{"paper_id":"17184402-8af7-4d4e-9036-58dc9becc541","body_text":"Congenital transmission of Chagas disease: The role of\nnewborn therapy on the disease’s dynamics\nMeriem Boukaabar1, Bismark Oduro 1, Paul Chataa 2*\n1 Department of Mathematics, Pennsylvania Western University, California, PA 15419,\nUSA.\n2 Department of Mathematics, University of Cape Coast, Cape Coast, Ghana.\n* paul.chataa@stu.ucc.edu.gh\nAbstract\nChagas disease, also known as American trypanosomiasis, is caused by a protozoan\nblood-borne pathogen called Trypanosoma cruzi. The World Health Organization\n(WHO) has classified Chagas as one of 21 neglected tropical diseases present in the\nworld and estimates that 6-7 million people are currently infected with Chagas.\nCongenital transmission of Chagas disease contributes to a significant amount of new\ninfections, especially in endemic areas where 22.5% of new infections are due to\ncongenital transmission. In this paper, we investigate the impact of congenital\ntransmission on the dynamics of Chagas disease through a mathematical model.\nSpecifically, we examine how treatment and the efficacy of the therapy for newborns\nimpact the progression and spread of Chagas disease.\nThe influence of newborn therapy on the dynamics of the model is thoroughly\ninvestigated, both theoretically and numerically. The results illustrate the importance of\nan effective treatment for newborns in reducing infected cases of the Chagas. We\nobserved that if vector transmission can be controlled, then at least 41% of the\nnewborns need to be treated to curb the disease, and varying the newborn treatment\nrate and its efficacy significantly shapes the disease’s spread. The finding further shows\nthat the therapy given to newborns is not sufficient but necessary to curb the\ntransmission of Chagas disease, and a comprehensive approach that includes vector and\nvertical transmission control strategy is essential for eradicating Chagas disease.\nIntroduction 1\nChagas disease, also known as American trypanosomiasis, is an anthropozoonosis 2\ndisease caused by a protozoan blood-borne pathogen called Trypanosoma cruzi [14]. 3\nThe disease is predominantly active in Latin America, where it is a major public health 4\nissue [3]. The World Health Organization (WHO) has classified Chagas as one of 21 5\nneglected tropical diseases in the world [8]. Additionally, the WHO estimates that 6-7 6\nmillion people are currently infected with Chagas, and 75 million people are at risk for 7\nacquiring the disease [10]. Higher incidence rates are typically associated with areas 8\nthat have poorly constructed housing, which serve as hiding places for the insect vectors 9\nthat transmit the disease [3]. The disease is vectorized by Triatomine (reduviid) bugs, 10\nalso known as “kissing bugs,” because they bite the host around their lips when they 11\nfeed [17]. When the bug feeds on humans, it defecates, which allows the T. cruzi to exit 12\nwith the feces and enter the host’s body [13]. This is one of the most common routes of 13\nFebruary 16, 2024 1/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\ninfection. Other common routes of infection include congenital transmission, 14\nconsumption of triatomine insects, needle sharing, and transfusional transmission [19]. 15\nThe highest number of new acute infection cases comes from vector and congenital 16\ntransmission [9]. This is especially true in Latin American countries, where 17\napproximately 22.5% of new infections are due to congenital transmission [6]. In both 18\nthe acute and chronic phases of the infection, the disease can be transmitted from the 19\ninfected mother through the placenta to the embryo or fetus [11]. In 1 − 10% of infants 20\nof infected mothers, congenital T. cruzi infection occurs [3]. Pregnant-infected women 21\ntypically have higher rates of premature births and miscarriages [7]. Typically, the 22\nmothers and the infected children are asymptomatic, which makes the diagnosis of 23\nChagas challenging [5]. Even in cases where symptoms are present, they are non-specific 24\nsymptoms like fevers, swollen lymph nodes, and hepatosplenomegaly [21]. Regardless of 25\nthe symptoms, all untreated infected infants are at a 20 − 30% risk