_at":"2025-02-25 12:44:45","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":21709845,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelative Transmissibility of Mumps Among Different Sexes and Age Groups in Chengdu. \u003c/strong\u003e(A: Minimum values; B: Median values; C: Maximum values)\u003c/p\u003e","description":"","filename":"Figure9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/6c828e13438e5ba1989ca073.jpg"},{"id":107928675,"identity":"498d0e0a-bb71-4e60-88c9-6aa9747f2fe9","added_by":"auto","created_at":"2026-04-27 16:11:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":70991311,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/312fcb5d-e5c3-42b6-b5c3-e6d4a2dc4c24.pdf"},{"id":77136358,"identity":"bec09121-783e-4397-ae14-e3d39c41b6b9","added_by":"auto","created_at":"2025-02-25 13:00:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1106581,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6052129/v1/9fba6af89388aaf3eb8d0fb9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sex, Age, and Urban Context: Modeling Social and Demographic Drivers of Mumps Transmission in Chengdu, China (2008–2019)","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMumps is an infectious disease caused by the mumps virus (MuV) that leads to swelling of the salivary glands[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This disease primarily spreads through respiratory droplets[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Globally, over 500,000 cases of mumps are reported annually[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Although the incidence rate has decreased with the administration of the mumps-containing vaccine (MuCV), mumps outbreaks still occur in areas with low vaccination rates[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. In China, mumps is a notifiable Class C infectious disease. Despite the inclusion of the Measles-Mumps-Rubella (MMR) vaccine in the national immunization program since 2008, over 250,000 cases of mumps infections are reported annually, with more than 90% occurring in children under 16 years old, particularly in the 5\u0026ndash;9 age group[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous studies have shown that the incidence of mumps varies by sex in different countries, with males having a significantly higher incidence than females[\u003cspan additionalcitationids=\"CR8 CR9 CR10\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. From 2004 to 2018, China reported 2,656,766 cases in males and 1,613,180 cases in females, with a male-to-female ratio of 1.64:1[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In Poland in 2020, the incidence rate for males was 1.8 per 100,000, and for females, it was 1.2 per 100,000, with a male-to-female ratio of 1.5:1[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. During 2000\u0026ndash;2007 in the United States, the average annual incidence rate for males was 9.95 per 100,000, while for females, it was 4.88 per 100,000, with a male-to-female ratio as high as 2.04:1[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The clinical manifestations of mumps also differ by sex, with acute MuV infection occurring more frequently in males[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. A cohort study showed that the overall incidence of mumps-related complications in males is 2.5 times that in females, possibly due to higher rates of meningitis and orchitis in males[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Another study found a male-to-female incidence ratio for meningitis of 6.67:1[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In the pre-vaccine era, the rate of mumps complications was higher. Among male patients, approximately 20% of cases would develop orchitis after puberty, while the incidence of oophoritis and mastitis in female patients was significantly lower than that of orchitis in males[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Common symptoms in children and adolescents, regardless of sex, include salivary gland swelling, fever, and headache[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Although these symptoms are usually mild, some cases may develop severe complications such as meningitis and pancreatitis, potentially impacting long-term health[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous studies, both domestically and internationally, have utilized various mathematical models to analyze the epidemic characteristics and development trends of mumps[\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. For instance, time series forecasting using the SARIMA-SVR model, the construction of the SVEILHR model with periodic transmission rates to study the relationship between seasonal fluctuations and mumps transmission, and the use of multi-groups SVEIAR models with infinite distribution delays to explore the impact of vaccination, asymptomatic infections, and population heterogeneity on mumps transmission[\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Shi et al. employed a mixed-effects quasi-Poisson regression model to assess the impact of MMR vaccination on mumps incidence in Guangzhou, China[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Despite these advancements in vaccination and disease control, the transmission characteristics of mumps between sexes and their influencing factors remain scientific questions with research gaps.\u003c/p\u003e \u003cp\u003eThis study aims to investigate the transmission characteristics of mumps between different sexes and the influence of sex and age on these characteristics. Specific questions include: 1) Are there significant differences in the transmissibility of mumps among different age groups? 2) How do sex and age affect the transmission pathways and speed of mumps? 3) Are current vaccination strategies sufficiently effective for different sexes and age groups, or do they require further optimization? Addressing these questions will not only fill existing research gaps but also provide scientific evidence for developing more precise prevention and control strategies, thereby further reducing the incidence and transmission risk of mumps.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStudy Design\u003c/h2\u003e \u003cp\u003eThis study builds on a previously established age-specific SEPIAR model by dividing the population into males and females to construct a sex- and age-specific SEPIAR transmission model[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Transmission-related parameters were adjusted according to the seasonality of mumps transmission to determine the transmission characteristics and epidemic features of mumps across different sexes and age groups.