Congenital transmission of Chagas disease: The role of newborn therapy on the disease’s dynamics

Chagas disease, also known as American trypanosomiasis, is caused by a protozoan blood-borne pathogen called Trypanosoma cruzi. The World Health Organization (WHO) has classified Chagas as one of 21 neglected tropical diseases present in the world and estimates that 6-7 million people are currently infected with Chagas. Congenital transmission of Chagas disease contributes to a significant amount of new infections, especially in endemic areas where 22.5% of new infections are due to congenital transmission. In this paper, we investigate the impact of congenital transmission on the dynamics of Chagas disease through a mathematical model. Specifically, we examine how treatment and the efficacy of the therapy for newborns impact the progression and spread of Chagas disease. The influence of newborn therapy on the dynamics of the model is thoroughly investigated, both theoretically and numerically. The results illustrate the importance of an effective treatment for newborns in reducing infected cases of the Chagas. We observed that if vector transmission can be controlled, then at least 41% of the newborns need to be treated to curb the disease, and varying the newborn treatment rate and its efficacy significantly shapes the disease’s spread. The finding further shows that the therapy given to newborns is not sufficient but necessary to curb the transmission of Chagas disease, and a comprehensive approach that includes vector and vertical transmission control strategy is essential for eradicating Chagas disease.

1 Chagas disease, also known as American trypanosomiasis, is an anthropozoonosis 2 disease caused by a protozoan blood-borne pathogen called Trypanosoma cruzi [14]. 3 The disease is predominantly active in Latin America, where it is a major public health 4 issue [3]. The World Health Organization (WHO) has classified Chagas as one of 21 5 neglected tropical diseases in the world [8]. Additionally, the WHO estimates that 6-7 6 million people are currently infected with Chagas, and 75 million people are at risk for 7 acquiring the disease [10]. Higher incidence rates are typically associated with areas 8 that have poorly constructed housing, which serve as hiding places for the insect vectors 9 that transmit the disease [3]. The disease is vectorized by Triatomine (reduviid) bugs, 10 also known as “kissing bugs,” because they bite the host around their lips when they 11 feed [17]. When the bug feeds on humans, it defecates, which allows the T. cruzi to exit 12 with the feces and enter the host’s body [13]. This is one of the most common routes of 13 February 16, 2024 1/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: 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. infection. Other common routes of infection include congenital transmission, 14 consumption of triatomine insects, needle sharing, and transfusional transmission [19]. 15 The highest number of new acute infection cases comes from vector and congenital 16 transmission [9]. This is especially true in Latin American countries, where 17 approximately 22.5% of new infections are due to congenital transmission [6]. In both 18 the acute and chronic phases of the infection, the disease can be transmitted from the 19 infected mother through the placenta to the embryo or fetus [11]. In 1 − 10% of infants 20 of infected mothers, congenital T. cruzi infection occurs [3]. Pregnant-infected women 21 typically have higher rates of premature births and miscarriages [7]. Typically, the 22 mothers and the infected children are asymptomatic, which makes the diagnosis of 23 Chagas challenging [5]. Even in cases where symptoms are present, they are non-specific 24 symptoms like fevers, swollen lymph nodes, and hepatosplenomegaly [21]. Regardless of 25 the symptoms, all untreated infected infants are at a 20 − 30% risk of developing severe 26 cardiac and intestinal complications later on in their life [2]. Ultimately, the faster the 27 diagnosis and subsequent treatment, the more effective it is [11]. There is a 90 − 95% 28 cure rate when the disease is recognized early, and treatment is used [20]. As infected 29 patients age, the cure rate decreases, so diagnosis should be a priority [16]. Current 30 diagnosis and treatment methods consist of a multistep method. Firstly, detection 31 requires maternal serological screening [18]. Typically, if a mother tests positive two 32 times in a row, the newborns are suspected of having Chagas disease and are tested [3]. 33 The most common method for testing newborns is examining cord blood from their 34 seropositive mothers using microscopy (also called the ”micro method”) or polymerase 35 chain reaction (PCR) techniques, anytime until they are one-month old [15]. Infants 36 who test positive via microscopy or PCR are considered to have Chagas disease [18]. 37 Unfortunately, these methods are unreliable; more than 50% of infections are not 38 recognized by microscopy [12]. Therefore, infants who are tested after one month of 39 birth or test negative are retested using serology when they are 9-12 months old [3]. 40 Treatment options include Benznidazole or Nifurtimox [10]. Treatment during 41 pregnancy is not currently recommended because of a lack of data on safety [16]. 