of developing severe 26\ncardiac and intestinal complications later on in their life [2]. Ultimately, the faster the 27\ndiagnosis and subsequent treatment, the more effective it is [11]. There is a 90 − 95% 28\ncure rate when the disease is recognized early, and treatment is used [20]. As infected 29\npatients age, the cure rate decreases, so diagnosis should be a priority [16]. Current 30\ndiagnosis and treatment methods consist of a multistep method. Firstly, detection 31\nrequires maternal serological screening [18]. Typically, if a mother tests positive two 32\ntimes in a row, the newborns are suspected of having Chagas disease and are tested [3]. 33\nThe most common method for testing newborns is examining cord blood from their 34\nseropositive mothers using microscopy (also called the ”micro method”) or polymerase 35\nchain reaction (PCR) techniques, anytime until they are one-month old [15]. Infants 36\nwho test positive via microscopy or PCR are considered to have Chagas disease [18]. 37\nUnfortunately, these methods are unreliable; more than 50% of infections are not 38\nrecognized by microscopy [12]. Therefore, infants who are tested after one month of 39\nbirth or test negative are retested using serology when they are 9-12 months old [3]. 40\nTreatment options include Benznidazole or Nifurtimox [10]. Treatment during 41\npregnancy is not currently recommended because of a lack of data on safety [16]. 42\nHowever, since the treatment options are highly effective for newborns, treatment 43\nshould begin as soon as the diagnosis is made [3]. Over the past couple of decades, there 44\nhave been stricter control measures and detection policies for Chagas disease [1]. 45\nDespite these measures, incidence rates have increased in non-endemic regions like 46\nEurope and North America due to migration from rural to urban areas [1]. The disease 47\nis no longer confined to Latin America and is now a worldwide issue [4]. As such, 48\nincreased diagnosis and better treatment of the disease is only a small step forward in 49\neradicating congenital Chagas disease. Significant government and health policies must 50\nalso be put in place to curb this disease. Furthermore, improving education and 51\nawareness regarding Chagas disease is crucial for healthcare workers. Combining these 52\nstrategies will hopefully minimize the prevalence of Chagas disease globally. 53\nA few articles have been published on using mathematical models to explore Chagas 54\ndisease dynamics, including [23–25,28]. Raimundo et al. in [26] focused on the 55\ncongenital transmission of Chagas disease in populations where vectorial transmission 56\nhas been eliminated. By considering both vertical transmission and the presence of 57\nvectorial transmission, our study expanded on this work. Furthermore, we also 58\nincorporated vector control measures into the model. Coffield et al. in [27] used a 59\nmathematical model to explore Chagas disease transmission by including congenital and 60\noral transmission modes in humans and domestic mammals. The research concluded 61\nthat while congenital transmission has a limited impact on infection, oral transmission 62\nin domestic mammals significantly contributes to the disease’s spread, highlighting the 63\nimportance of considering alternative transmission modes in disease control 64\nstrategies [27]. None of these published papers explored the impact of congenital 65\nFebruary 16, 2024 2/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nFig 1. Schematic diagram of the model. See Table 1 for meanings of\nparameters/variables.\ntransmission and newborn therapy in controlling the disease; this emphasizes the 66\nsignificance of our study in filling this research gap. 67\nMaterials and methods 68\nIn this section, we develop a compartmental model that reflects the dynamics of Chagas 69\ndisease in both human and vector populations. The vector population is divided into 70\ntwo classes at time t: susceptible vectors (S v) and infected vectors ( Iv). The human 71\npopulation is divided into four classes at time t: infected acute humans ( Ia), infected 72\nchronic humans (Ic), susceptible humans (S h), and newborn babies from infected 73\nmothers (M). The natural death rate