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eData Collection\u003c/h3\u003e\n\u003cp\u003eThis study collected demographic data from the Chengdu Statistical Yearbook from 2008 to 2019, including annual total population numbers, birth rates, and death rates for each district, to establish a demographic database. Mumps report data from January 1, 2008, to December 31, 2019, were collected from the Chinese Disease Prevention and Control Information System (CISDCP), including sex, age, date of onset, and diagnosis date, to establish a mumps database. The diagnosis of mumps was based on the standards set by the National Health Commission of the People's Republic of China. Reviews of mumps-related natural history literature were conducted, obtaining parameters such as disease course, incubation period, infectious period, and the proportion of asymptomatic infections[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan additionalcitationids=\"CR29\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eModel construction\u003c/h3\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eSex- and Age-specific SEPIAR model\u003c/h2\u003e \u003cp\u003eBased on the epidemic characteristics and transmission patterns of mumps in Chengdu, this study explores the transmissibility of mumps among different sexes and builds a sex-specific SEPIAR model. In this model, the population is divided into six categories: Susceptible (\u003cem\u003eS\u003c/em\u003e), Exposed (\u003cem\u003eE\u003c/em\u003e), Pre-symptomatic (\u003cem\u003eP\u003c/em\u003e), Symptomatic Infected (\u003cem\u003eI\u003c/em\u003e), Asymptomatic Infected (\u003cem\u003eA\u003c/em\u003e), and Recovered/Removed (\u003cem\u003eR\u003c/em\u003e). The total population is further divided into eight groups by sex and age, with subscripts \u003cem\u003em\u003c/em\u003e and \u003cem\u003ef\u003c/em\u003e representing males and females, and subscripts \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e representing the four age groups for males and females, respectively (\u003cem\u003ei\u003c/em\u003e: males \u0026minus;\u0026thinsp;1: 0\u0026ndash;4 years, 2: 5\u0026ndash;9 years, 3: 10\u0026ndash;14 years, 4: 15 years and above; \u003cem\u003ej\u003c/em\u003e: females \u0026minus;\u0026thinsp;5: 0\u0026ndash;4 years, 6: 5\u0026ndash;9 years, 7: 10\u0026ndash;14 years, 8: 15 years and above). This model is based on the following assumptions:\u003c/p\u003e \u003cp\u003e1) \u003cem\u003eN\u003c/em\u003e represents the total population (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e for the number of males, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e for the number of females), \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e is the birth rate, and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e is the natural death rate.\u003c/p\u003e \u003cp\u003e2) The infection rate coefficient after effective contact between \u003cem\u003eS\u003c/em\u003e and \u003cem\u003eI\u003c/em\u003e is \u003cem\u003eβ\u003c/em\u003e, and asymptomatic infected individuals \u003cem\u003eA\u003c/em\u003e are infectious, with an infectiousness of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e (0\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;1) times that of symptomatic infected individuals \u003cem\u003eI\u003c/em\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e (0\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;1) times that of presymptomatic individuals \u003cem\u003eP\u003c/em\u003e. Additionally, there is transmissibility between different sexes (with \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjmi\u003c/em\u003e\u003c/sub\u003e representing the coefficient for females infecting males and \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emifj\u003c/em\u003e\u003c/sub\u003e for males infecting females). Thus, at time \u003cem\u003et\u003c/em\u003e, for males, the number of new infections is \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emimi\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjmi\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e).\u003c/p\u003e \u003cp\u003e3) The proportion of asymptomatic infected individuals is \u003cem\u003eρ\u003c/em\u003e. Exposed individuals transition through a latent period (1/\u003cem\u003eω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), a non-infectious incubation period (1/\u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), and an infectious incubation period (1/\u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e) to become asymptomatic infected (\u003cem\u003eA\u003c/em\u003e), pre-symptomatic (\u003cem\u003eP\u003c/em\u003e), and symptomatic infected (\u003cem\u003eI\u003c/em\u003e) cases, respectively. At time \u003cem\u003et\u003c/em\u003e, for males, the numbers transitioning from \u003cem\u003eE\u003c/em\u003e to \u003cem\u003eA\u003c/em\u003e and \u003cem\u003eP\u003c/em\u003e are \u003cem\u003eρω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e and (1-\u003cem\u003eρ\u003c/em\u003e) \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e, respectively, and the number transitioning from \u003cem\u003eP\u003c/em\u003e to \u003cem\u003eI\u003c/em\u003e is \u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e. The model assumes the incubation period of mumps equals the latent period.\u003c/p\u003e \u003cp\u003e4) Symptomatic and asymptomatic cases transition to the recovered/removed (\u003cem\u003eR\u003c/em\u003e) class after infectious periods of 1/\u003cem\u003eγ\u003c/em\u003e and 1/\u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, respectively.\u003c/p\u003e \u003cp\u003eThe sex- and age-specific model framework is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and its equations are as follows:\u003c/p\u003e \u003cp\u003eDifferential Equations for Males\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{i=1}^{n}{\\beta\\:}_{mimi}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j=1}^{n}{\\beta\\:}_{fjmi}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{i=1}^{n}{\\beta\\:}_{mimi}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j=1}^{n}{\\beta\\:}_{fjmi}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003eρω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e - (1 - \u003cem\u003eρ\u003c/em\u003e) \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eρω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eγA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e = (1-\u003cem\u003eρ\u003c/em\u003e) \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- ω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- γ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eγA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ei\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, 2, \u0026hellip;, \u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ej\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, 2, \u0026hellip;, \u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003cp\u003eDifferential Equations for Females\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j=1}^{n}{\\beta\\:}_{fjfj}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{i=1}^{n}{\\beta\\:}_{mifj}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j=1}^{n}{\\beta\\:}_{fjfj}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e) + \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{i=1}^{n}{\\beta\\:}_{mifj}\\)\u003c/span\u003e\u003c/span\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emi\u003c/em\u003e\u003c/sub\u003e) - \u003cem\u003eρω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e - (1 \u003cem\u003e- ρ\u003c/em\u003e) \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eρω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003eγA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e - \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e = (1-\u003cem\u003eρ\u003c/em\u003e) \u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- ω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- γ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ed\u003c/em\u003e(\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e)/\u003cem\u003edt\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eγA\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e- d\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003efj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ei\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, 2, \u0026hellip;, \u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ej\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, 2, \u0026hellip;, \u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThis study considers the seasonality of mumps transmission, which is dynamic and