42 However, since the treatment options are highly effective for newborns, treatment 43 should begin as soon as the diagnosis is made [3]. Over the past couple of decades, there 44 have been stricter control measures and detection policies for Chagas disease [1]. 45 Despite these measures, incidence rates have increased in non-endemic regions like 46 Europe and North America due to migration from rural to urban areas [1]. The disease 47 is no longer confined to Latin America and is now a worldwide issue [4]. As such, 48 increased diagnosis and better treatment of the disease is only a small step forward in 49 eradicating congenital Chagas disease. Significant government and health policies must 50 also be put in place to curb this disease. Furthermore, improving education and 51 awareness regarding Chagas disease is crucial for healthcare workers. Combining these 52 strategies will hopefully minimize the prevalence of Chagas disease globally. 53 A few articles have been published on using mathematical models to explore Chagas 54 disease dynamics, including [23–25,28]. Raimundo et al. in [26] focused on the 55 congenital transmission of Chagas disease in populations where vectorial transmission 56 has been eliminated. By considering both vertical transmission and the presence of 57 vectorial transmission, our study expanded on this work. Furthermore, we also 58 incorporated vector control measures into the model. Coffield et al. in [27] used a 59 mathematical model to explore Chagas disease transmission by including congenital and 60 oral transmission modes in humans and domestic mammals. The research concluded 61 that while congenital transmission has a limited impact on infection, oral transmission 62 in domestic mammals significantly contributes to the disease’s spread, highlighting the 63 importance of considering alternative transmission modes in disease control 64 strategies [27]. None of these published papers explored the impact of congenital 65 February 16, 2024 2/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Fig 1. Schematic diagram of the model. See Table 1 for meanings of parameters/variables. transmission and newborn therapy in controlling the disease; this emphasizes the 66 significance of our study in filling this research gap. 67

68 In this section, we develop a compartmental model that reflects the dynamics of Chagas 69 disease in both human and vector populations. The vector population is divided into 70 two classes at time t: susceptible vectors (S v) and infected vectors ( Iv). The human 71 population is divided into four classes at time t: infected acute humans ( Ia), infected 72 chronic humans (Ic), susceptible humans (S h), and newborn babies from infected 73 mothers (M). The natural death rate of vectors is denoted by µv, and the model 74 assumes all newborns from non-infected mothers are susceptible. If a susceptible vector 75 feeds on an infected acute or infected chronic human, the rate of disease transmission 76 from the human to the vector is represented by βhv, and the susceptible vector moves to 77 the infected vector class and stays there for life. When an infected vector bites a 78 susceptible human, the disease is transmitted at a rate of βvh, and the susceptible 79 human is moved to the infected acute stage. From there, the infected acute human can 80 progress to the infected chronic human class; this progression rate is denoted by k. 81 Individuals in the infected chronic class remain in that class for life unless they leave the 82 population through natural death at rate µh or the death rate from Chagas given by δh. 83 The birth rate of infected acute and infected chronic mothers combined, represented by 84 bh(Ic + Ia), is what comprises M class. If properly and fully treated, newborns from 85 infected mothers can be moved to the susceptible human class at the rate of α = ωr 86 where r is the treatment rate newborn, and ω is the treatment efficacy. Newborns who 87 are not properly treated become classified as infected acute humans at (1 − α). A 88 diagram depicting the dynamics explained in this section is shown in Figure 1. 89 Under the assumptions described above and the diagram, we obtain the following 90 system of nonlinear ordinary differential equations. 91 February 16, 2024 3/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint T able 1. Parameters of the disease model and their meanings. Parameter Meaning βvh The transmission rate from infected vectors to a susceptible human βhv The transmission rate from infected human to susceptible vectors µh Death from unrelated causes rate of human µv Death rate of vectors δh Death rate from the disease of humans in the chronic stage bh Birth rate of humans bv Recruitment rate of the vectors. This depends on an available blood meal, including birds and alternative hosts k The progression rate from infected human in the acute to the chronic stage p Progression rates from M to Sh or Ia class r Treatment rate of newborn ω Efficacy rate of the treatment dSv dt = bv − λvSv − µvSv dIv dt = λvSv − µvIv dSh dt = bh + αpM − λhSh − µhSh dIa dt = λhSh + (1 − α)pM − (k + µh)Ia dIc dt = kIa − (µh + δh)Ic dM dt = bh(Ia + Ic) − pM (1) Where 92 λv = βhv  Ia + Ic Nh  , λ h =  βvhIv Nv  , N v = Sv + Iv, N h = Sh + Ia + Ic + M. DF E =  bv µv , 0, bh µh , 0, 0, 0  , (2) A next-generation approach is defined as the dominant eigenvalue (spectral radius) 93 of the matrix F V −1 [30–32], where F and V −1 are matrices determined as: 94 F = [ ∂Fi(x0) ∂xj ] and V = [ ∂Vi(x0) ∂xj ]. Here, xj is the number of infested units, x0 is the 95 disease-free equilibrium, Fi is the rate of appearance of new infection in the infected 96 compartments, Vi = V − i − V + i with V − i denoting the rate at which infected individuals 97 are transferred out of the infected compartments and V + i denoting the rate at which 98 individuals are transferred into the infected compartments. 