of vectors is denoted by µv, and the model 74\nassumes all newborns from non-infected mothers are susceptible. If a susceptible vector 75\nfeeds on an infected acute or infected chronic human, the rate of disease transmission 76\nfrom the human to the vector is represented by βhv, and the susceptible vector moves to 77\nthe infected vector class and stays there for life. When an infected vector bites a 78\nsusceptible human, the disease is transmitted at a rate of βvh, and the susceptible 79\nhuman is moved to the infected acute stage. From there, the infected acute human can 80\nprogress to the infected chronic human class; this progression rate is denoted by k. 81\nIndividuals in the infected chronic class remain in that class for life unless they leave the 82\npopulation through natural death at rate µh or the death rate from Chagas given by δh. 83\nThe birth rate of infected acute and infected chronic mothers combined, represented by 84\nbh(Ic + Ia), is what comprises M class. If properly and fully treated, newborns from 85\ninfected mothers can be moved to the susceptible human class at the rate of α = ωr 86\nwhere r is the treatment rate newborn, and ω is the treatment efficacy. Newborns who 87\nare not properly treated become classified as infected acute humans at (1 − α). A 88\ndiagram depicting the dynamics explained in this section is shown in Figure 1. 89\nUnder the assumptions described above and the diagram, we obtain the following 90\nsystem of nonlinear ordinary differential equations. 91\nFebruary 16, 2024 3/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nT able 1. Parameters of the disease model and their meanings.\nParameter Meaning\nβvh The transmission rate from infected vectors to a susceptible human\nβhv The transmission rate from infected human to susceptible vectors\nµh Death from unrelated causes rate of human\nµv Death rate of vectors\nδh Death rate from the disease of humans in the chronic stage\nbh Birth rate of humans\nbv Recruitment rate of the vectors. This depends on an available blood\nmeal, including birds and alternative hosts\nk The progression rate from infected human in the acute to the chronic\nstage\np Progression rates from M to Sh or Ia class\nr Treatment rate of newborn\nω Efficacy rate of the treatment\ndSv\ndt = bv − λvSv − µvSv\ndIv\ndt = λvSv − µvIv\ndSh\ndt = bh + αpM − λhSh − µhSh\ndIa\ndt = λhSh + (1 − α)pM − (k + µh)Ia\ndIc\ndt = kIa − (µh + δh)Ic\ndM\ndt = bh(Ia + Ic) − pM\n(1)\nWhere 92\nλv = βhv\n\u0012 Ia + Ic\nNh\n\u0013\n, λ h =\n\u0012 βvhIv\nNv\n\u0013\n, N v = Sv + Iv, N h = Sh + Ia + Ic + M.\nDF E =\n\u0012 bv\nµv\n, 0, bh\nµh\n, 0, 0, 0\n\u0013\n, (2)\nA next-generation approach is defined as the dominant eigenvalue (spectral radius) 93\nof the matrix F V −1 [30–32], where F and V −1 are matrices determined as: 94\nF = [ ∂Fi(x0)\n∂xj\n] and V = [ ∂Vi(x0)\n∂xj\n]. Here, xj is the number of infested units, x0 is the 95\ndisease-free equilibrium, Fi is the rate of appearance of new infection in the infected 96\ncompartments, Vi = V −\ni − V +\ni with V −\ni denoting the rate at which infected individuals 97\nare transferred out of the infected compartments and V +\ni denoting the rate at which 98\nindividuals are transferred into the infected compartments. 99\nWe will use the next generation method to compute the control reproduction number 100\nRc Fi =\n\n\nFIv\nFIa\nFIc\nFM\n\n =\n\n\nλvSv\nλhSh\n0\nbh(Ia + Ic)\n\n 101\nFebruary 16, 2024 4/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nand 102\nVi =\n\n\nVIv\nVIa\nVIc\nVM\n\n =\n\n\nµhIv\n−(1 − α)pM + (k + µh)Ia\n−kIa + (µh + δh)Ic\npM\n\n . 103\nTherefore 104\nF =\n\n\n\n0 βhvS∗\nv\nN ∗\nh\nβhvS∗\nv\nN ∗\nh\n0\nβvhS∗\nh\nN ∗\nv\n0 0 0\n0 0 0 0\n0 bh bh 0\n\n. 105\nand 106\nV =\n\n\nµv 0 0 0\n0 k + µh 0 −(1 − α)p\n0 −k µ h + δh 0\n0 0 0 p\n\n, 107\nwhere S∗\nh = bh\nµh\n= N ∗\nh and S∗\nv = bv\nµv\n= N ∗\nv . 108\nBy the next generation method, the reproduction number is the spectral radius 109\nF V −1. That is, 110\nR2\nc = 4B2\n1 B2\n2(k + µh + δh)\nb2\nh(1 − α)2(k + µh + δh)µ2v + Ψ +\np\nΨb2\nh(1 − α)2(k + µh + δh)µ2v\n,\nwhere 111\nB1 = βhvS∗\nv\nN ∗\nh\nB2 = βvhS∗\nh\nN ∗v\nΨ = 4B1B2µv(k + µh)(µh + δh) + bh(1 − α)2µ3\nv(k + µh + δh).