primarily affects the infection rate coefficient (\u003cem\u003eβ\u003c/em\u003e)[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. In this model, the mumps transmission rates within and between different age groups (\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emimi\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjfj\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emifj\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjmi\u003c/em\u003e\u003c/sub\u003e) are also influenced by seasonal variations[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Therefore, the following trigonometric functions were established as shown below:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\beta\\:={\\beta\\:}_{0}[1+{sin}\\left(\\frac{2\\pi\\:\\left(t+\\alpha\\:\\right)}{T}\\right)]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this equation, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003et\u003c/em\u003e, \u003cem\u003eα\u003c/em\u003e, and \u003cem\u003eT\u003c/em\u003e represent the baseline relative transmission rate, time, a constant to adjust the time position, and the time span of the seasonal cycle, respectively.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eParameter Estimation\u003c/h3\u003e\n\u003cp\u003eAccording to the model and natural history of mumps, eight parameters are involved: natural birth rate (\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e), natural death rate (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e), infection rate coefficient by sex and age group (\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emifj\u003c/em\u003e\u003c/sub\u003e, where subscripts \u003cem\u003em\u003c/em\u003e and \u003cem\u003ef\u003c/em\u003e represent males and females, and subscripts \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e (\u003cem\u003ei\u003c/em\u003e\u0026thinsp;\u0026ne;\u0026thinsp;\u003cem\u003ej\u003c/em\u003e) represent age groups 1 to 8), proportion of asymptomatic infected individuals (\u003cem\u003eρ\u003c/em\u003e), relative rate of the latent period (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), relative rate of the non-infectious incubation period (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), relative rate of the infectious period (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e), removal rate of asymptomatic infected individuals (\u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), and removal rate of symptomatic infected individuals (\u003cem\u003eγ\u003c/em\u003e). A systematic review further confirmed that the proportion of asymptomatic mumps cases ranges between 15% and 27%, suggesting \u003cem\u003eρ\u003c/em\u003e be set to 0.20[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The incubation period for mumps is 16\u0026ndash;18 days. Since mumps patients can secrete MuV in saliva from about seven days before gland swelling to nine days after onset, the infectious and recovery periods for mumps patients are 7 days and 9 days, respectively, thus \u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1/7 and \u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1/9, with values of 0.14 and 0.11, respectively[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The latent and non-infectious periods of mumps, which refer to the difference between the incubation period and the infectious period, are both 9\u0026ndash;11 days. This gives a value of 10 days, so \u003cem\u003eω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1/10, with a value of 0.10. Considering the actual epidemic definition of mumps in Chengdu and previous research, the course range is set to 5\u0026ndash;25 days, with a value of 16 days, and \u003cem\u003eγ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1/16, with a value of 0.06. Additionally, the values of parameters \u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e are set to 0.30[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The meanings and estimated values of each parameter, as well as the initial settings of variables, are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptions and Values of Parameters in the Sex- and Age-Specific SEPIAR Model of Mumps\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescriptions\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBirth Rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStatistical Yearbook\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eyears\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.01067\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDeath Rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStatistical Yearbook\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eyears\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.00773\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emimi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTransmission Coefficient Between Male Age Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCurve fitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjmi\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTransmission Coefficient from Females to Male Age Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCurve fitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003efjfj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTransmission Coefficient Between Female Age Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCurve fitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003emifj\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTransmission Coefficient from Males to Female Age Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCurve fitting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Transmission Rate of Asymptomatic to Symptomatic Individuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Transmission Rate of Presymptomatic to Symptomatic Individuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u0026ndash;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eρ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProportion of Asymptomatic Individuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.15\u0026ndash;0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eω\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Rate of Latent Period\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.09\u0026ndash;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eω\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Rate of Non-infectious Period\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.09\u0026ndash;0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eω\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Rate of Infectious Period\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.14286\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eγ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRecovery Rate of Asymptomatic Infected Individuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.04\u0026ndash;0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.06250\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eγ\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRecovery Rate of Symptomatic Infected Individuals\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edays\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.04\u0026ndash;0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.11111\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eQuantitative Evaluation of Transmissibility\u003c/h2\u003e \u003cp\u003ePrevious studies have shown that the transmissibility of the MuV is often quantified by the basic reproduction number (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)[\u003cspan additionalcitationids=\"CR40\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is