99 We will use the next generation method to compute the control reproduction number 100 Rc Fi =   FIv FIa FIc FM   =   λvSv λhSh 0 bh(Ia + Ic)   101 February 16, 2024 4/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint and 102 Vi =   VIv VIa VIc VM   =   µhIv −(1 − α)pM + (k + µh)Ia −kIa + (µh + δh)Ic pM   . 103 Therefore 104 F =    0 βhvS∗ v N ∗ h βhvS∗ v N ∗ h 0 βvhS∗ h N ∗ v 0 0 0 0 0 0 0 0 bh bh 0  . 105 and 106 V =   µv 0 0 0 0 k + µh 0 −(1 − α)p 0 −k µ h + δh 0 0 0 0 p  , 107 where S∗ h = bh µh = N ∗ h and S∗ v = bv µv = N ∗ v . 108 By the next generation method, the reproduction number is the spectral radius 109 F V −1. That is, 110 R2 c = 4B2 1 B2 2(k + µh + δh) b2 h(1 − α)2(k + µh + δh)µ2v + Ψ + p Ψb2 h(1 − α)2(k + µh + δh)µ2v , where 111 B1 = βhvS∗ v N ∗ h B2 = βvhS∗ h N ∗v Ψ = 4B1B2µv(k + µh)(µh + δh) + bh(1 − α)2µ3 v(k + µh + δh). (3) Let us consider a scenario that allows a perfect treatment that is α = 1. 112 RL = lim α− →1 R2 c = B1B2 (k + µh + δh) µv(k + µh)(µh + δh) . (4) Equation 4 shows that perfect treatment of newborns is insufficient to exterminate the 113 infection if RL > 1. In addition to the newborn therapy, control measures that would 114 reduce RL below unity are required to eradicate the disease. 115 Stability Analysis Results 116 In this section, we determine the local and global stability of the disease-free 117 equilibrium. 118 First, we determine the local stability of the disease-free equilibrium by computing 119 the eigenvalues of the linearized Jacobian matrix at the disease-free equilibrium and 120 obtain 121 February 16, 2024 5/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint J0(DF E) =        −µv 0 0 − βhvS⋆ v N ⋆ h − βhvS⋆ v N ⋆ h 0 0 −µv 0 βhvS⋆ v N ⋆ h βhvS⋆ v N ⋆ h 0 0 − βvhS⋆ h N ⋆ v −µh 0 0 αp 0 βvhS⋆ h N ⋆ v 0 − (k + µh) 0 (1 − α) p 0 0 0 k − (µh + δh) 0 0 0 0 bh bh −p        . From the Jacobian matrix J0(DF E), the first two eigenvalues are obtain to be 122 ϱ1 = −µv < 0, ϱ2 = −µh < 0. The remaining four eigenvalues are given by the 4 × 4 123 matrix 124 J1(DF E) =    −µv βhvS⋆ v N ⋆ h βhvS⋆ v N ⋆ h 0 βvhS⋆ h N ⋆ v − (k + µh) 0 (1 − α) p 0 k − (µh + δh) 0 0 bh bh −p     . Consider βvhS⋆ h µvN ⋆ v R1 + R2 → R2, we have 125 J1(DF E) =     −µv βhvS⋆ v N ⋆ h βhvS⋆ v N ⋆ h 0 0 βvhS⋆ hβhvS⋆ v µvN ⋆ h N ⋆ v − (k + µh) βvhS⋆ hβhvS⋆ v µvN ⋆ h N ⋆ v (1 − α) p 0 k − (µh + δh) 0 0 bh bh −p     . It follows J1(DF E) that 126 J1(DF E) =    −µv B1 B1 0 0 B1B2 µv − (k + µh) B1B2 µv (1 − α) p 0 k − (µh + δh) 0 0 bh bh −p    . From column 1, the eigenvalue is ϱ3 = −µv < 0. The remaining three eigenvalues are 127 given by the 3 × 3 matrix 128 J2(DF E) =    B1B2 µv − (k + µh) β1β2 µv (1 − α) p k − (µh + δh) 0 bh bh −p    . February 16, 2024 6/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Consider 1 (1−α) R1 + R3 → R1, we obtain 129 J2(DF E) =   B1B2−µv(k+µh)+µvbh(1−α) µv(1−α) B1B2+µvbh(1−α) µv(1−α) 0 k − (µh + δh) 0 bh bh −p   . From column 3, the eigenvalue is ϱ4 = −p < 0. The remaining two eigenvalues are given 130 by the 2 × 2 matrix 131 J3(DF E) =   B1B2−µv(k+µh)+µvbh(1−α) µv(1−α) B1B2+µvbh(1−α) µv(1−α) k − (µh + δh)   . Consider µv(1−α)(µh+δh) β1β2+µvbh(1−α) R1 + R2 → R1, it follows that 132 J3(DF E) =   µv(1−α)(µh+δh)[B1B2−µv(k+µh)+µvbh(1−α)] µv(1−α)[B1B2+µvbh(1−α)] + k 0 k − (µh + δh)   . Hence, the eigenvalues of the matrix J3(DF E) are obtain to be 133 ϱ5 = − (µh + δh) < 0, ϱ6 = µv (1 − α) (µh + δh) [B1B2 − µv (k + µh) + µvbh (1 − α)] µv (1 − α) [β1β2 + µvbh (1 − α)] + k. Further simplification of ϱ6 gives 134 ϱ6 = (µh + δh + k) − µv (k + µh) (µh + δh) B1B2 + µvbh (1 − α) = µv (k + µh) (µh + δh) B1B2 + µvbh (1 − α) (B1B2 + µvbh (1 − α)) (µh + δh + k) µv (k + µh) (µh + δh) − 1  Thus, ϱ6 < 0 if and only if (B1B2+µvbh(1−α))(µh+δh+k) µv(k+µh)(µh+δh) < 1. Hence, the disease-free 135 state of the model system is locally asymptotically stable when the above condition is 136 satisfied. 137 Observe that for α = 1, we have 138 ϱ6 = µv(k+µh)(µh+δh) B1B2 (RL − 1) , leading to the following result. 139 Theorem 1. For α = 1, the disease-free equilibrium of the system is locally 140 asymptotically stable if RL 1. 141 Next, we will apply the approach of Castillo-Chavez et al [22] to prove the global 142 stability of the disease-free equilibrium. The approach is defined in the theorem below. 143 Theorem 2. If a model system can be written in the form: 144 dX dt = F (X, 0), dI dt = G(X, I), G(X, 0) = 0, where X ∈ ℜ m denotes the number of uninfected compartments and I ∈ ℜ n, denotes the 145 number of infected compartments, including latent, exposed, and acute individuals. 146 U (X ⋆, 0) denotes the disease-free equilibrium of the system. Then the conditions (H1) 147 and (H2) must be satisfied to guarantee local asymptotic stability. 148 February 16, 2024 7/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint H1 : For dX dt = F (X, 0), X ⋆ is globally asymptotically stable. 