Immune boosting and the perils of interpreting pertussis seroprevalence studies

pertussis; pertussis infection; pertussis vaccines; seroprevalence; serosurveys Corresponding author: Dr. Matthieu Domenech de Cellès. Address: Max Planck Institute for Infection Biology, Charitéplatz 1, Campus Charité Mitte, 10117 Berlin, Germany. Email: domenech@mpiib- berlin.mpg.de *These authors contributed equally. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 2/34

Seroepidemiology has significant potential for uncovering the unreported burden of infectious diseases. However, for diseases without well -defined serological correlates of protection, the phenomenon of immune boosting—whereby pathogen exposure triggers a detectable immune response without causing a transmissible infection—can complicate the interpretation of seroprevalence data from serosurveys. This issue is relevant to pertussis, a highly contagious and vaccine -preventable disease that remains a significant public health concern worldwide. Here, we aimed to evaluate the reliability of pertussis serosurveys—in particular, how immune boosting may cause these studies to overestimate transmissible infections—based on a population-based model of pertussis transmission that tracked the dynamics of infection, immune boosting, and seropositivity of IgG against pertussis toxin. By fitting this model to seroprevalence data from the late whole -cell pertussis vaccine era in six European countries, we estimated immunity conferred by infection or vaccination to last, on average, for several decades. We then predicted the prevalence and positive predictive value (PPV) —the proportion of true positives— of seropositivity in serosurveys among adult age groups across twelve countries broadly representative of transmission patterns worldwide. Overall, we predicted a low PPV across multiple scenarios, especially in young adults aged 20–39 years, where it dropped below 50% in almost all tested scenarios. Thus, the common interpret ation of seroprevalence as a measure of recent infections may lead to an overly pessimistic view of pertussis circulation. Our model is applicable to numerous other infectious disease systems and may be used to efficiently synthesize evidence from multiple data streams, including case-based and seroprevalence data. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 3/34

Pertussis, also known as whooping cough, is a highly contagious respiratory disease caused predominantly by infection with the bacterium Bordetella pertussis, as well as other bacteria of the Bordetella genus (1). Historically, this common childhood disease led to high infant mortality (2), until the development and widespread use of whole -cell pertussis (wP) vaccines significantly reduced reported cases during the second half of the twentieth century (3, 4). While wP vaccines remain widely used globally, many high -income countries have switched to acellular pertussis (aP) vaccines that became available in the 1990s (5, 6). Despite relatively high vaccine coverage worldwide (~85% for the primary series in the last ten years (7)), the burden of pertussis remains considerable, with an estimated 161,000 global deaths in children <5 years in 2014, mostly in low -income countries (8). Unexpectedly, a long -term resurgence of pertussis has also been observed in several high -income countries with sustained high vaccination coverage, including the USA, Sweden, and Denmark (5). Although reported pertussis cases plummeted shortly after the start of the COVID-19 pandemic (9–11), many countries—especially in Europe (12)—are now witnessing large epidemics, resulting in infant deaths (13). These alarming trends highlight the ongoing threats of pertussis, which remains one of the least controlled vaccine-preventable diseases worldwide. A major challenge in pertussis epidemiological research is to accurately estimate the rates of pertussis infections. Standard surveillance systems often fall short because infections are reported only when cases exhibit symptoms, seek healthcare, and receive a clinical or laboratory diagnosis—with potential case loss at every step (14). For pertussis, this problem is thought to be acute for at least three reasons. First, asymptomatic infections may be common, especially (but not only) among vaccinated age groups (15). Second, clinical diagnosis based on typical pertussis symptoms —such as paroxysmal coughing, whooping, and posttussive vomiting —can be inaccurate (16). Third, non -pediatricians may lack awareness of pertussis disease and fail to diagnose it in adult patients (17). These factors collectively contribute to case underreporting, which is estimated to be substantial for pertussis (18–20). . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 4/34 Due to the limitations of standard surveillance data, seroepidemiology is frequently used to assess the prevalence of antibodies against B. pertussis antigens, typically immunoglobulin G (IgG) against pertussis toxin (PT, a toxin unique to B. pertussis ) (21). However, since serological correlates of protection remain unidentified for pertussis (22), anti-PT IgG titers do not correlate well with immunity against infection. Indeed, anti -PT IgG antibodies from vaccination decrease to undetectable levels within a few years, while protection persists for longer (22). This continued protection may be attributed to the relatively slow progression of pertussis infection (mean serial interval of ~3 weeks (23)), such that recall responses from memory cells may be rapid enough to provide partial protection, even in the absence of circulating antibodies (24). Hence, in most seroprevalence studies, or serosurveys, seropositivity is interpreted as evidence of a recent infection, where the recency depends on the IgG threshold used to define seropositivity. As both symptomatic (25) and asymptomatic (26) infections generally induce an immune response, serosurveys can hypothetically quantify recent transmission levels, including asymptomatic infections. As a result, the baseline hypothesis of many serosurveys is that seroprevalence is a more accurate measure of pertu ssis circulation compared to case -based surveillance data, especially among adults (21). Seemingly supporting this view, studies have found significant discrepancies between infection rates derived from serosurveys and those reported through surveillance data, with serosurveys often revealing infection rates that are much higher—sometimes by several orders of magnitude (21). Several investigators, however, have questioned this view and cautioned that serological data may lack specificity (27, 28). This criticism is based on the fact that serology alone cannot distinguish between infection and subclinical immune boosting (29). In other words, exposure to B. pertussis may trigger an immune boost—or anamnestic response—in individuals protected by earlier infection or vaccination, leading to seropositivity but not to a productive infection that can be transmitted to other hosts ( i.e., a transmissible infection). To clarify our terminology regarding the outcomes of B. pertussis exposures resulting in seropositivity, we henceforth restrict our definition of infection to an exposure leading to transmissible infection (either symptomatic or asymptomatic), and we define other exposures as . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 5/34 subclinical immune boosts. We believe this definition is justified, as transmissible infections are arguably the most pertinent from an epidemiological and evolutionary perspective. Empirical evidence supports the idea that immune boosting occurs for pertussis (30). A household study conducted as part of the aP clinical trial in Sweden reported frequent observations of seropositivity without culture positivity (31). Similarly, in a human challenge experiment in adults aged 18 –45, the highest inoculum dose of 100,000 cfu caused seroconversion in all participants; however, extensive environmental sampling could not detect any bacterial shedding, thus suggesting the ab sence of transmissible infection (26). In a study of aP vaccines in adults over 50 years in Australia, vaccine effectiveness was substantially underestimated when cases were identified by single -titer serology, compared to PCR -confirmed cases; the authors interpreted this discrepancy as evide nce of case misclassification and poor diagnostic specificity of serology in their setting (32). This body of evidence suggests that serosurveys may overestimate the incidence of pertussis infections. Despite occasional mentions of these complexities (28, 29), the potential unreliability of serosurveys and the implications of immune boosting on the interpretation of seropositivity are frequently overlooked in the literature. To support this assertion, we reviewed 19 pertussis seroprevalence studies published in the last five years (see PRISMA flow diagram in Fig. S1). We specifically examined how investigators interpreted seropositivity and whether they addressed the issue of immune boosting or, more broadly, the possibility of false positives among seropositiv e cases. Through this analysis, we identified two broad categories of seroprevalence studies with distinct aims. In the first category of studies (Table S1), the investigators considered low to moderate anti -PT IgG thresholds to evaluate immune protection. However, the threshold to differentiate protection from lack of protection varied across studies, ranging from 5 IU/mL (33, 34) to 50 IU/mL (35). Furthermore, these studies were inherently limited because anti -PT IgG titers do not correlate well with immunity, as the serological correlates of protection remain unidentified for pertussis (22). Only two studies explicitly recognized this limitation (33, 36). . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 6/34 In the second group of studies (Table S2), the investigators defined moderate to high anti -PT IgG thresholds to evaluate recent exposure or infection. With few exceptions (36–39) , the threshold considered was 100 IU/mL; based on this cut-off, seropositivity was generally interpreted as evidence of exposure or infection within the last year. However, a few studies interpreted seropositivity as evidence of more immediate exposure or infection (acute infection (33, 34) or within the past 58.6 days (40)), and many studies did not explicitly define what constitutes recency. In four studies (33, 37, 41, 42), the term “exposure” was used instead of “infection," but no definition of exposure was provided. Notably, the issues of immune boosting and false positives were not discussed in any study, highlighting a lack of awareness surrounding this problem. Because of this lack of awareness, the reliability of serosurveys has not been systematically examined. Bridging this knowledge gap is essential to reconcile the different estimates of pertussis infection from serosurveys and case -based surveillance and to evaluate the impact of pertussis vaccines more accurately. Here, we developed a population -based model of pertussis transmission that tracked the dynamics of infection, immune boosting, and seropositivity. Through a comprehensive simulation study, we aime d to predict the prevalence and reliability of seropositivity in various countries worldwide. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 7/34

Model structure We developed a stochastic model of pertussis transmission that generated serological endpoints in addition to standard prevalence and incidence endpoints (Fig. 1). Briefly, the backbone of this model was similar to that of a previous model developed to explain the epidemiology of pertussis in the USA (43, 44). The model distinguished between primary infections in fully susceptible individuals (i.e., never vaccinated or infected) and secondary infections in susceptible individuals whose immunity was primed by earlier vaccination or infection. Based on earlier evidence in the USA (43, 44), we assumed that vaccine-derived immunity was imperfect and might immediately fail (primary vaccine failure), with subsequent waning immunity. Similarly, infection-derived immunity was assumed to wane over time. To generate serological endpoints, the model tracked the population -level dynamics of anti -PT IgG seroconversions, seropositivity, and seroreversions (Fig. 1). Unless otherwise stated, seropositivity was defined as an antibody titer exceeding 100 IU/mL, a standard threshold used in multiple seroprevalence studies (Refs. (21, 45) and Table S2). Following recovery from either a primary or secondary infection, seropositivity was assumed to occur and last, on average, 𝑡! years. In individuals with either infection- or vaccine-derived immunity, exposure to B. pertussis also led to seropositivity (but not to transmissible infection) at a rate proportional to the force of infection 𝜆. Because such seropositive cases arise due to immune boosting, the proportionality constant 𝜌 is called the immune-boosting coefficient (30). This parameter controls the sensitivity of immune boosting: for 𝜌 1 an exposure insufficient for infection can still