an indicator of the transmissibility of an infectious disease, defined as the expected number of new cases directly generated by one infectious case during its infectious period in a fully susceptible population. The higher the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e value, the greater the transmissibility of the disease. When \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is less than 1, the disease will not cause an outbreak, and the number of cases will gradually reduce to zero, leading to disease elimination. When \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is greater than 1, the disease will spread. Therefore, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is used as a threshold parameter to predict whether an infection will spread and to assess the potential transmissibility and spread of emerging pathogens. As the epidemic progresses, due to the implementation of government intervention policies, changes in individual behaviors (such as wearing masks, reducing travel), and the reduction in the number of susceptible individuals (due to increased infections or vaccination), the ideal model conditions for defining \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e are no longer met. At this point, using \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e to measure transmissibility is no longer suitable, and the effective reproduction number (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e) or time-dependent reproduction number (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) should be used instead. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e is the expected number of secondary infections caused by a single individual during their entire infectious period in a susceptible population after control measures are implemented. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e refers to the expected number of secondary infections spread by a single infected individual. In this study, we first calculate \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e and then obtain the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e based on the time variations in the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e expression (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e(\u003cem\u003et\u003c/em\u003e)\u003c/sub\u003e, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e(\u003cem\u003et\u003c/em\u003e)\u003c/sub\u003e, ...). Therefore, we use \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e to assess the relative transmissibility of mumps within and between different sexes and age groups. This study employs the next-generation matrix (NGM) method to calculate \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e, using different age groups of males as an example[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Assuming balanced birth and death rates, we use the first type of next-generation matrix method (Van den Driessche and Watmough Approach) to calculate \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e, and then derive the time-dependent \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e by substituting the real-time state function \u003cem\u003eS\u003c/em\u003e\u003csub\u003e(\u003cem\u003et\u003c/em\u003e)\u003c/sub\u003e into the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e expression. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is also obtained by substituting the disease-free equilibrium into the \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e expression. The calculation procedure is detailed in Additional file 1.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSimulation Method and Statistical Analyses\u003c/h3\u003e\n\u003cp\u003eThis study utilized MATLAB (R2021a) and Berkeley Madonna 8.3.18 (developed by Robert Macey and George Oster of the University of California at Berkeley. Copyright\u0026copy;1993\u0026ndash;2001 Robert I. Macey \u0026amp; George F. Oster) to fit the actual mumps incidence in Chengdu's entire population and by sexes and age groups from 2008 to 2019. The simulation method (fourth-order Runge-Kutta method with a tolerance setting of 0.001) was the same as in previous studies[\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Data processing, analysis, and the creation of figures and tables were performed using R (Version 4.4.1, R Foundation for Statistical Computing, Vienna, Austria) and GraphPad Prism (version 9.3.0, GraphPad Software, San Diego, California, USA). Coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) values and \u003cem\u003eP\u003c/em\u003e values were used to calculate and evaluate the goodness of fit for mumps incidence in Chengdu's entire population and by sexes and age groups, all calculated by GraphPad Prism 9.3.0.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eFrom 2008 to 2019, Chengdu reported a total of 40,087 mumps cases, with an annual incidence rate of 21.72 per 100,000. The lowest incidence rate was in 2016, at 10.67 per 100,000, and the highest was in 2011, at 40.83 per 100,000. According to the mumps epidemic curve in Chengdu from 2008 to 2019 (annual data) and the timing of the national immunization program (NPI), the mumps epidemic trend in Chengdu can be divided into three distinct phases: 1) Stage of Insignificant Vaccine Effect (January 2008 to December 2011): During this period, the effect of the mumps vaccine was not significant. Although free vaccinations were provided for children aged 18\u0026ndash;24 months, the annual incidence initially decreased after 2008 but then significantly increased after 2010. The number of mumps cases decreased from 4,963 in 2008 to 3,177 in 2009, a reduction of 35.99% with an absolute incidence difference of 14.37 per 100,000. However, it then rose sharply to 5,951 cases in 2011, a 46.61% increase compared to 2009, with an absolute incidence difference of 16.14 per 100,000. 2) Stage of Significant Vaccine Effect (January 2012 to December 2016): During this period, the MMR vaccine had a significant effect. With the gradual expansion of MMR vaccine coverage, mumps was effectively controlled. The number of mumps cases decreased from 5,657 in 2012 to 1,983 in 2016, a reduction of 64.95% with an absolute incidence difference of 26.77 per 100,000. 3) Stage of Mumps Case Resurgence (January 2017 to December 2019): During this period, the number of cases rebounded. The number of mumps cases increased slightly each year, peaking at 2,709 cases in 2019, a 14.17% increase compared to 2017, with an absolute incidence difference of 1.16 per 100,000. These results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA. The monthly trend of mumps incidence from 2008 to 2019 shows clear periodic and seasonal trends, with epidemic peaks occurring every 4\u0026ndash;5 years. Each year has two peak months, from May to July and from November to December, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB.\u003c/p\u003e \u003cp\u003eFrom 2008 to 2019, mumps predominantly affected the 5\u0026ndash;14 age group. The annual average incidence rates for males aged 5\u0026ndash;9 and 10\u0026ndash;14 were 7.97 per 100,000 and 4.31 per 100,000, respectively, while for females aged 5\u0026ndash;9 and 10\u0026ndash;14, the rates were 5.23 per 100,000 and 2.93 per 100,000, respectively. In 2012, the incidence rates peaked for all groups, with males aged 5\u0026ndash;9 and 10\u0026ndash;14 reaching 14.30 per 100,000 and 8.59 per 100,000, and females aged 5\u0026ndash;9 and 10\u0026ndash;14 reaching 9.27 per 100,000 and 5.69 per 100,000, respectively. The annual incidence trends for all age groups were generally consistent with the overall incidence trend in Chengdu, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA. Among all cases, the number of male cases was 23,955, with an average annual reported incidence rate of 48.25 per 100,000; the number of female cases was 16,132, with an average annual reported incidence rate of 31.08 per 100,000. The incidence ratio of males to females was 1.55:1 (Mann-Whitney U\u0026thinsp;=\u0026thinsp;0, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001). There were considerable differences in mumps incidence rates between different age groups of both sexes. The median incidence rate for males aged 0\u0026ndash;4 was 129.70 per 100,000 [IQR: (98.13\u0026ndash;211.50) per 100,000]; for females, it was 92.99 per 100,000 [IQR: (72.52\u0026ndash;136.60) per 100,000], with a male-to-female ratio of 1.39:1. For males aged 5\u0026ndash;9, the median incidence rate was 267.20 per 100,000 [IQR: (191.60-469.30) per 100,000]; for females, it was 174.90 per 100,000 [IQR: (126.9-310.50) per 100,000], with a ratio of 1.53:1. For males aged 10\u0026ndash;14, the median incidence rate was 143.40 per 100,000 [IQR: (82.97\u0026ndash;271.30) per 100,000]; for females, it was 92.55 per 100,000 [IQR: (49.44\u0026ndash;201.5) per 100,000], with a ratio of 1.55:1. For males aged 15 and above, the median incidence rate was 3.10 per 100,000 [IQR: (2.20\u0026ndash;4.91) per 100,000]; for females, it was 3.61 per 100,000 [IQR: (2.21\u0026ndash;4.92) per 100,000], with a ratio of 0.86:1. Specific data and trends are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB. From an occupational distribution perspective, during 2008\u0026ndash;2019, the highest cumulative number of reported cases was among students (including different age groups), totaling 20,615 cases, accounting for 51.42% of the total cases. This was followed by children in kindergartens and nursery schools and scattered children, with cumulative cases of 12,573 and 3,576, respectively, accounting for 31.36% and 8.92% of the total cases, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFrom 2008 to 2019, Chengdu's districts and counties reported a total of 38,300 mumps cases, with an average annual incidence rate of 25.36 per 100,000 people. Looking at the cumulative number of cases by districts and counties, Jinniu District reported the most cases, with 3,791 cases (9.90%), followed by Wuhou District with 3,422 cases (8.96%). Pujiang County reported the fewest cases, with only 440 cases (1.15%). The annual incidence rates by district and county showed a trend of initial increase, followed by a decrease, and then a slight rise over the years. After 2008, the mumps epidemic gradually spread from central Chengdu to surrounding areas, peaking in 2011. From 2011 to 2015, the epidemic trend showed a decline, then a rise, and then a decline again, followed by a slight increase in subsequent years. Overall, compared to other regions, Wenjiang District and Jinniu District had relatively high average annual incidence rates of 45.45 per 100,000 and 43.25 per 100,000, respectively. Jianyang City had the lowest average annual incidence rate of 3.26 per 100,000. These results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThis study used a sex- and age-specific SEPIAR model to fit the actual mumps prevalence rate in Chengdu's total population and in different sexes and age groups (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The fitting effect for the actual incidence rate of the entire population across all ages and sexes in Chengdu was very good (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.73, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA. Among all sexes and age groups, the fitting \u003cem\u003eR\u003c/em\u003e\u0026sup2; ranged from 0.13 to 0.50, and all were statistically significant (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The best fitting was for males aged 5\u0026ndash;9 years (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.50, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), followed by females aged 5\u0026ndash;9 years (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.49, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eGoodness-of-Fit Tests for the Entire Population and Different Sexes and Age Groups in Chengdu\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClassification\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAge groups\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEntire Population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eMales\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u0026ndash;4 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u0026ndash;9 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u0026ndash;14 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ge;\u0026thinsp;15 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eFemales\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u0026ndash;4 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u0026ndash;9 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u0026ndash;14 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ge;\u0026thinsp;15 years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBased on the sex- and age-specific SEPIAR model, the calculation of mumps transmissibility for the entire population and by sexes and age groups in Chengdu showed that the overall daily transmissibility trend of mumps was consistent with its incidence rate. The peak of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e always occurred 1\u0026ndash;2 months before the incidence peak, and from 2005 to 2019, there were clear seasonal patterns and two transmission peaks each year, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. During the period from 2008 to 2019, the relative \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e trends between sexes and age groups also showed two distinct peaks each year. Among these, the average relative transmission risk of females aged 10\u0026ndash;14 to males aged 0\u0026ndash;4 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e71\u003c/sub\u003e) was 1.71, to males aged 5\u0026ndash;9 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e72\u003c/sub\u003e) was 2.17, to males aged 10\u0026ndash;14 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e73\u003c/sub\u003e) was 1.56, and to females aged 0\u0026ndash;4 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e75\u003c/sub\u003e) was 0.71. Additionally, the average relative transmission risk among females aged 5\u0026ndash;9 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e66\u003c/sub\u003e) was 0.35. For males aged 5\u0026ndash;9, the average relative transmission risk to females aged 5\u0026ndash;9 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e26\u003c/sub\u003e) was 0.46, and to females aged 10\u0026ndash;14 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e27\u003c/sub\u003e) was 0.50. For males aged 10\u0026ndash;14, the average relative transmission risk to females aged 5\u0026ndash;9 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e36\u003c/sub\u003e) was 0.25. Overall, the age group of females aged 10\u0026ndash;14 posed a higher transmission risk to males aged 0\u0026ndash;14 (mean of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e71\u003c/sub\u003e, mean of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e72\u003c/sub\u003e and mean of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e73\u003c/sub\u003e values all greater than 1), whereas the transmission risk of different male age groups to other age groups was much lower than that of females, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. From the calculated median and range