\n(3)\nLet us consider a scenario that allows a perfect treatment that is α = 1. 112\nRL = lim\nα− →1\nR2\nc = B1B2 (k + µh + δh)\nµv(k + µh)(µh + δh) . (4)\nEquation 4 shows that perfect treatment of newborns is insufficient to exterminate the 113\ninfection if RL > 1. In addition to the newborn therapy, control measures that would 114\nreduce RL below unity are required to eradicate the disease. 115\nStability Analysis Results 116\nIn this section, we determine the local and global stability of the disease-free 117\nequilibrium. 118\nFirst, we determine the local stability of the disease-free equilibrium by computing 119\nthe eigenvalues of the linearized Jacobian matrix at the disease-free equilibrium and 120\nobtain 121\nFebruary 16, 2024 5/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nJ0(DF E) =\n\n\n\n\n\n\n\n−µv 0 0 − βhvS⋆\nv\nN ⋆\nh\n− βhvS⋆\nv\nN ⋆\nh\n0\n0 −µv 0 βhvS⋆\nv\nN ⋆\nh\nβhvS⋆\nv\nN ⋆\nh\n0\n0 − βvhS⋆\nh\nN ⋆\nv\n−µh 0 0 αp\n0 βvhS⋆\nh\nN ⋆\nv\n0 − (k + µh) 0 (1 − α) p\n0 0 0 k − (µh + δh) 0\n0 0 0 bh bh −p\n\n\n\n\n\n\n\n.\nFrom the Jacobian matrix J0(DF E), the first two eigenvalues are obtain to be 122\nϱ1 = −µv < 0, ϱ2 = −µh < 0. The remaining four eigenvalues are given by the 4 × 4 123\nmatrix 124\nJ1(DF E) =\n\n\n\n−µv\nβhvS⋆\nv\nN ⋆\nh\nβhvS⋆\nv\nN ⋆\nh\n0\nβvhS⋆\nh\nN ⋆\nv\n− (k + µh) 0 (1 − α) p\n0 k − (µh + δh) 0\n0 bh bh −p\n\n\n\n\n.\nConsider βvhS⋆\nh\nµvN ⋆\nv\nR1 + R2 → R2, we have 125\nJ1(DF E) =\n\n\n\n\n−µv\nβhvS⋆\nv\nN ⋆\nh\nβhvS⋆\nv\nN ⋆\nh\n0\n0 βvhS⋆\nhβhvS⋆\nv\nµvN ⋆\nh N ⋆\nv\n− (k + µh) βvhS⋆\nhβhvS⋆\nv\nµvN ⋆\nh N ⋆\nv\n(1 − α) p\n0 k − (µh + δh) 0\n0 bh bh −p\n\n\n\n\n.\nIt follows J1(DF E) that 126\nJ1(DF E) =\n\n\n\n−µv B1 B1 0\n0 B1B2\nµv\n− (k + µh) B1B2\nµv\n(1 − α) p\n0 k − (µh + δh) 0\n0 bh bh −p\n\n\n\n.\nFrom column 1, the eigenvalue is ϱ3 = −µv < 0. The remaining three eigenvalues are 127\ngiven by the 3 × 3 matrix 128\nJ2(DF E) =\n\n\n\nB1B2\nµv\n− (k + µh) β1β2\nµv\n(1 − α) p\nk − (µh + δh) 0\nbh bh −p\n\n\n\n.\nFebruary 16, 2024 6/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nConsider 1\n(1−α) R1 + R3 → R1, we obtain 129\nJ2(DF E) =\n\n\nB1B2−µv(k+µh)+µvbh(1−α)\nµv(1−α)\nB1B2+µvbh(1−α)\nµv(1−α) 0\nk − (µh + δh) 0\nbh bh −p\n\n\n.\nFrom column 3, the eigenvalue is ϱ4 = −p < 0. The remaining two eigenvalues are given 130\nby the 2 × 2 matrix 131\nJ3(DF E) =\n\n\nB1B2−µv(k+µh)+µvbh(1−α)\nµv(1−α)\nB1B2+µvbh(1−α)\nµv(1−α)\nk − (µh + δh)\n\n .\nConsider µv(1−α)(µh+δh)\nβ1β2+µvbh(1−α) R1 + R2 → R1, it follows that 132\nJ3(DF E) =\n\n\nµv(1−α)(µh+δh)[B1B2−µv(k+µh)+µvbh(1−α)]\nµv(1−α)[B1B2+µvbh(1−α)] + k 0\nk − (µh + δh)\n\n .\nHence, the eigenvalues of the matrix J3(DF E) are obtain to be 133\nϱ5 = − (µh + δh) < 0,\nϱ6 = µv (1 − α) (µh + δh) [B1B2 − µv (k + µh) + µvbh (1 − α)]\nµv (1 − α) [β1β2 + µvbh (1 − α)] + k.\nFurther simplification of ϱ6 gives 134\nϱ6 = (µh + δh + k) − µv (k + µh) (µh + δh)\nB1B2 + µvbh (1 − α)\n= µv (k + µh) (µh + δh)\nB1B2 + µvbh (1 − α)\n\u0012(B1B2 + µvbh (1 − α)) (µh + δh + k)\nµv (k + µh) (µh + δh) − 1\n\u0013\nThus, ϱ6 < 0 if and only if (B1B2+µvbh(1−α))(µh+δh+k)\nµv(k+µh)(µh+δh) < 1. Hence, the disease-free 135\nstate of the model system is locally asymptotically stable when the above condition is 136\nsatisfied. 137\nObserve that for α = 1, we have 138\nϱ6 = µv(k+µh)(µh+δh)\nB1B2\n(RL − 1) ,\nleading to the following result. 139\nTheorem 1. For α = 1, the disease-free equilibrium of the system is locally 140\nasymptotically stable if RL < 1 and unstable if RL > 1. 141\nNext, we will apply the approach of Castillo-Chavez et al [22] to prove the global 142\nstability of the disease-free equilibrium. The approach is defined in the theorem below. 143\nTheorem 2. If a model system can be written in the form: 144\ndX\ndt = F (X, 0), dI\ndt = G(X, I), G(X, 0) = 0,\nwhere X ∈ ℜ m denotes the number of uninfected compartments and I ∈ ℜ n, denotes the 145\nnumber of infected compartments, including latent, exposed, and acute individuals. 146\nU (X ⋆, 0) denotes the disease-free equilibrium of the system. Then the conditions (H1) 147\nand (H2) must be satisfied to guarantee local asymptotic stability. 148\nFebruary 16, 2024 7/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nH1 : For dX\ndt = F (X, 0), X ⋆ is globally asymptotically stable. 