in immune boosting. The latter scenario, known as hypersensitive boosting, can also be interpreted as follows: an exposure dose of B. pertussis antigen lower than what is needed for infection can still result in immune boosting. We note that, in this model, seropositivity implies protection from infection; the converse, however, is not true, as seronegative individuals ( V and R compartments in Fig. 1) can still be protected. Hence, . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 8/34 seropositivity is assumed to be sufficient but not necessary for protection against infection, consistent with the fact that anti-PT IgG antibodies are not a serological correlate of protection (22). We also note that seropositivity due to recent vaccination is ignored in this model. This assumption is justified because recently vaccinated individuals are generally excluded from serosurveys to limit the risk of false positives from causes different from exposure or infection (45). By design, this model thus produced serological endpoints—such as seroprevalence and sero-incidence rates—comparable to serosurveys. In the following, we focus only on seroprevalence, the endpoint most typically estimated in these surveys (see Fig. 1 for t he model-based definition). However, because we assume that seropositivity lasts, on average, one year (see below), the seroprevalence approximately equals the yearly sero-incidence rate in our model. To assess whether seropositivity can reliably indicate a recent infection, we further calculated the positive predictive value (PPV) of serology, which is defined here as the conditional probability of past infection given seropositivity. Equivalently, the PPV represents the proportion of true cases among seropositive cases in serosurveys (PPV = true positives / (true positives + false positives)); it ranges from 0 (all seropositives result from immune boosting) to 1 (all seropositives result from a transmissible infection). Hence, this model allowed us to parsimoniously capture and study the interpretation problem described in the introduction: without other information, seroprevalence includes both recent transmissible infections and immune boosts; consequently, seropositivity does not always indicate a recent infection, which may lead to false positives and a low PPV of serology for a given prevalence of actual infections. Model parametrization Fixed model parameters The model was structured by age, dividing individuals into two age groups during the first year of life and into 1-year age groups from ages 1 to 79, resulting in a total of 81 age groups. The first age group represented newborns aged <2 or <3 months, refl ecting current pertussis vaccination schedules that recommend administering the first vaccine dose a few months after birth (5). Contacts between age . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 9/34 groups were parameterized using social contact matrices (SCMs) derived from the work of Mistry et al. (46). These SCMs were available in 35 countries worldwide and provided an age resolution of one year from age 0 to 79, enabling us to accurately capture contact patterns among infants and preschool children. Additionally, the model incorporated country -specific population age structures based on demographic data from 2010, as provided by Mistry et al. (46). The main transmission parameters were fixed based on earlier modeling studies (43, 44) . These parameters included the average latent and infectious periods and the relative transmissibility of secondary infections (Table 1). Importantly, since we focused exclusively on infection endpoints, we did not add an observation model to link our model outputs to reported disease cases. Some serological parameters were assumed to be known and fixed according to a previous modeling study of the kinetics of anti -PT IgG after a lab -confirmed infection [5]. Specifically, we used the posterior distribution from the best-fitting power decay model described by Teunis et al. (25) to estimate the average time to seroconversion after exposure ( 𝑡" = 23 days) and the average duration of seropositivity (𝑡! = 1 year), both defined for a seropositivity threshold of 100 IU/mL. Estimated model parameters In contrast to the fixed parameters described above, the immune -boosting coefficient and the duration of immunity were assumed to be unknown. This assumption was justified because of structural differences between our model and previous immune-boosting models (30, 47–49), which prevented us from directly incorporating estimates from earlier studies. For example, though both our model and Lavine et al.’s model (30, 48) stratify immunity into a boosted and waning stage, the duration spent in the boosted stage (representing the duration of seropositivity) is shorter in our model. As a result, using the estimates from Lavine et al. would lead to a higher force of infection in our model, requiring parametric adjustment (e.g., by increasing immune boosting or extending the duration of immunity) to ensure comparability between the two models. In addition, there remains considerable uncertainty in . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 10/34 the estimates of the immune -boosting coefficient, which were estimated at ≥10 in Ref. (30) and 6.6 (0.6–66) in Ref. (48). To simplify our analysis, we further assumed that infection - and wP-derived immunities had identical properties in terms of immune boosting (𝜌# = 𝜌$ = 𝜌) and the average duration of protection (𝛼# %& = 𝛼$ %& = 𝛼%&). This assumption is supported by immunological evidence showing that both natural infection and wP vaccination elicit a similar immune response (50, 51), as well as epidemiological evidence from modeling studies (49, 52). To estimate these two unknown parameters, we fitted our model to seroprevalence data from two large serosurveys in Europe (53, 54). We focused on these two studies because their results were standardized to ensure comparability of the serological assays across the participating countries. The first study, conducted in six countries in the mid-1990s, covered all age groups and reported seroprevalence based on a seropositivity threshold of 125 IU/mL (53). The second study, conducted in fourteen countries during the early 2010s, focused only on adults aged 20 –39 and reported seroprevalence based on a seropositivity threshold of 100 IU/mL (54). To include countries in our study, we applied three criteria: 1. Social contact data available from Mistry et al. (46) 2. Stable high (>80%) vaccine coverage from the start of wP vaccination until the collection of serological samples. 