149 H2 : G(X, I) = AI − ˆG(X, 0) ≥ 0 for (X, I) ∈ ∆, where A = DiG(X ⋆, 0) is a Metzler 150 matrix ( the off-diagonal elements of A are non-negative) and ∆ is the region 151 where the model makes biological sense and mathematically well-posed. Then the 152 fixed point U0 = (X ⋆, 0) is globally asymptotically stable equilibrium of the Chagas 153 infection model provided R0 < 1. 154 Theorem 3. The disease-free equilibrium 155 DF E =  bv µv , 0, bh µh , 0, 0, 0  is globally asymptotically stable if the conditions (H1) and (H2) are satisfied. 156 Proof. From the model system, we have X ∈ ℜ 2 = (S⋆ v , S⋆ h) and 157 I ∈ ℜ 4 = (I ⋆ v , I⋆ a , I⋆ c , M ⋆). Hence, for condition (H 1), we have 158 dX dt = F (X, 0) = bv − βhvSvIa Nv − βhvSvIc Nv − µvSv bh + αpM − βvhShIv Nh − µhSh ! and 159 dI dt = G(X, I) =   βhvSvIa Nv + βhvSvIc Nv − µvIv βvhShIv Nh + (1 − α) pM − (k + µh) Ia kIa − (µh + δh) Ic bhIa + bhIc − pM   . It follows that 160 F (X, 0) = −µv 0 0 −µh  . The eigenvaules from the matrix F (X, 0) are obtained to be 161 π1 = −µv < 0, π2 = −µh < 0. Since all the eigenvalues of the matrix F (X, 0) are negative, it follows that X ⋆ is always 162 globally asymptotically stable. Also, applying Theorem (2) to the Chagas disease model 163 system gives 164 ˆG(X, I) = AI − G(X, I) =      0 βhvS⋆ v N ⋆ v βhvS⋆ v N ⋆ v 0 βvhS⋆ h N ⋆ h − (k + µh) 0 − (1 − α) p 0 k − (µh + δh) 0 0 bh bh −p        Iv Ia Ic M   −     βhvSvIa Nv + βhvSvIc Nv − µvIv βvhShIv Nh + (1 − α) pM − (k + µh) Ia kIa − (µh + δh) Ic bhIa + bhIc − pM     February 16, 2024 8/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Hence, 165 ˆG(X, I) =     βhvS⋆ v Ia N ⋆ v + βhvS⋆ v Ic N ⋆ v βvhS⋆ hIv N ⋆ h − (k + µh) Ia − (1 − α) pM kIa − (µh + δh) Ic bhIa + bhIc − pM      −    βhvSvIa Nv + βhvSvIc Nv − µvIv βvhShIv Nh + (1 − α) pM − (k + µh) Ia kIa − (µh + δh) Ic bhIa + bhIc − pM    Therefore, 166 ˆG0(X, I) =    h βhvS⋆ v Ia N ⋆ v − βhvSvIa Nv i + h βhvS⋆ v Ic N ⋆ v − βhvSvIc Nv i + µvIv βvhS⋆ hIv N ⋆ h − βvhShIv Nh 0 0    =    βhvIa N ⋆ v [S⋆ v − Sv] + βhvIc N ⋆ v [S⋆ v − Sv] βvhIv N ⋆ h [S⋆ h − Sh] 0 0    . So, A is a Metzler matrix with non-negative off-diagonal elements. We observed that 167 ˆG0(X, I) =     βhvIa N ⋆ v [S⋆ v − Sv] + βhvIc N ⋆ v [S⋆ v − Sv] βvhIv N ⋆ h [S⋆ h − Sh] 0 0     ≥ 0, because βhvIa N ⋆ v [S⋆ v − Sv] + βhvIc N ⋆ v [S⋆ v − Sv] ≥ 0 and βvhIv N ⋆ h [S⋆ h − Sh] ≥ 0. Therefore, the 168 disease-free equilibrium DF E is globally asymptotically stable. 169 Numerical Simulation Results 170 In this section, we show the analysis of the numerical simulation of the proposed model. 171 We used literature values and assumed some parameter values to conduct numerical 172 February 16, 2024 9/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint simulations using Matlab for the spread of the Chagas disease. The initial conditions of 173 the state variables are given to be Sh(0) = 5000, Ia(0) = 1000, Ic(0) = 4000, 174 Sv(0) = 500000, Ic(0) = 100000, M(0) = 0 and the rest of the parameters and their 175 values are presented in Table 2. T able 2. Parameters of the disease model and their sources. Parameter Value Source βvh 0.0000032 – 0.0000096 per day [28] βhv 0.0000012–0.0000036 per day [28] µv 0.005 per day [29] µh 0.000042 per day [29] δh 0.00013– 0.00018 per day [29] bh 70/365 per day [35] bv 183.68–551.04 per day [34] k 0.02675 [29] p 0.995 Assumed r 0.000274 per day Assumed ω 90 - 90% [20] 176 Simulation and Scenario Analysis 177 In this section, we used a mathematical model to conduct numerical simulations that 178 depict the dynamics of Chagas disease. These simulations encompassed various 179 scenarios, allowing us to observe how different conditions influence the congenital 180 transmission of Chagas disease. This, in turn, provided valuable insights for optimizing 181 control strategies for Chagas disease. Past approaches for managing the disease have 182 included vector control and early treatment of newborns born to infected mothers. 183 Consequently, we explored scenarios with different newborn treatment rates (r ), 184 treatment efficacy (ω), and varying transmission rates from vectors to humans ( βvh) 185 and humans to vectors ( βhv). All other parameters and values are given in Table 2. 186 First, we examined how varying α, which is the product of the newborn treatment 187 rate (r) and the treatment efficacy (ω ), affects the infected population. Essentially, α 188 represents the rate at which newborns born to infected mothers transition from their 189 initial infected state to the susceptible healthy class after receiving proper treatment. 190 Initially, we set α to 0.4125, a value determined through a systematic analysis of the 191 reproduction number (R c). We plotted Rc against different combinations of newborn 192 treatment rates (r) and treatment efficacy (ω ) values. Our objective was to identify 193 parameter combinations that resulted in a realistic range of Rc values while ensuring 194 Rc remained below 1. This specific baseline value ( α = 0.4125) was achieved with 195 newborn treatment rate (r ) and treatment efficacy (ω ) values of 0.75 and 0.55, 196 respectively. We also modified α by increasing and decreasing it in increments of 25%, 197 50%, and 75% to examine how varying α values affected the spread and incidence of the 198 disease. This led to seven different α values: the baseline α of 0.4125, a 25% increase 199 (α = 0.5156), a 25% decrease ( α = 0.3094), a 50% increase ( α = 0.6188), a 50% decrease 200 (α = 0.2063), a 75% increase (α = 0.7219), and a 75% decrease (α = 0.1031). Figure 2 201 illustrates the population of infected individuals over a 15-year period given these α 202 values. The graph exhibits an exponential growth pattern from left to right, which was 203 consistent across all variations of α values, signifying an increase in the acutely infected 204 February 16, 2024 10/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Fig 2. The acutely infected population increases over a period of 15 years for all values of α. Relative to the baseline, increasing α leads to a decrease in infections, while decreasing α corresponds to an increase in infections. population in each scenario over 15 years. We calculated the area under the curve 205 (AUC), providing a measure of the infected population over time for each α value. 