149\nH2 : G(X, I) = AI − ˆG(X, 0) ≥ 0 for (X, I) ∈ ∆, where A = DiG(X ⋆, 0) is a Metzler 150\nmatrix ( the off-diagonal elements of A are non-negative) and ∆ is the region 151\nwhere the model makes biological sense and mathematically well-posed. Then the 152\nfixed point U0 = (X ⋆, 0) is globally asymptotically stable equilibrium of the Chagas 153\ninfection model provided R0 < 1. 154\nTheorem 3. The disease-free equilibrium 155\nDF E =\n\u0012 bv\nµv\n, 0, bh\nµh\n, 0, 0, 0\n\u0013\nis globally asymptotically stable if the conditions (H1) and (H2) are satisfied. 156\nProof. From the model system, we have X ∈ ℜ 2 = (S⋆\nv , S⋆\nh) and 157\nI ∈ ℜ 4 = (I ⋆\nv , I⋆\na , I⋆\nc , M ⋆). Hence, for condition (H 1), we have 158\ndX\ndt = F (X, 0) =\n \nbv − βhvSvIa\nNv\n− βhvSvIc\nNv\n− µvSv\nbh + αpM − βvhShIv\nNh\n− µhSh\n!\nand 159\ndI\ndt = G(X, I) =\n\n\nβhvSvIa\nNv\n+ βhvSvIc\nNv\n− µvIv\nβvhShIv\nNh\n+ (1 − α) pM − (k + µh) Ia\nkIa − (µh + δh) Ic\nbhIa + bhIc − pM\n\n .\nIt follows that 160\nF (X, 0) =\n\u0012−µv 0\n0 −µh\n\u0013\n.\nThe eigenvaules from the matrix F (X, 0) are obtained to be 161\nπ1 = −µv < 0,\nπ2 = −µh < 0.\nSince all the eigenvalues of the matrix F (X, 0) are negative, it follows that X ⋆ is always 162\nglobally asymptotically stable. Also, applying Theorem (2) to the Chagas disease model 163\nsystem gives 164\nˆG(X, I) = AI − G(X, I)\n=\n\n\n\n\n\n0 βhvS⋆\nv\nN ⋆\nv\nβhvS⋆\nv\nN ⋆\nv\n0\nβvhS⋆\nh\nN ⋆\nh\n− (k + µh) 0 − (1 − α) p\n0 k − (µh + δh) 0\n0 bh bh −p\n\n\n\n\n\n\n\nIv\nIa\nIc\nM\n\n\n−\n\n\n\n\nβhvSvIa\nNv\n+ βhvSvIc\nNv\n− µvIv\nβvhShIv\nNh\n+ (1 − α) pM − (k + µh) Ia\nkIa − (µh + δh) Ic\nbhIa + bhIc − pM\n\n\n\n\nFebruary 16, 2024 8/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nHence, 165\nˆG(X, I) =\n\n\n\n\nβhvS⋆\nv Ia\nN ⋆\nv\n+ βhvS⋆\nv Ic\nN ⋆\nv\nβvhS⋆\nhIv\nN ⋆\nh\n− (k + µh) Ia − (1 − α) pM\nkIa − (µh + δh) Ic\nbhIa + bhIc − pM\n\n\n\n\n\n−\n\n\n\nβhvSvIa\nNv\n+ βhvSvIc\nNv\n− µvIv\nβvhShIv\nNh\n+ (1 − α) pM − (k + µh) Ia\nkIa − (µh + δh) Ic\nbhIa + bhIc − pM\n\n\n\nTherefore, 166\nˆG0(X, I) =\n\n\n\nh\nβhvS⋆\nv Ia\nN ⋆\nv\n− βhvSvIa\nNv\ni\n+\nh\nβhvS⋆\nv Ic\nN ⋆\nv\n− βhvSvIc\nNv\ni\n+ µvIv\nβvhS⋆\nhIv\nN ⋆\nh\n− βvhShIv\nNh\n0\n0\n\n\n\n=\n\n\n\nβhvIa\nN ⋆\nv\n[S⋆\nv − Sv] + βhvIc\nN ⋆\nv\n[S⋆\nv − Sv]\nβvhIv\nN ⋆\nh\n[S⋆\nh − Sh]\n0\n0\n\n\n\n.\nSo, A is a Metzler matrix with non-negative off-diagonal elements. We observed that 167\nˆG0(X, I) =\n\n\n\n\nβhvIa\nN ⋆\nv\n[S⋆\nv − Sv] + βhvIc\nN ⋆\nv\n[S⋆\nv − Sv]\nβvhIv\nN ⋆\nh\n[S⋆\nh − Sh]\n0\n0\n\n\n\n\n≥ 0,\nbecause βhvIa\nN ⋆\nv\n[S⋆\nv − Sv] + βhvIc\nN ⋆\nv\n[S⋆\nv − Sv] ≥ 0 and βvhIv\nN ⋆\nh\n[S⋆\nh − Sh] ≥ 0. Therefore, the 168\ndisease-free equilibrium DF E is globally asymptotically stable. 169\nNumerical Simulation Results 170\nIn this section, we show the analysis of the numerical simulation of the proposed model. 171\nWe used literature values and assumed some parameter values to conduct numerical 172\nFebruary 16, 2024 9/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nsimulations using Matlab for the spread of the Chagas disease. The initial conditions of 173\nthe state variables are given to be Sh(0) = 5000, Ia(0) = 1000, Ic(0) = 4000, 174\nSv(0) = 500000, Ic(0) = 100000, M(0) = 0 and the rest of the parameters and their 175\nvalues are presented in Table 2.\nT able 2. Parameters of the disease model and their sources.\nParameter Value Source\nβvh 0.0000032 – 0.0000096 per\nday\n[28]\nβhv 0.0000012–0.0000036 per\nday\n[28]\nµv 0.005 per day [29]\nµh 0.000042 per day [29]\nδh 0.00013– 0.00018 per day [29]\nbh 70/365 per day [35]\nbv 183.68–551.04 per day [34]\nk 0.02675 [29]\np 0.995 Assumed\nr 0.000274 per day Assumed\nω 90 - 90% [20]\n176\nSimulation and Scenario Analysis 177\nIn this section, we used a mathematical model to conduct numerical simulations that 178\ndepict the dynamics of Chagas disease. These simulations encompassed various 179\nscenarios, allowing us to observe how different conditions influence the congenital 180\ntransmission of Chagas disease. This, in turn, provided valuable insights for optimizing 181\ncontrol strategies for Chagas disease. Past approaches for managing the disease have 182\nincluded vector control and early treatment of newborns born to infected mothers. 