3. Switch to aP vaccines for primary immunization ≤5 years before the collection of serological samples. These criteria, thus, restricted our analysis to countries with mature and stable vaccination programs before or very shortly after the switch to aP vaccines. Of note, we did not consider a more recent European serosurvey (41) because all participating countries had switched to aP vaccines >5 years before sample collection. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 11/34 In each selected country, we ran 10 stochastic simulations from the beginning of wP vaccination until the serological survey period. We then calculated the model -predicted seroprevalence in adults aged 20–44 (for countries from Ref. (53)) or 20 –39 (for countries from Ref. (54)). For model -data comparison, we used weighted linear regression with the observed seroprevalence as the outcome and the predicted seroprevalence as an offset, with weights equal to the inverse variance of the observed seroprevalence estimates. Such weighting allowed us to account for the statistical uncertainty due to the limited sample size of the serosurveys. In this regression model, the opposite of the intercept thus represented the mean weighted squared error (MWSE) between the model predictions and the data. We repeated this procedure for multiple pairs of the immune-boosting coefficient and average duration of immunity (𝜌, 𝛼%&). Specifically, we considered four values of immune -boosting (0.5, 1, 2, 5) and multiple average durations of immunity ranging from 10 to 90 years (by increments of 10 years). Of note, in the absence of immune boosting (𝜌 = 0), the duration of vaccine-derived immunity follows an exponential distribution (with rate 𝛼) and the duration of infection -derived immunity a generalized Erlang distribution (a sum of two exponential distributions with rates 1/𝑡! and 𝛼). In both cases, the duration of immunity is inherently variable, with a large fraction of individuals losing immunity before the average duration (63% for the exponential distribution). Any pair resulting in a non -significant MWSE (i.e., not significantly different from 0) was considered an admissible estimate consistent with the data. For a given immune -boosting level, we calculated an approximate 95% confidence interval for the average duration of immunity as the range of all admissible estimates. Model predictions across representative countries NGM clustering To get a broader picture of the potential shortcomings of seropositivity, we predicted the seroprevalence and PPV of serology from serosurveys across various countries worldwide. To simplify our analysis, we did not consider all 35 countries with social contact data available from Mistry et al. (46). Instead, . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 12/34 we clustered the next-generation matrices (NGMs) to identify groups of countries with broadly similar transmission dynamics. In every country, we first calculated the NGM and the corresponding basic reproduction number ( R0, defined as the leading eigenvalue of the NGM) (55). Next, we computed the pairwise Manhattan distance between every pair of country -level NGMs to create a dissimilarity matrix encompassing all countries. Finally, we applied agglomerative nested hierarchical clustering and used the silhouette

to determine the optimal number of clusters. For every cluster with ≥2 countries, we selected the country with the largest population as the representative for that cluster. Simulation protocol In every representative country identified through NGM clustering, we simulated our serotransmission model for 150 years to reach equilibrium in the prevaccine era and another 150 years in the vaccine era. We ran ten replicate stochastic simulations and recorded the seroprevalence in three adult age groups— 20–39, 40–59, and 60–79—for the last twenty years of the simulated period (200 simulation -years in each age group). We considered these specific age groups because serosurveys often focus on adults (41, 54), in whom pertussis is less likely to be reported. Numerical implementation & Code availability statement The serotransmission model was developed using the pomp package (version 5.10) (56, 57) in R version 4.4.1 (58). The NGM clustering was performed using the R package clValid (59), with visualization done using the package factoextra (60). All programming codes are currently available on GitHub (https://gitfront.io/r/MDdC/xSdjztUmzRY3/Pertussis-seroprevalence/) and will be archived in Edmond, the Open Data Repository of the Max Planck Society, after publication. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 13/34

Estimation and model fit to seroprevalence data After applying our inclusion criteria (Table S5), we selected six countries for the model -data comparison of seroprevalence. These included four countries (Finland, France, East Germany, and the Netherlands) from Ref. (53) and two countries (Lithuania and Romania) from Ref. (54). Serological samples were collected approximately 30 –45 years after the start of wP vaccination in the first four countries and 50 years after in the latter two. In all six countries, the primary vaccine series started 2–3 months after birth with an addi tional booster dose at age 1 –3 years, and the vaccination coverage remained high (over 85%) until the serosurvey (Table S6). Keeping in mind the different seropositivity thresholds used in the two studies (100 IU/mL and 125 IU/mL), the seroprevalence estimates were fairly consistent across countries, ranging from 0.9% (standard error [SE]: 0.2 %) in the Netherlands to 2.9% (SE: 0.5%) in Finland. The model fit to seroprevalence data for every immune -boosting scenario is displayed in Fig. 2. The average duration of infection/wP-derived immunity was estimated at several decades in all scenarios, with point estimates ranging from 30 to 50 years (Table 2). These averages translated into a fraction of 10–15% of vaccinees losing immunity within 5 years and 18 –28% within 10 years. These estimates resulted in a low MWSE (<0.5%) in every scenario, demonstrating strong model -data agreement irrespective of the fixed boosting level. Hence, the immune-boosting coefficient could not be estimated from these data. Across the scenarios, the PPV of serology decreased as immune boosting increased, with a range (across countries) of 47 –62% for the lowest boosting level and 6–12% for the highest (Table 2). These results suggest that the seroprevalence data were consistent with a long average duration of immunity, with immune boosting accounting for a large part —if not the majority —of seropositive cases. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 14/34 NGM clustering The clustering analysis identified 11 clusters among the 35 country-level NGMs. We decided to separate the China NGM (initially grouped with the NGMs from Australia, Canada, and the US), resulting in 12 clusters overall. As shown in the resulting dendrogram (Fig. S2), the number of countries in each cluster varied, ranging from 1 (Israel, China) to 5. Some clusters comprised countries from the same geographical region (e.g., the Norway-Denmark and France-Italy-UK clusters), while others included geographically distant countries ( e.g., the India -South Africa cluster). To reduce our subsequent analysis, we selected one representative country from each cluster, resulting in the following 12 countries: China, Czechia (aka the Czech Republic), Denmark, Germany, India, Israel, Japan, the Netherlands, Sweden, Switzerland, the UK, and the USA. The corresponding SCMs are plotted in Fig. S3. Model predictions in 12 representative countries The model reached equilibrium across all boosting levels in the 12 countries (see Fig. S4 for representative time series in the USA). Even though our model did not include seasonality in transmission, the simulated seroprevalence exhibited multiannual cycles in the hyper-sensitive boosting scenarios (𝜌 > 1). This behavior has been reported in previous theoretical analyses of hyper -sensitive boosting models (30, 61). Figure 3 shows the variation in seroprevalence and PPV across countries, age groups, and immune - boosting levels based on an average duration of immunity of 40 years (consistent with the seroprevalence data for all boosting levels; see Table 2). The predicted seroprevalence ranged from 0.5 to 2.5%, displaying large variability across scenarios. The key factors contributing to this variability were age and immune-boosting levels, with seroprevalence predicted to increase as age decreased or immune boosting i ntensified. In contrast, variations in SCMs resulted in less variability in seroprevalence. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 15/34 The PPV of serology in seroprevalence studies ranged from 20 to 80% across scenarios. As for the seroprevalence, the PPV varied sensitively with the strength of immune boosting and age. Specifically, the PPV increased with age but decreased as the immune -boosting strength increased. Consequently, seropositivity was predicted to be most reliable in the elderly (60 –79 yr) when boosting was low and least reliable in young adults (20–39 yr) when boosting was high. In Table 3, we present additional predictions of seroprevalence and PPV across all scenarios consistent with the empirical seroprevalence data. Overall, the median predicted seroprevalence (PPV) from the model was in the range 0.6 –2.2% in 20 –39, 0.4 –1.8% i n 40 –59, and 0.2 –1.1% in 60 –79. These additional simulations confirmed the variations observed in Fig. 3: for fixed duration of immunity and immune-boosting strength, seroprevalence decreased while the PPV of serology increased in older age groups; in cont rast, when the duration of immunity and age were held constant, stronger boosting resulted in higher seroprevalence but lower PPV. Additionally, at fixed age and immune-boosting level, a shorter duration of immunity led to both higher seroprevalence and PP V of serology. These results illustrate that the reliability of serology in seroprevalence studies varies with age and the characteristics of immunity, which complicates the interpretation of serosurveys when these characteristics are unknown. To better understand how the prevalence and reliability of seropositivity vary with age, we dissected seroprevalence across different age groups (Fig. 4). At a fixed boosting level, the force of infection decreased with age, reflecting general age-specific contact patterns, particularly the lower contact rates in the elderly (Fig. S3). Meanwhile, the fraction susceptible to infection increased with age due to the gradual loss of infection-/wP-derived immunity. As a result of these two effects, the seroprevalence due to true infections peaked in the intermediate age group of 40 –59 yo. Conversely, the seroprevalence resulting from immune boosts declined as age increased, as loss of immunity gradually reduced protection against infection and thus opportunities for immune boosting in older age groups. Overall, this decline outweighed the variations in the true seroprevalence so that the overall seroprevalence decreased with age. Consequently, seropositivity was less frequent but also more likely to represent a . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 16/34 true infection because of reduced immune boosts in older age groups. These results highlight the complexity of interpreting seropositivity and suggest that seroprevalence may not even qualitatively capture age variations in infection. We repeated these simulations to examine how immune-boosting strength affects seroprevalence (Fig. 4). In a given age group, the force of infection was predicted to decrease as the strength of immune boosting increased. This effect can be explained as follows: assuming all other factors remain constant, increasing the strength of immune boosting is analogous to extending the duration of immunity (Fig. 1), resulting in reduced circulation and a lower prevalence of infection —and thus a lower force of infection—across age groups. As a result, the seroprevalence due to true infections decreased with stronger immune boosting. In contrast, the seroprevalence from immune boosts increased with immune- boosting strength. This increase dominated the variations in seroprevalence from true infections, so that the overall seroprevalence increased with immune -boosting strength. Thus, higher levels of immune boosting resulted in fewer true positives ( i.e., seropositive cases after a true infection) and more false positives (i.e., seropositive cases after an immune boost). By definition of the PPV, these two effects combined to diminish the PPV of serology in seroprevalence studies (as also observed in Fig. 3 and Table 3). In conclusion, these results illustrate how the complex interplay between waning immunity, immune boosting, and the age -specific contact patterns and force of infection sensitively determines seroprevalence and the reliability of seropositivity as an indicator of recent infection in seroprevalence studies. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 17/34