206 The respective AUC values for the different scenarios were as follows: 207 • Baseline scenario ( α = 0.4125): AUC = 102,232 208 • 25% increase in α (α = 0.5156): AUC = 80,519 209 • 25% decrease in α (α = 0.3094): AUC = 127,568 210 • 50% increase in α (α = 0.6188): AUC = 61,928 211 • 50% decrease in α (α = 0.2063): AUC = 157,102 212 • 75% increase in α (α = 0.7219): AUC = 46,023 213 • 75% decrease in α (α = 0.1031): AUC = 191,497 214 The calculated percentage changes represent the difference in the infected population 215 compared to the baseline scenario, illustrating the impact of adjusting α values on 216 disease dynamics. The percentage change values were as follows: 217 • Percentage change for a 25% increase in α: −21.2% 218 February 16, 2024 11/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint • Percentage change for a 25% decrease in α: 24.7% 219 • Percentage change for a 50% increase in α: −39.4% 220 • Percentage change for a 50% decrease in α: 53.6% 221 • Percentage change for a 75% increase in α: −54.9% 222 • Percentage change for a 75% decrease in α: 87.3% 223 Interpreting these results, a 25% increase in α correlated with a 21 .2% decrease in 224 the infected population relative to the baseline. Conversely, a 25% decrease in α 225 corresponded to a 24.7% increase in the infected population. Similarly, a 50% increase 226 in α resulted in a 39.4% reduction in the infected population, signifying significant 227 progress in disease management. Meanwhile, a 50% decrease in α led to a 53.6% 228 increase in the infected population. A 75% increase in α correlated with a 54 .9% 229 reduction in the infected population, while a 75% decrease in α resulted in an 87.3% 230 increase in infections. These results underscore how α, representing newborn treatment 231 rate and treatment effectiveness, influences disease spread. Ultimately, increasing α 232 leads to a decrease in the infected population, while decreasing α leads to an increase in 233 the infected population. 234 Further Exploring Impact of α 235 To further explore the impact of α, we considered scenarios by setting α to its minimum 236 (α = 0) and maximum (α = 1) values. An α value of 0 would mean that none of the 237 newborns from infected mothers would transition from their infected state to a healthy 238 state. This could be explained by two situations: the newborns from infected mothers 239 would either not be getting treated ( r = 0), or they would receive treatment that did not 240 work (ω = 0). On the other hand, an α value of 1 would mean that all of the newborns 241 from infected mothers would transition from their infected state to a healthy state, 242 indicating that all of the newborns received treatment ( r = 1) which was 100% effective 243 (ω = 1). Figure 3 shows the population of infected individuals over a period of 15 years 244 when α is at its minimum value of 0. This AUC for this case is 231,509 individuals; this 245 corresponds to a 126.3% increase in the infected population. In contrast, Figure 4 shows 246 the infected population’s trajectory over 15 years at the maximum α value of 1. The 247 AUC for α = 1 is 13,735 individuals. Comparing this with the earlier baseline scenario, 248 the infected population’s percentage change stands at −86.5%. This considerable 249 reduction from the baseline suggests that maximizing the newborn treatment rate and 250 efficacy rate is effective in reducing the burden of Chagas disease. 251 Impact of Vector Control 252 Finally, the influence of vector control on Chagas disease dynamics is considered. In 253 Chagas disease transmission dynamics, two parameters describe the interactions between 254 vectors and humans: βvh, representing the transmission rate from infected vectors to 255 susceptible humans, and βhv, signifying the transmission rate from infected humans to 256 susceptible vectors. The baseline values for these parameters are given in Table 2. 257 To investigate the dynamics of Chagas disease when there is no transmission of the 258 disease from vectors to humans, the impact of varying βvh on the acutely infected 259 population is explored. Figure 5 illustrates the dynamics of the acutely infected 260 population under the same baseline α value (α = 0.4125) but with different values for 261 βvh. In the baseline scenario ( α = 0.4125 and βvh = 0.0000036), the infected population 262 remains considerable, as indicated by the area under the curve of 102,231.8543. 263 February 16, 2024 12/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Fig 3. The number of acutely infected individuals experiences its highest increase over 15 years when the α value is set to 0. February 16, 2024 13/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Fig 4. The number of acutely infected individuals decreases over 15 years when α = 1. February 16, 2024 14/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint Fig 5. The number of acutely infected individuals decreases over 15 years when βvh = 0. However, in the scenario where βvh is set to zero, the infected population is significantly 264 reduced, reflected by the much lower area under the curve of 80,519. This substantial 265 21% decrease in the infected population emphasizes the importance of vector control 266 measures in reducing the spread and impact of Chagas disease. 267