183\nConsequently, we explored scenarios with different newborn treatment rates (r ), 184\ntreatment efficacy (ω), and varying transmission rates from vectors to humans ( βvh) 185\nand humans to vectors ( βhv). All other parameters and values are given in Table 2. 186\nFirst, we examined how varying α, which is the product of the newborn treatment 187\nrate (r) and the treatment efficacy (ω ), affects the infected population. Essentially, α 188\nrepresents the rate at which newborns born to infected mothers transition from their 189\ninitial infected state to the susceptible healthy class after receiving proper treatment. 190\nInitially, we set α to 0.4125, a value determined through a systematic analysis of the 191\nreproduction number (R c). We plotted Rc against different combinations of newborn 192\ntreatment rates (r) and treatment efficacy (ω ) values. Our objective was to identify 193\nparameter combinations that resulted in a realistic range of Rc values while ensuring 194\nRc remained below 1. This specific baseline value ( α = 0.4125) was achieved with 195\nnewborn treatment rate (r ) and treatment efficacy (ω ) values of 0.75 and 0.55, 196\nrespectively. We also modified α by increasing and decreasing it in increments of 25%, 197\n50%, and 75% to examine how varying α values affected the spread and incidence of the 198\ndisease. This led to seven different α values: the baseline α of 0.4125, a 25% increase 199\n(α = 0.5156), a 25% decrease ( α = 0.3094), a 50% increase ( α = 0.6188), a 50% decrease 200\n(α = 0.2063), a 75% increase (α = 0.7219), and a 75% decrease (α = 0.1031). Figure 2 201\nillustrates the population of infected individuals over a 15-year period given these α 202\nvalues. The graph exhibits an exponential growth pattern from left to right, which was 203\nconsistent across all variations of α values, signifying an increase in the acutely infected 204\nFebruary 16, 2024 10/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nFig 2. The acutely infected population increases over a period of 15 years for all\nvalues of α. Relative to the baseline, increasing α leads to a decrease in infections, while\ndecreasing α corresponds to an increase in infections.\npopulation in each scenario over 15 years. We calculated the area under the curve 205\n(AUC), providing a measure of the infected population over time for each α value. 206\nThe respective AUC values for the different scenarios were as follows: 207\n• Baseline scenario ( α = 0.4125): AUC = 102,232 208\n• 25% increase in α (α = 0.5156): AUC = 80,519 209\n• 25% decrease in α (α = 0.3094): AUC = 127,568 210\n• 50% increase in α (α = 0.6188): AUC = 61,928 211\n• 50% decrease in α (α = 0.2063): AUC = 157,102 212\n• 75% increase in α (α = 0.7219): AUC = 46,023 213\n• 75% decrease in α (α = 0.1031): AUC = 191,497 214\nThe calculated percentage changes represent the difference in the infected population 215\ncompared to the baseline scenario, illustrating the impact of adjusting α values on 216\ndisease dynamics. The percentage change values were as follows: 217\n• Percentage change for a 25% increase in α: −21.2% 218\nFebruary 16, 2024 11/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\n• Percentage change for a 25% decrease in α: 24.7% 219\n• Percentage change for a 50% increase in α: −39.4% 220\n• Percentage change for a 50% decrease in α: 53.6% 221\n• Percentage change for a 75% increase in α: −54.9% 222\n• Percentage change for a 75% decrease in α: 87.3% 223\nInterpreting these results, a 25% increase in α correlated with a 21 .2% decrease in 224\nthe infected population relative to the baseline. Conversely, a 25% decrease in α 225\ncorresponded to a 24.7% increase in the infected population. Similarly, a 50% increase 226\nin α resulted in a 39.4% reduction in the infected population, signifying significant 227\nprogress in disease management. Meanwhile, a 50% decrease in α led to a 53.6% 228\nincrease in the infected population. A 75% increase in α correlated with a 54 .9% 229\nreduction in the infected population, while a 75% decrease in α resulted in an 87.3% 230\nincrease in infections. These results underscore how α, representing newborn treatment 231\nrate and treatment effectiveness, influences disease spread. Ultimately, increasing α 232\nleads to a decrease in the infected population, while decreasing α leads to an increase in 233\nthe infected population. 