of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e between sexes and age groups from 2005 to 2019, the top three were: relative \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e of females aged 10\u0026ndash;14 to males aged 5\u0026ndash;9 (median\u0026thinsp;=\u0026thinsp;1.18, range: 2.21\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6\u0026ndash;16.05), relative \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e of females aged 10\u0026ndash;14 to males aged 0\u0026ndash;4 (median\u0026thinsp;=\u0026thinsp;0.75, range: 5.29\u0026times;10\u0026ndash;14\u0026ndash;13.19), and relative \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e within females aged 10\u0026ndash;14 (median\u0026thinsp;=\u0026thinsp;0.55, range: 3.41\u0026times;10\u0026ndash;13\u0026ndash;14.52), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e "},{"header":"Discussion","content":"\u003cp\u003eIn this study, we employed a sex- and age-specific SEPIAR model to more accurately assess the transmissibility of mumps within the population, fully considering population heterogeneity factors. By accounting for the differences in MuV transmission between different sexes and age groups, this model can more accurately reflect the transmission characteristics of mumps across various sexes and age groups. The goodness-of-fit test results indicate that the model is highly effective and can accurately reflect the actual incidence of mumps in different sexes and age groups in Chengdu from 2008 to 2019.\u003c/p\u003e \u003cp\u003eDuring the period from 2008 to 2019, the trend of mumps in Chengdu underwent three stages. The first was the ineffective vaccine stage (2008\u0026ndash;2011), during which the effect of the mumps vaccine was not significant. Although free vaccination was provided for children aged 18\u0026ndash;24 months, the number of cases initially declined (from 2008 to 2009) but then increased significantly after 2010. This indicates that the initial vaccination efforts were insufficient to maintain a low incidence rate[\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The likely reason is that before 2008, the MMR vaccine was classified as a second-class vaccine in Chengdu, following the principles of voluntary, self-paid vaccination. However, due to irregular or inadequate vaccination practices, the vaccination coverage rate was low, resulting in a low level of mumps antibodies. As the number of susceptible individuals accumulated over the years, the chance of mumps infection increased, leading to a rise in reported cases and incidence rates. After 2008, Chengdu followed EPI requirements to provide free MMR vaccination to children aged 18\u0026ndash;24 months. However, children born before 2008 were already beyond the recommended vaccination age and became the target group of unvaccinated children. These children were in their school-entry age and were highly susceptible to MuV infection. Therefore, vaccinating only the current 18\u0026ndash;24 months old children did not control the incidence among high-risk groups. The second stage was the effective vaccine stage (2012\u0026ndash;2016). With the expansion of MMR vaccine coverage, the incidence of mumps was effectively controlled. The number of cases decreased significantly from 5,657 in 2012 to 1,983 in 2016. The marked decline in incidence during this period highlighted the effectiveness of expanding MMR vaccine coverage in controlling mumps outbreaks. The final stage was the resurgence of cases (2017\u0026ndash;2019). During this period, mumps cases increased slightly, reaching a peak of 2,709 cases in 2019. The re-emergence of cases suggests gaps in vaccine coverage, waning immunity, or changes in virus transmission dynamics. Many studies indicate that children who received one dose of the MMR vaccine are increasingly likely to contract mumps again over time. The decline in vaccine-induced immunity may be one of the reasons for the resurgence of mumps cases in Chengdu after 2017[\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. Continuous monitoring and potential booster vaccination strategies are necessary.\u003c/p\u003e \u003cp\u003eThe incidence of mumps exhibits clear seasonality, with two annual peak periods (May to July and November to December). To address this seasonal trend, it is necessary to implement targeted interventions (such as wearing masks while traveling, vaccination, etc.), particularly during identified peak seasons and high-risk transmission periods. Analyzing the population distribution of mumps in Chengdu, it primarily affects the 5\u0026ndash;14 age group, with incidence rates in males consistently significantly higher than in females. This aligns with previous studies[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. In terms of occupational distribution, students account for the majority of cases, followed by children in kindergartens and diaspora children. Previous research has shown that mumps outbreaks typically occur in densely populated school environments. Boys are generally more active and have more social contacts than girls, implying higher exposure and thus a greater risk of contracting the MuV[\u003cspan additionalcitationids=\"CR51 CR52\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. Since students usually start school in March and September, susceptible populations accumulate significantly in the following 2\u0026ndash;3 months. Once a MuV infection occurs, it can trigger a large-scale outbreak. This also explains why there are two peak months for mumps incidence each year[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe incidence rates of mumps across Chengdu's districts and counties vary significantly. Wenjiang District and Jinniu District have relatively high average annual incidence rates of 45.45 per 100,000 and 43.25 per 100,000, respectively. Jianyang City has the lowest average annual incidence rate, at only 3.26 per 100,000. The high number of mumps cases in Jinniu District and Wenjiang District is likely due to well-established medical facilities and surveillance systems that allow for more accurate recording and reporting of actual cases. Additionally, a large population base increases the opportunity for exposure to infection sources. Studies indicate that insufficient medical standards and a lack of awareness in epidemic reporting by primary healthcare institutions are critical reasons for the spread of mumps in less economically developed areas. Moreover, inconsistencies in MMR vaccination rates are due to differences in socioeconomic status and healthcare conditions across districts[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Additionally, the massive migration of people from surrounding counties to the main urban areas of Chengdu has rapidly increased the population density in the urban districts. This migration phenomenon has intensified crowding, raising the risk of infectious disease transmission[\u003cspan additionalcitationids=\"CR55\" citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe peak of \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e always occurs 1\u0026ndash;2 months before the peak in incidence, indicating that the transmissibility of mumps increases before the actual reported cases rise. This fact suggests an early intervention window. During this period, public health measures should be taken, such as increasing vaccination or conducting awareness campaigns to reduce transmission. Health authorities should time these campaigns and interventions to coincide with these periods to reduce the overall disease burden during peak seasons. Examining the relative transmissibility by specific sexes and age groups, females aged 10\u0026ndash;14 have a higher transmission risk to males aged 0\u0026ndash;14 (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e \u0026gt; 1), while males of different age groups have a much lower transmission risk to other age groups (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e \u0026lt; 1). This indicates that males have high susceptibility but low transmissibility, while females have lower susceptibility but higher transmissibility. Females have a higher transmissibility than males. There are several possible reasons for this: males and females exhibit significant differences in humoral and cell-mediated immune responses after MMR vaccination[\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e]. Studies show that after receiving two doses of the MMR vaccine, females have significantly higher neutralizing antibody titers than males (120.8 IU/mL vs. 98.7 IU/mL, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.038), while males have higher levels of secreted MIP-1α, MIP-1β, TNFα, IL-6, IFNγ, and IL-1β. These results indicate that sex significantly influences mumps-specific humoral and cell-mediated immune responses[\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. Sex hormones such as estrogen and testosterone may account for these differences, as they can regulate immune system functions[\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. For example, estrogen is believed to enhance B-cell activity, thereby increasing antibody production. Therefore, when females are infected with the MuV, clinical manifestations such as bilateral parotitis may be less pronounced, potentially leading to delays in implementing control measures and increasing transmission risk. Research has found that males typically exhibit weaker cell-mediated immune responses to viral infections like measles, potentially leading to slower recovery post-infection or less apparent vaccine protection compared to females[\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. Studies exploring how sex affects vaccine-induced cellular immunity have found that males generally produce fewer antibodies post-MMR vaccination than females, especially after two doses[\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. This finding suggests significant differences in the immune system response mechanisms between males and females. Additionally, studies indicate that sex differences in susceptibility to mumps may be due to sex hormone environments or immune gene differences on the X chromosome[\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThese findings suggest that differences in immune system response mechanisms between males and females could influence vaccine strategy development. Although males have higher incidence and complication rates of mumps compared to females, females have higher transmissibility and are more likely to transmit the MuV to males. Therefore, in control efforts, we should focus on protecting susceptible females and controlling infected females to reduce their high transmission potential to susceptible males, thereby lowering the overall incidence of mumps in the population and achieving better intervention outcomes.\u003c/p\u003e \u003cp\u003eIn summary, we recommend prioritizing the expansion of the MuCV vaccination program to ensure comprehensive coverage, including timely catch-up vaccinations for high-risk age groups that missed the initial vaccination phase (such as children born before 2008). Strengthening public health surveillance is crucial for the early detection and monitoring of mumps cases. This involves enhancing reporting mechanisms and the ability of healthcare institutions to collect data promptly and accurately. Addressing socioeconomic disparities by implementing policies that provide free or subsidized vaccines for impoverished communities and ensuring equitable access to healthcare services is vital. Additionally, public health campaigns are recommended to raise awareness of the importance of vaccination and preventive measures, particularly in high-risk periods and areas with low vaccination rates. Practitioners should focus on targeted vaccination measures for school-aged children (especially those aged 5\u0026ndash;14), ensuring these measures are implemented before the peak transmission seasons. It is crucial to implement preventive measures during the identified window period (1\u0026ndash;2 months before the incidence peak), such as increasing vaccination and public health education, to strengthen early intervention strategies. Health interventions tailored to different sexes should also be considered, including customized vaccination strategies for males and females, especially females aged 10\u0026ndash;14, involving monitoring antibody levels and post-vaccination immune responses to address differences in immune reactions. Seasonal preparedness is crucial, requiring targeted interventions such as mask-wearing campaigns and increased vaccination efforts during high-risk periods to effectively reduce mumps incidence. There are some limitations to this study. Firstly, while the study considers the impact of sex and age on mumps transmission, the specific mechanisms of vaccine-induced cell-mediated immune responses are not fully understood. Further research is needed to explore how sex hormones and genetic factors contribute to sex differences. Secondly, the study has limited monitoring time for long-term immunity and persistence of immunity against mumps. Future longitudinal studies could better determine the need and timing for booster doses. Additionally, the impact of socioeconomic factors on vaccine coverage and mumps incidence requires further analysis to develop more targeted interventions. Finally, it is necessary to evaluate the effectiveness of public health campaigns and interventions, including community engagement and behavior changes, to improve overall vaccination rates and reduce mumps transmission. Addressing these limitations can further enhance mumps control strategies.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study validated the SEPIAR model, which, by considering sex and age differences, accurately reflects the transmission characteristics of mumps in Chengdu from 2008 to 2019. The inconsistencies in vaccination methods before 2008 indicate the need for continuous monitoring, timely catch-up, and booster vaccinations to address waning immunity. The incidence of mumps is highly seasonal, with peak periods from May to July and November to December each year. The highest incidence is among males aged 5\u0026ndash;14, and outbreaks typically occur in densely populated school environments. Therefore, it is necessary to implement targeted interventions during these high-risk periods, such as vaccine registration before students enter school, enhanced vaccination campaigns, and public health education. It is recommended to improve the medical reporting system in less economically developed areas, enhance infrastructure, and focus on increasing the awareness and capacity of primary healthcare institutions to report cases. Females aged 10\u0026ndash;14 pose a higher transmission risk compared to males. Therefore, public health measures should prioritize early interventions for females, focusing on protecting susceptible females and controlling infected females. Additionally, sex-specific strategies should be considered, such as prioritizing vaccinations for females upon reaching the appropriate age to improve overall mumps control levels.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMuV\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eMumps virus\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMuCV\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003emumps-containing vaccines\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eMMR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003emeasles-mumps-rubella\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSEPIAR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSusceptible \u0026ndash; Exposed \u0026ndash; Pre-symptomatic \u0026ndash; Symptomatic Infected \u0026ndash; Asymptomatic Infected \u0026ndash; Recovered\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCISDCP\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eChinese Disease Prevention and Control Information System\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ebasic reproduction number\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eeffective reproduction number\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003etime-dependent reproduction number\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eNGM\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003enext-generation matrix\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003ecoefficient of determination\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eNPI\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003enational immunization program\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study was approved by the Medical Ethics Committee of Chengdu Center for Disease Control and Prevention. Only broad information (such as the date of illness onset) of the cases were collected with no identifying patient information and therefore the informed consent was waived by the ethics committee/institutional review board (IRB) of Medical Ethics Committee of Chengdu Center for Disease Control and Prevention. All methods were carried out in accordance with the relevant guidelines and regulations of the Helsinki Declaration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData that supporting the findings of this study are available from the Chengdu Center for Disease Control and Prevention but there are restrictions on the availability of these data, which were used with permission in this study, and are therefore not publicly available. However, data may be obtained from the authors with permission from Director Liang Wang ([email protected]) upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTY: Conceptualization, Methodology,\u0026nbsp;Software, Formal analysis, Visualization and Writing - Original Draft. XD, JL, LL and LX: Data curation and Investigation. YW: Supervision. LW: Writing- Reviewing and Editing. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was partly supported by the Major\u0026nbsp;and\u0026nbsp;Application\u0026nbsp;Projects\u0026nbsp;of\u0026nbsp;Chengdu\u0026nbsp;Science\u0026nbsp;and\u0026nbsp;Technology\u0026nbsp;Key\u0026nbsp;R\u0026amp;D\u0026nbsp;Support\u0026nbsp;Plan (2021-YF09-00061-SN).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to express their sincerest gratitude to the following people, without whom the study would not have been possible: (1) study participants for providing data, and (2) field investigators for collecting the data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHviid A, Rubin S, Muhlemann K. 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Vaccine. 2016;34(14):1657\u0026ndash;64.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-public-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"pubh","sideBox":"Learn more about [BMC Public Health](http://bmcpublichealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/pubh/default.aspx","title":"BMC Public Health","twitterHandle":"@BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Mumps, Sex disparities, Age disparities, Time-dependent reproduction number, China","lastPublishedDoi":"10.21203/rs.3.rs-6052129/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6052129/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eObjectives\u003c/h2\u003e \u003cp\u003eThis study investigates mumps epidemiology in Chengdu (2008\u0026ndash;2019), focusing on sex and age-specific transmission characteristics.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eA sex- and age-specific Susceptible \u0026ndash; Exposed \u0026ndash; Pre-symptomatic \u0026ndash; Symptomatic Infected \u0026ndash; Asymptomatic Infected \u0026ndash; Recovered (SEPIAR) model, adjusted for seasonal variations, was employed to categorize the population and analyze transmission dynamics.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eOver the study period, 40,087 mumps cases were reported in Chengdu, with an annual incidence of 21.72 per 100,000, peaking in 2011 at 40.83 per 100,000. Incidence rates were highest among male students aged 5\u0026ndash;14, with significant seasonal peaks in May-July and November-December. District-wise, Wenjiang and Jinniu had the highest rates (45.45 and 43.25 per 100,000), while Jianyang city had the lowest (3.26 per 100,000). The SEPIAR model demonstrated robust fitting across demographics (\u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.13\u0026ndash;0.73, \u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Notably, females aged 10\u0026ndash;14 exhibited the highest transmission risk to males aged 0\u0026ndash;14, with all mean time-varying reproduction numbers (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) exceeding 1. The median \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e for females aged 10\u0026ndash;14 to males aged 5\u0026ndash;9 was 1.18, to males aged 0\u0026ndash;4 was 0.75, and within the same age group was 0.55.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThis study underscores the critical role of sex and age in mumps transmission and validates the utility of the SEPIAR model for outbreak analysis. To mitigate transmission, we recommend: 1) targeted vaccination campaigns during seasonal peaks, 2) prioritizing booster doses for females aged 10\u0026ndash;14, 3) strengthening surveillance in high-incidence districts, and 4) improving healthcare reporting in rural regions. These strategies are vital for achieving sustained mumps control in megacities.\u003c/p\u003e","manuscriptTitle":"Sex, Age, and Urban Context: Modeling Social and Demographic Drivers of Mumps Transmission in Chengdu, China (2008–2019)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-25 12:44:39","doi":"10.21203/rs.3.rs-6052129/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-02-19T10:59:11+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-02-19T08:03:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-02-19T08:00:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Public Health","date":"2025-02-18T03:17:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-public-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"pubh","sideBox":"Learn more about [BMC Public Health](http://bmcpublichealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/pubh/default.aspx","title":"BMC Public Health","twitterHandle":"@BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3767007c-9491-41bd-8cf5-dd632b3fface","owner":[],"postedDate":"February 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-27T16:09:02+00:00","versionOfRecord":{"articleIdentity":"rs-6052129","link":"https://doi.org/10.1186/s12889-026-27302-7","journal":{"identity":"bmc-public-health","isVorOnly":false,"title":"BMC Public Health"},"publishedOn":"2026-04-21 15:58:24","publishedOnDateReadable":"April 21st, 2026"},"versionCreatedAt":"2025-02-25 12:44:39","video":"","vorDoi":"10.1186/s12889-026-27302-7","vorDoiUrl":"https://doi.org/10.1186/s12889-026-27302-7","workflowStages":[]},"version":"v1","identity":"rs-6052129","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6052129","identity":"rs-6052129","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}