268 The results from our mathematical model that investigates the dynamics of Chagas 269 disease provide valuable information about the factors influencing the congenital 270 transmission of this disease. In this section, we discuss the implications of our findings 271 and their significance for strengthening control strategies for Chagas disease. 272 The newborn treatment rate ( r) and treatment efficacy (ω ) are represented by α, 273 which plays a significant role in shaping the dynamics of Chagas disease. Our results 274 highlight that changing α has a significant impact on the spread of the disease. 275 Increasing α results in a reduction in the infected population by 21.2%, 39.4%, and 276 54.9% for 25%, 50%, and 75% α increases, respectively. Conversely, decreasing α by the 277 same percentages leads to an increase in the infected population by 24.7%, 53.6%, and 278 87.3%. This finding highlights the importance of effective treatment of newborns born 279 to infected mothers as it can greatly reduce the burden of Chagas disease. Additionally, 280 the results show the impact of minimizing ( α = 0) and maximizing newborn treatment 281 February 16, 2024 15/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint rates and efficacy ( α = 1). Minimizing α, which suggests that newborns from infected 282 mothers would either not receive treatment ( r = 0) or receive treatment that does not 283 work (ω = 0), led to a 126.4% increase in the infected population. On the other hand, 284 maximizing α led to an 86.5% reduction in the infected population. When α = 1, this 285 guarantees the maximum impact and effectiveness, as it implies that 100% of newborns 286 are receiving treatment, and the treatment is 100% effective. However, it’s essential to 287 acknowledge that such a scenario is realistic but not sufficient to eradicate Chagas 288 disease, as 13.4% of infections continue to exist despite the most optimal treatment 289 scenario. Thus, finding a balance between treatment rates and efficacy that is both 290 effective and achievable is crucial in disease management. 291 While our results underscore the significant impact of treatment rate (r ) and 292 treatment efficacy (ω) in influencing the spread of Chagas disease, it is crucial to 293 recognize that these factors alone are necessary but not sufficient for eliminating the 294 disease burden. A more comprehensive approach that includes newborn therapy and 295 vector control strategies is crucial to effectively combat Chagas disease. This is 296 important because Chagas disease primarily spreads through the triatomine bugs, which 297 serve as vectors for the Trypanosoma cruzi parasite. These vectors play a pivotal role in 298 disease transmission, and their control is essential for reducing human infections. Our 299 simulations demonstrate the substantial impact of reducing the transmission of the 300 disease from vectors to humans by setting βvh to zero. The adjustment, setting βvh to 301 zero while maintaining the baseline α value (α = 0.4125), resulted in a significant 21% 302 decrease in the infected population compared to the scenario where βvh = 0.0000036. 303 This underscores how essential vector control measures are. Vector control includes 304 various strategies, such as insecticide spraying, addressing poor housing conditions, and 305 initiating educational programs to reduce human-vector contact. Implementing vector 306 control strategies can effectively complement the efforts to improve treatment rates and 307 efficacy and further reduce disease transmission. 308 Based on our results, it is clear that a multifaceted approach is imperative for 309 managing Chagas disease. This approach includes increasing the newborn treatment, 310 enhancing the treatment efficiency, and implementing vector control measures. 311 High treatment rates and treatment efficacy are important for controlling and 312 reducing the burden of Chagas disease; however, they do not address vector-borne 313 transmission. Hence, it becomes clear that vector control has to be part of the 314 multifaceted approach to mitigate Chagas disease transmission. Public health 315 interventions should consider these varied methods of disease control to develop 316 exhaustive strategies that regulate both congenital transmission and vector-to-human 317 transmission routes. 318 Further research in Chagas disease control should focus on developing integrated approaches that include both treatment and vector control strategies. Based on our research, we recommend initiatives that raise awareness about Chagas disease and promote early diagnosis and treatment. With these combined efforts, the burden of Chagas disease can be significantly reduced, protecting many people from its harmful effects.