234\nFurther Exploring Impact of α 235\nTo further explore the impact of α, we considered scenarios by setting α to its minimum 236\n(α = 0) and maximum (α = 1) values. An α value of 0 would mean that none of the 237\nnewborns from infected mothers would transition from their infected state to a healthy 238\nstate. This could be explained by two situations: the newborns from infected mothers 239\nwould either not be getting treated ( r = 0), or they would receive treatment that did not 240\nwork (ω = 0). On the other hand, an α value of 1 would mean that all of the newborns 241\nfrom infected mothers would transition from their infected state to a healthy state, 242\nindicating that all of the newborns received treatment ( r = 1) which was 100% effective 243\n(ω = 1). Figure 3 shows the population of infected individuals over a period of 15 years 244\nwhen α is at its minimum value of 0. This AUC for this case is 231,509 individuals; this 245\ncorresponds to a 126.3% increase in the infected population. In contrast, Figure 4 shows 246\nthe infected population’s trajectory over 15 years at the maximum α value of 1. The 247\nAUC for α = 1 is 13,735 individuals. Comparing this with the earlier baseline scenario, 248\nthe infected population’s percentage change stands at −86.5%. This considerable 249\nreduction from the baseline suggests that maximizing the newborn treatment rate and 250\nefficacy rate is effective in reducing the burden of Chagas disease. 251\nImpact of Vector Control 252\nFinally, the influence of vector control on Chagas disease dynamics is considered. In 253\nChagas disease transmission dynamics, two parameters describe the interactions between 254\nvectors and humans: βvh, representing the transmission rate from infected vectors to 255\nsusceptible humans, and βhv, signifying the transmission rate from infected humans to 256\nsusceptible vectors. The baseline values for these parameters are given in Table 2. 257\nTo investigate the dynamics of Chagas disease when there is no transmission of the 258\ndisease from vectors to humans, the impact of varying βvh on the acutely infected 259\npopulation is explored. Figure 5 illustrates the dynamics of the acutely infected 260\npopulation under the same baseline α value (α = 0.4125) but with different values for 261\nβvh. In the baseline scenario ( α = 0.4125 and βvh = 0.0000036), the infected population 262\nremains considerable, as indicated by the area under the curve of 102,231.8543. 263\nFebruary 16, 2024 12/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nFig 3. The number of acutely infected individuals experiences its highest increase over\n15 years when the α value is set to 0.\nFebruary 16, 2024 13/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nFig 4. The number of acutely infected individuals decreases over 15 years when α = 1.\nFebruary 16, 2024 14/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nFig 5. The number of acutely infected individuals decreases over 15 years when\nβvh = 0.\nHowever, in the scenario where βvh is set to zero, the infected population is significantly 264\nreduced, reflected by the much lower area under the curve of 80,519. This substantial 265\n21% decrease in the infected population emphasizes the importance of vector control 266\nmeasures in reducing the spread and impact of Chagas disease. 267\nDiscussion 268\nThe results from our mathematical model that investigates the dynamics of Chagas 269\ndisease provide valuable information about the factors influencing the congenital 270\ntransmission of this disease. In this section, we discuss the implications of our findings 271\nand their significance for strengthening control strategies for Chagas disease. 272\nThe newborn treatment rate ( r) and treatment efficacy (ω ) are represented by α, 273\nwhich plays a significant role in shaping the dynamics of Chagas disease. Our results 274\nhighlight that changing α has a significant impact on the spread of the disease. 