In this study, we aimed to evaluate the reliability of pertussis seroprevalence studies, particularly how the well-documented phenomenon of immune boosting may lead such studies to overestimate pertussis infections. To address this, we developed a new mode l of pertussis transmission that tracked the dynamics of seroprevalence, enabling a comparison with empirical estimates from serosurveys. Fitting this model to two large European serosurveys in the late wP era, we estimated infection -/wP-derived immunity t o last, on average, for several decades. We then predicted the prevalence and PPV of seropositivity among adult age groups in twelve countries broadly representative of transmission patterns worldwide. Overall, we predicted a low PPV of serology for seropr evalence studies across multiple scenarios, especially in young adults aged 20 –39 yr, where it fell below 50% in almost all scenarios tested. We conclude that the issue of immune boosting is likely severe, making raw seroprevalence estimates potentially misleading when interpreted in isolation. Our model can be useful for analyzing seroprevalence data, ideally in conjunction with case-based incidence data to synthesize all available evidence and derive more accurate estimates of pertussis infections. When comparing our model to seroprevalence data from two large European serosurveys, we found the best model-data agreement for average durations of infection -/wP-derived immunity of 30 –50 years (uncertainty range: 20 –80 years). As our model did not includ e several real -world complexities of pertussis (such as seasonality in transmission, variations in vaccine coverage or changes in demographic structure), we emphasize this estimation is only approximate. Nevertheless, these durations are consistent with previous estimates from immune-boosting models fitted to case report incidence data. Wearing & Rohani estimated that durations of infection -/wP-derived immunity of 20 –40 yr best reproduced the interepidemic periods, and of 40–100 yr the patterns of epidemic fade-outs observed in the wP era in England and Wales (assuming an immune boosting level of 0.5) (47). Based on incidence data in the prevaccine era in Copenhagen, Denmark, Lavine et al. estimated infection-derived immunity to last on average 34 (95% CI: 17–66) years, a value well identified despite considerable uncertainty in the immune-boosting parameter (6.6, 95% CI: 0.66 –66) (48). Using the same model, Rozhnova et al. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 18/34 found that an average duration infection-derived immunity of 40 years (assuming an immune boosting coefficient of 1) resulted in periodic epidemic patterns consistent with those observed in the prevaccine era in Ontario, Canada, and London, UK (62). Although differences in model structure preclude an exact comparison of all available estimates, our

add to the large body of modeling and epidemiological evidence about the long protection conferred by natural infection and wP vaccines against pertussis and the marked impact of wP vaccines on pertussis transmission (63–65). They also suggest that, due to immune boosting and the high transmissibility of pertussis, seroprevalence estimates of a few percent in adults are expected for imperfect yet highly effective vaccines, even in populations with near -perfect pediatric vacc ination coverage. In contrast to the duration of immunity, all tested values for immune boosting resulted in an equally good model-data agreement. Hence, we could not estimate this parameter based on seroprevalence data alone. Other attempts to identify this parameter based on incidence data yielded similarly uncertain estimates (30, 48, 49) . A lower bound of 0.66 was identified in Lavine et al.’s study in Copenhagen (48). A lower bound of 10 was estimated based on prevaccine era data in Massachusetts, USA (30), but a subsequent study in the USA reported such levels to be too high to reproduce the observed patterns of pertussis resurgence from the 1970s (52). Given this admittedly limited evidence, we believe the range we considered (0.5 –5) is reasonable, but we acknowledge the remaining uncertainties. Consequently, a promising avenue for future research will be to fit our model to multiple real -world data so urces to more accurately estimate the level of immune boosting and the rates of pertussis symptomatic and asymptomatic infections. Our results suggest that interpreting raw estimates of pertussis seroprevalence is challenging, if not impossible. Specifically, we find that the prevalence and reliability of seropositivity result from a complex interplay between immune boosting, waning i mmunity, and age-specific contact patterns. In particular, we predict that the PPV of serology in seroprevalence studies varies with age, with the lowest . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 19/34 values in young adults (20–39 yo) who more often experience immune boosting. Strikingly, in almost all scenarios tested, the PPV fell below 50% in this age group. In other words, interpreting seropositivity as evidence of a recent infection may be incorrec t more than half of the time in this age group. This finding is noteworthy, as our review showed that this interpretation was nearly universal in seroprevalence studies. In the older age groups (40 –59 yo, 60–79 yo), the reliability of seropositivity was better but still low in many scenarios, with the maximum PPV ranging from 27–40% at the highest boosting level to 79 –85% at the lowest. Hence, in line with earlier suspicions (27–29) and empirical evidence (26, 31, 32) , our results highlight that the issue of immune boosting is consequential when analyzing pertussis seroprevalence data. More broadly, our study emphasizes the key difference between exposure and infection, as seropositivity always indicates the former but not necessarily the latter. Another implication of our study is that comparing case report data to seroprevalence data will not yield valid estimates of under -reporting. As immune boosting will generally cause seroprevalence to overestimate true infection rates, this ratio will tend to underestimate the reporting probability or, equivalently, overestimate under -reporting. This overestimation will, in turn, lead to an ove rly pessimistic understanding of the impact of pertussis vaccines on pertussis circulation. Hence, our results lead us to question the widespread, but likely misguided, narrative about the high circulation and shortcomings of pertussis vaccines that has emerged from the analysis of multiple serosurveys. Our study has several important limitations that relate to the formulation of our model. First, we assumed that the serological parameters did not vary with age, as the serological data available (25) did not permit an age -specific parametrization. However, age variations in the immune response —e.g., because of immunosenescence—may cause these parameters to differ between age groups, especially in the elderly (66). Second, given the limited information in seroprevalence data, we made the simplifying assumption that infection- and wP-derived immunities had identical properties (in terms of immune boosting and duration of protection). This assumption is justified by epidemiological evidence (49, 52) and immunological evidence showing that natural infection and wP vaccination trigger a similar . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 20/34 immune response (50, 51) . Nevertheless, this assumption would be invalid for aP vaccines, which trigger a different immune response (67) that may be less prone to subsequent boosting by natural exposure (68). Epidemiological evidence also shows that these vaccines, though effective at reducing transmission and inducing herd immunity (5, 69), confer shorter-lived protection against infection, with waning rates of 2–10% per year (43, 44, 52, 70). Hence, extending our model to the aP era would require a separate parametrization for infection/wP -derived aP -derived immunities. This complication prevented us from considering more recent seroprevalence data, especially those from another large serosurvey in adults aged 40 –59 conducted in 18 European countries in 2015 (41). Still, we note that the seroprevalence estimates in this study (range: 2.7 –5.8% across 13/18 countries) were only moderately larger than those considered here. Other limitations of this study relate to our estimation method. First, we only considered data from two large serosurveys conducted in European countries, as their serological results were standardized and ensured comparability across countries. However, many other seroprevalence data are available and could be used to estimate the parameters and test the predictions of our model (21). Nevertheless, seroprevalences of similar magnitude (a few percent) have been estimated among adults in various other countries (e.g., in Australia (71), Israel (72), Japan (21), and the USA (21)), so we believe our results should remain robust even with the inclusion of additional data. Second, as discussed above, when fitting our model to seroprevalence data, we did not consider seasonal or long-term parameter variations that may affect seroprevalence. Thus, our estimates are approximate, though they generally agree with previous estimates from more detailed models. Third, we assumed identical properties of wP vaccines across the six countries, although these vaccines were produced by different n ational or commercial manufacturers during the study period (53, 73). Finally, even though we tested a range of realistic values, we could not estimate the strength of immune boosting, a parameter that sensitively controls the prevalence and reliability of seropositivity. Acknowledging these limitations, our model could serve as a building block to investigate the remaining unknowns in pertussis epidemiology. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 21/34 There is growing interest in collecting serological data to inform the immunity landscape and tap into the “epidemiological dark matter” of infectious diseases (74–76). For pathogens with identified correlates of protection (like neutralizing antibodies for measles and mumps (77, 78) ), serology is relatively unequivocal and can directly inform specific variables of transmission models, such as recovered or vaccinated compartments. In the case of pertussis and other pathogens (74), however, the picture is much more complex, as seropositivity is not a marker of immunity but of recent exposure. As a result, interpreting serological data is inherently ambiguous and requires careful consideration of waning immunity and immune boosting using transmission models. Hence, our model —or variations thereof—may prove useful for analyzing seroprevalence data and synthesizing evidence from other sources, including case notification data. Eventually, fitting such models to all available data will improve our estimates of pertussis infection rates and help resolve the ongoing disagreements within the field. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 22/34

We thank Peter Teunis for sharing codes and data to estimate the serological parameters. This study was funded by the Max Planck Society. Data and code availability All programming codes are currently available on GitHub (https://gitfront.io/r/MDdC/xSdjztUmzRY3/Pertussis-seroprevalence/) and will be archived in Edmond, the Open Data Repository of the Max Planck Society, after publication. Competing interests P.R. received funding from Sanofi for a research project on pertussis vaccines. All other others declare no competing interests related to this study. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 23/34 Figures Figure 1: Schematic representation of the serotransmission model. For clarity, only one age group is depicted, and demographic transitions such as birth, aging, and death are not represented. The serological parameters are highlighted in blue, and the seropositive states are circled in blue (see Table S3 for the defini tion of all state variables). Following either primary (state variables 𝑆&, 𝐸&, 𝐼&) or secondary infection (state variables 𝑆', 𝐸', 𝐼'), individuals are assumed to remain seropositive for an average duration 𝑡! (state variable 𝑅(,&). Upon exposure to B. pertussis, seronegative individuals with either infection -derived (state variable 𝑅) or vaccine -derived immunity (state variable 𝑉) against infection may undergo an immune boost and become seropositive (state variables 𝑅( and 𝑉(, respectively). State variables with an E index represent individuals exposed to B. pertussis and about to seroconvert. The diagram highlights a key issue with seroprevalence studies: generally, seroprevalence (represented as 𝑆" = 𝑅(,& + 𝑅(,' + 𝑉(, the sum of the blue states) includes both recent infections (𝑅(,&) and immune boosts from individuals with immunity derived from earlier infection (𝑅(,') or vaccination (𝑉(). Consequently, seropositivity does not always indicate a recent infection, which may lead to false positives and a low positive predictive value (defined here as 𝑃𝑃𝑉 = 𝑅(,&/𝑆"). In this model, infections are defined by their ability to transmit to other hosts, whereas immune boosts do not contribute to transmission. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 24/34 Figure 2: Model fit to empirical seroprevalence data in six European countries . Abbreviations: PPV: positive predictive value of serology; IU: international unit. The dashed line is the identity line, representing a perfect match between the model and the data. The 2-letter codes indicate the countries considered for model-data comparison: DE (East Germany), FI (Finland), FR (France), LT (Lithuania), NL (Netherlands), and RO (Romania). The data and predictions represent seroprevalence in adults aged 20–39 in Lithuania and Romania (54) or 20–44 in other countries (53). For each immune-boosting level (𝜌), the graph shows the model predictions for the duration of infection/wP -derived immunity that produced the best fit to the seroprevalence data (see Table 2 for the corresponding value). . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 25/34 Figure 3: Predicted seroprevalence in 12 representative countries . In each country, the location (size) of the points indicates the median seroprevalence (PPV) from 200 simulation -years (10 model simulations, each spanning 20 years). The panel title specifies the fixed value of the boosting coefficient for infection- or vaccine-derived immunity (𝜌). The average duration of infection - or vaccine-derived immunity was set to 𝛼%& = 40 years in all simulations, a value within the confidence interval for all tested values of the boosting coefficient (see Table 2). . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 26/34 Figure 4: Breakdown of seroprevalence and illustration of age-specific transmission dynamics in the US. The values shown represent the median across 200 simulation years (derived from 10 model simulations, each spanning 20 years) for six model variables indicated by the panels’ titles (see Figure 1 for the corresponding mathematical definitions indicated b etween parentheses). The color indicates the fixed value of the boosting coefficient for infection - or vaccine -derived immunity ( 𝜌). In all simulations, the average duration of infection- or vaccine-derived immunity was set to 𝛼%& = 40 years, a value within the confidence interval for all tested values of the boosting coefficient (see Table 2). All the variables are dimensionless except for the force of infection, which is expressed as a yearly rate. The y-axis values differ between panels. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 27/34 Tables Parameter Meaning Value(s) Source/Comment 𝜎%& Average latent period 8 days (43) 𝛾%& Average infectious period 15 days (43) 𝜃 Relative infectiousness of secondary infections 0.99 (43) 𝑀*+ Social contact matrix Fig. S3 (46) Country-specific 𝑅, Basic reproduction number 11–16 Country-specific 𝑡" Average time from exposure to seroconversion 23 days (25) 𝑡! Average duration of seropositivity after seroconversion 1 yr (seropositivity cut-off of 100 IU/mL) 0.75 yr (seropositivity cut-off of 125 IU/mL) (25) 𝑝$ Effective vaccination coverage (all doses) 0.9 Table S6 𝑣 Effective vaccination rate Calculated from 𝑝$ Supplementary

𝜌 Boosting coefficient of infection/wP-derived immunity 0.5, 1, 2, 5 Range of values tested based on earlier studies (30, 47, 48, 62) Assumption: 𝜌 = 𝜌$ = 𝜌# 𝛼%& Average duration of infection/wP-derived immunity (if no immune boosting) Estimated based on empirical serosurveys in the late wP era Assumption: 𝛼%& = 𝛼$ %& = 𝛼# %& Table 1: Main model parameters. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 28/34 Table 2: Estimates of the average duration of immunity. MWSE stands for mean weighted squared error, while PPV represents the positive predictive value of serology. The uncertainty interval indicates the range of values for which the MWSE was not significantly different from zero. The PPV range indicates the range of median PPV across the six countries included in the model-data comparison and across scenarios where the MWSE was non-significant. Fixed value of boosting coefficient (𝜌) Estimate (uncertainty interval) of the average duration of infection/wP-derived immunity (𝛼%&), years MWSE, % PPV range, % 0.5 30 (20–40) –0.4 47–62 1.0 30 (30–50) 0.0 29–41 2.0 40 (30–60) –0.1 16–27 5.0 50 (40–80) 0.1 6–12 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 29/34 Table 3: Predicted seroprevalence and positive predictive value of serology across 12 representative countries . The values indicate the median (95% prediction intervals) from 200 simulation years (10 model simulations, each spanning 20 years) across the 12 countries. . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint 30/34

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World Health Organization, The immunological basis for immunization series: module 16: mumps (World Health Organization, 2020). . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint S1 E1 I1 RP,1 RE S2 E2 I2 R RP,2 V VE VP 1/tp 1/tn 1/tp 1/tn λ λ σ σ ρV λ ρRλ v v γ αV αR 1/tn Seroconversion (true infection) Seroconversion (immune boost) Seroreversion Seropositive (true infection) Seropositive (immune boost) Vaccination . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint FI FRDE LT NL RO FI FR DE LT NL RO FI FR DE LT NL RO FI FR DE LT NL RO ρ = 2 ρ = 5 ρ = 0.5 ρ = 1 0 2 4 6 0 2 4 6 0 2 4 6 8 0 2 4 6 8 Observed seroprevalence (%) Predicted seroprevalence (%) PPV (%) 10 20 30 40 50 IgG seropositivity threshold 100 IU/mL 125 IU/mL . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint ρ = 2 ρ = 5 ρ = 0.5 ρ = 1 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 UK USA Switzerland Sweden Netherlands Japan Israel India Germany Denmark Czechia China UK USA Switzerland Sweden Netherlands Japan Israel India Germany Denmark Czechia China Seroprevalence (%) Country Age group (yrs) 20−39 40−59 60−79 PPV (%) 20 40 60 80 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint Fraction immune to infection (V + R) Seroprevalence from immune boosts (VP + RP2) Fraction susceptible to infection (S1 + S2) Seroprevalence from true infections (RP1) Force of Infection (λ) Overall seroprevalence 20−39 40−59 60−79 20−39 40−59 60−79 0.5 1.0 1.5 2.0 0.2 0.3 0.0 0.5 1.0 1.5 0.2 0.4 0.6 40 50 60 30 40 50 60 Age group (yrs) Value (%) Boosting coefficient (ρ) 0.5 1 2 5 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 19, 2025. ; https://doi.org/10.1101/2025.03.18.25324179doi: medRxiv preprint