1. Benatar AF, Danesi E, Besuschio SA, Bortolotti S, Cafferata ML, Ramirez JC, Albizu CL, Scollo K, Baleani M, Lara L, Agolti G, Seu S, Adamo E, Lucero RH, Irazu L, Rodriguez M, Poeylaut-Palena A, Longhi SA, Esteva M, Althabe F, Rojkin F, Bua J, Sosa-Estani S, Schijman AG; Congenital Chagas Disease Study Group. Prospective multicenter evaluation of real-time PCR Kit prototype for early diagnosis of congenital Chagas disease. EBioMedicine. 2021 Jul;69:103450. February 16, 2024 16/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint doi: 10.1016/j.ebiom.2021.103450. Epub 2021 Jun 26. PMID: 34186488; PMCID: PMC8243352. 2. Bern C, Martin DL, Gilman RH. Acute and congenital Chagas disease. Adv Parasitol. 2011;75:19-47. doi: 10.1016/B978-0-12-385863-4.00002-2. PMID: 21820550. 3. Bern C, Montgomery SP, Herwaldt BL, et al. Evaluation and Treatment of Chagas Disease in the United States: A Systematic Review. JAMA. 2007;298(18):2171–2181. doi:10.1001/jama.298.18.2171 4. Bonney K. M. (2014). Chagas disease in the 21st century: a public health success or an emerging threat?. Parasite (Paris, France), 21, 11. https://doi.org/10.1051/parasite/2014012 5. Bustos PL, Milduberger N, Volta BJ, Perrone AE, Laucella SA and Bua J (2019) Trypanosoma cruzi Infection at the Maternal-Fetal Interface: Implications of Parasite Load in the Congenital Transmission and Challenges in the Diagnosis of Infected Newborns. Front. Microbiol. 10:1250. doi: 10.3389/fmicb.2019.01250 6. Carlier Y, Truyens C. Congenital Chagas disease as an ecological model of interactions between Trypanosoma cruzi parasites, pregnant women, placenta and fetuses. Acta Trop. 2015 Nov;151:103-15. doi: 10.1016/j.actatropica.2015.07.016. Epub 2015 Aug 17. PMID: 26293886. 7. Cevallos AM, Hern´ andez R. Chagas’ disease: pregnancy and congenital transmission. Biomed Res Int. 2014;2014:401864. doi: 10.1155/2014/401864. Epub 2014 May 15. PMID: 24949443; PMCID: PMC4052072. 8. da N´ obrega, A. A., de Ara´ ujo, W. N., & Vasconcelos, A. (2014). Mortality due to Chagas disease in Brazil according to a specific cause. The American journal of tropical medicine and hygiene, 91(3), 528–533. https://doi.org/10.4269/ajtmh.13-0574 9. Fabbro DL, Danesi E, Olivera V, Codeb´ o MO, Denner S, Heredia C, Streiger M, Sosa-Estani S. Trypanocide treatment of women infected with Trypanosoma cruzi and its effect on preventing congenital Chagas. PLoS Negl Trop Dis. 2014 Nov 20;8(11):e3312. doi: 10.1371/journal.pntd.0003312. PMID: 25411847; PMCID: PMC4239005. 10. Garc´ ıa-Huertas P, Cardona-Castro N. Advances in the treatment of Chagas disease: Promising new drugs, plants and targets. Biomed Pharmacother. 2021 Oct;142:112020. doi: 10.1016/j.biopha.2021.112020. Epub 2021 Aug 12. PMID: 34392087. 11. Hector Freilij, & Jaime Altcheh. (1995). Congenital Chagas’ Disease: Diagnostic and Clinical Aspects. Clinical Infectious Diseases, 21(3), 551–555. http://www.jstor.org/stable/4458866 12. Jurado Medina L, Chassaing E, Ballering G, Gonzalez N, Marqu´ e L, Liehl P, Pottel H, de Boer J, Chatelain E, Zrein M, Altcheh J. Prediction of parasitological cure in children infected with Trypanosoma cruzi using a novel multiplex serological approach: an observational, retrospective cohort study. Lancet Infect Dis. 2021 Aug;21(8):1141-1150. doi: 10.1016/S1473-3099(20)30729-5. Epub 2021 Apr 6. PMID: 33836157. February 16, 2024 17/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint 13. Klotz, S. A., Dorn, P. L., Mosbacher, M., & Schmidt, J. O. (2014). Kissing bugs in the United States: risk for vector-borne disease in humans. Environmental health insights, 8(Suppl 2), 49–59. https://doi.org/10.4137/EHI.S16003 14. Lidani KCF, Andrade FA, Bavia L, Damasceno FS, Beltrame MH, Messias-Reason IJ and Sandri TL (2019) Chagas Disease: From Discovery to a Worldwide Health Problem. Front. Public Health 7:166. doi: 10.3389/fpubh.2019.00166 15. Llenas-Garc´ ıa J, Wikman-Jorgensen P, Gil-Anguita C, Ramos-Sesma V, Torr´ us-Tendero D, Mart´ ınez-Go˜ ni R, Romero-Nieto M, Garc´ ıa-Abell´ an J, Esteban-Giner MJ, Antelo K, Navarro-Cots M, Bu˜ nuel F, Amador C, Garc´ ıa-Garc´ ıa J, Gasc´ on I, Telenti G, Fuentes-Campos E, Torres I, Gimeno-Gasc´ on A, Ru´ ız-Garc´ ıa MM, Navarro M, Ramos-Rinc´ on JM. Chagas disease screening in pregnant Latin American women: Adherence to a systematic screening protocol in a non-endemic country. PLoS Negl Trop Dis. 2021 Mar 24;15(3):e0009281. doi: 10.1371/journal.pntd.0009281. PMID: 33760816; PMCID: PMC8021187. 