275\nIncreasing α results in a reduction in the infected population by 21.2%, 39.4%, and 276\n54.9% for 25%, 50%, and 75% α increases, respectively. Conversely, decreasing α by the 277\nsame percentages leads to an increase in the infected population by 24.7%, 53.6%, and 278\n87.3%. This finding highlights the importance of effective treatment of newborns born 279\nto infected mothers as it can greatly reduce the burden of Chagas disease. Additionally, 280\nthe results show the impact of minimizing ( α = 0) and maximizing newborn treatment 281\nFebruary 16, 2024 15/19\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint \n\nrates and efficacy ( α = 1). Minimizing α, which suggests that newborns from infected 282\nmothers would either not receive treatment ( r = 0) or receive treatment that does not 283\nwork (ω = 0), led to a 126.4% increase in the infected population. On the other hand, 284\nmaximizing α led to an 86.5% reduction in the infected population. When α = 1, this 285\nguarantees the maximum impact and effectiveness, as it implies that 100% of newborns 286\nare receiving treatment, and the treatment is 100% effective. However, it’s essential to 287\nacknowledge that such a scenario is realistic but not sufficient to eradicate Chagas 288\ndisease, as 13.4% of infections continue to exist despite the most optimal treatment 289\nscenario. Thus, finding a balance between treatment rates and efficacy that is both 290\neffective and achievable is crucial in disease management. 291\nWhile our results underscore the significant impact of treatment rate (r ) and 292\ntreatment efficacy (ω) in influencing the spread of Chagas disease, it is crucial to 293\nrecognize that these factors alone are necessary but not sufficient for eliminating the 294\ndisease burden. A more comprehensive approach that includes newborn therapy and 295\nvector control strategies is crucial to effectively combat Chagas disease. This is 296\nimportant because Chagas disease primarily spreads through the triatomine bugs, which 297\nserve as vectors for the Trypanosoma cruzi parasite. These vectors play a pivotal role in 298\ndisease transmission, and their control is essential for reducing human infections. Our 299\nsimulations demonstrate the substantial impact of reducing the transmission of the 300\ndisease from vectors to humans by setting βvh to zero. The adjustment, setting βvh to 301\nzero while maintaining the baseline α value (α = 0.4125), resulted in a significant 21% 302\ndecrease in the infected population compared to the scenario where βvh = 0.0000036. 303\nThis underscores how essential vector control measures are. Vector control includes 304\nvarious strategies, such as insecticide spraying, addressing poor housing conditions, and 305\ninitiating educational programs to reduce human-vector contact. Implementing vector 306\ncontrol strategies can effectively complement the efforts to improve treatment rates and 307\nefficacy and further reduce disease transmission. 308\nBased on our results, it is clear that a multifaceted approach is imperative for 309\nmanaging Chagas disease. This approach includes increasing the newborn treatment, 310\nenhancing the treatment efficiency, and implementing vector control measures. 311\nHigh treatment rates and treatment efficacy are important for controlling and 312\nreducing the burden of Chagas disease; however, they do not address vector-borne 313\ntransmission. Hence, it becomes clear that vector control has to be part of the 314\nmultifaceted approach to mitigate Chagas disease transmission. Public health 315\ninterventions should consider these varied methods of disease control to develop 316\nexhaustive strategies that regulate both congenital transmission and vector-to-human 317\ntransmission routes. 318\nFurther research in Chagas disease control should focus on developing integrated\napproaches that include both treatment and vector control strategies. Based on our\nresearch, we recommend initiatives that raise awareness about Chagas disease and\npromote early diagnosis and treatment. 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(which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 20, 2024. ; https://doi.org/10.1101/2024.02.18.24302989doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}