16. Meymandi, S., Hernandez, S., Park, S. et al. Treatment of Chagas Disease in the United States. Curr Treat Options Infect Dis 10, 373–388 (2018). https://doi.org/10.1007/s40506-018-0170-z 17. Nguyen T, Waseem M. Chagas Disease. [Updated 2021 Nov 7]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2022 Jan-. Available from: https://www.ncbi.nlm.nih.gov/books/NBK459272/ 18. Picado, A., Cruz, I., Redard-Jacot, M., Schijman, A. G., Torrico, F., Sosa-Estani, S., Katz, Z., & Ndung’u, J. M. (2018). The burden of congenital Chagas disease and implementation of molecular diagnostic tools in Latin America. BMJ global health, 3(5), e001069. https://doi.org/10.1136/bmjgh-2018-001069 19. Requena-M´ endez A, Albajar-Vi˜ nas P, Angheben A, Chiodini P, Gasc´ on J, Mu˜ noz J; Chagas Disease COHEMI Working Group. Health policies to control Chagas disease transmission in European countries. PLoS Negl Trop Dis. 2014 Oct 30;8(10):e3245. doi: 10.1371/journal.pntd.0003245. PMID: 25357193; PMCID: PMC4214631. 20. Soriano-Arandes A, Angheben A, Serre-Delcor N, Trevi˜ no-Maruri B, G´ omez I Prat J, Jackson Y. Control and management of congenital Chagas disease in Europe and other non-endemic countries: current policies and practices. Trop Med Int Health. 2016 May;21(5):590-6. doi: 10.1111/tmi.12687. Epub 2016 Mar 17. PMID: 26932338. 21. Steverding, D. The history of Chagas disease. Parasites Vectors 7, 317 (2014). https://doi.org/10.1186/1756-3305-7-317 22. Castillo-Chavez, C., Blower, S., Van den Driessche, P., Kirschner, D. and Yakubu, A. Mathematical approaches for emerging and reemerging infectious diseases: an introduction. Springer Science and Business Media, (2002) 23. Oduro B., Grijalva M.J., Just W. (2018). Models of disease vector control: When can aggressive initial intervention lower long-term cost? Bulletin of Mathematical Biology, 80 (4), pp. 788-824 February 16, 2024 18/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint 24. Oduro B., Grijalva M.J., Just W. (2019). A model of insect control with imperfect treatment. Journal of Biological Dynamics, 13 (NO. 1), pp. 518-537, 10.1080/17513758.2019.1640293 25. Spagnuolo, A. M., Shillor, M., Stryker, G. A. (2011). A model for Chagas disease with controlled spraying. Journal of Biological Dynamics 5 299–317. 26. Raimundo, S. M., Massad, E., and Yang, H. M. (2010). Modelling congenital transmission of Chagas’ disease. Biosystems, 99(3), 215-222. https://doi.org/10.1016/j.biosystems.2009.11.005 27. Coffield DJ Jr, Spagnuolo AM, Shillor M, Mema E, Pell B, Pruzinsky A, et al. (2013) A Model for Chagas Disease with Oral and Congenital Transmission. PLoS ONE 8(6): e67267. https://doi.org/10.1371/journal.pone.0067267 28. Oduro B., Naandam S., Mock D., Miloua A., Chataa P. (202?)The impact of continuous insecticide spraying on the spread of Chagas disease. Applied Mathematical Analysis and Computation: Springer Proceedings in Mathematics & Statistics. 29. Cruz-Pachecoa, G., Estevab L., Vargas, C. (2012). Control measures for Chagas disease. Mathematical Biosciences 237 49–60. 30. Diekmann, O., Heesterbeek, J. A. P, Britton, T. (2012). Mathematical Tools for Understanding Infectious Disease Dynamics. Kindle Edition . Princeton University Press. 31. Driessche, P. V., Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180 29–48. 32. Heesterbeek, J. A. P. (2002). A brief history of R0 and a recipe for its calculation. Acta Biotheo 50 189—204. 33. Korobeinikov, A. (2007). Global properties of infectious disease models with nonlinear incidence. Bull Math Biol 69 1871–1886. 34. Spagnuolo, A. M., Shillor, M., Kingsland, L., Thatcher, A., Toeniskoetter, M., Wood, B. (2012). A logistic delay differential equation model for Chagas disease with interrupted spraying schedules. Journal of biological dynamics 6(2) 377-394. 35. Hidayat, D., Nugraha, E. S., Nuraini, N. (2018). A mathematical model of Chagas disease transmission. In AIP Conference Proceedings 1937(1) 020008. AIP Publishing LLC. February 16, 2024 19/19 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint