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10.1371/journal.pone.0308136
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Congenital transmission of Chagas disease: The role of newborn therapy on the disease’s dynamics
Congenital transmission of Chagas disease: The role of newborn therapy on the disease’s dynamics
Boukaabar Meriem Conceptualization Formal analysis Methodology Writing – original draft 1
Oduro Bismark Conceptualization Formal analysis Methodology Supervision Writing – review & editing 1
https://orcid.org/0009-0002-5595-2132
Chataa Paul Conceptualization Formal analysis Methodology 2 *
1 Department of Mathematics, Pennsylvania Western University, California, PA, United States of America
2 Department of Mathematics, University of Cape Coast, Cape Coast, Ghana
Rychtář Jan Editor
Virginia Commonwealth University, UNITED STATES OF AMERICA
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: paul.chataa@stu.ucc.edu.gh
2024
19 9 2024
19 9 e030813621 2 2024
15 7 2024
© 2024 Boukaabar et al
2024
Boukaabar et al
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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 congenital transmission’s impact on Chagas disease dynamics through a mathematical model. Specifically, we examine how treating a proportion of infants born to infected individuals impacts 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 treating a high proportion of newborns to reduce the number of infected cases of the disease. The findings show that the therapy given to newborns is necessary but not sufficient to curb the transmission of Chagas disease, and a comprehensive approach that includes vector and vertical transmission control strategies is essential for eradicating Chagas disease. We also observed that if vector transmission can be controlled, then at least 55% of the newborns need to be treated to eliminate the disease.

The author(s) received no specific funding for this work. Data AvailabilityThe research was not based on data. We estimated our parameter values from literature that was duly cited in the manuscript. Therefore, all relevant data are included in the manuscript.
Data Availability

The research was not based on data. We estimated our parameter values from literature that was duly cited in the manuscript. Therefore, all relevant data are included in the manuscript.
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pmcIntroduction

Chagas disease, also known as American trypanosomiasis, is an anthropozoonosis disease caused by a protozoan blood-borne pathogen called Trypanosoma cruzi [1]. The disease is predominantly active in Latin America, where it is a major public health issue [2]. The World Health Organization (WHO) has classified Chagas as one of 21 neglected tropical diseases in the world [3]. Additionally, the WHO estimates that 6-7 million people are currently infected with Chagas, and 75 million people are at risk for acquiring the disease [4]. Higher incidence rates are typically associated with areas that have poorly constructed housing, which serve as hiding places for the insect vectors that transmit the disease [2]. The disease is vectorized by Triatomine (reduviid) bugs, also known as “kissing bugs,” because they bite the host around their lips when they feed [5]. When the bug feeds on humans, it defecates, which allows the T. cruzi to exit with the feces and enter the host’s body [6]. This is one of the most common routes of infection. Other common routes of infection include congenital transmission, consumption of triatomine insects, needle sharing, and transfusional transmission [7]. The highest number of new acute infection cases comes from vector and congenital transmission [8]. This is especially true in Latin American countries, where approximately 22.5% of new infections are due to congenital transmission [9]. In both the acute and chronic phases of the infection, the disease can be transmitted from the infected mother through the placenta to the embryo or fetus [10]. In 1–10% of infants of infected mothers, congenital T. cruzi infection occurs [2]. Pregnant-infected women typically have higher rates of premature births and miscarriages [11]. Typically, the mothers and the infected children are asymptomatic, which makes the diagnosis of Chagas challenging [12]. Even in cases where symptoms are present, they are non-specific symptoms like fevers, swollen lymph nodes, and hepatosplenomegaly [13]. Regardless of the symptoms, all untreated infected infants are at a 20–30% risk of developing severe cardiac and intestinal complications later on in their life [14]. Ultimately, the faster the diagnosis and subsequent treatment, the more effective it is [10]. There is a 90–95% cure rate when the disease is recognized early, and treatment is used [15]. As infected patients age, the cure rate decreases, so diagnosis should be a priority [16]. Current diagnosis and treatment methods consist of a multistep method. Firstly, detection requires maternal serological screening [17]. Typically, if a mother tests positive two times in a row, the newborns are suspected of having Chagas disease and are tested [2]. The most common method for testing newborns is examining cord blood from their seropositive mothers using microscopy (also called the “micro method”) or polymerase chain reaction (PCR) techniques, anytime until they are one-month old [18]. Infants who test positive via microscopy or PCR are considered to have Chagas disease [17]. Unfortunately, these methods are unreliable; more than 50% of infections are not recognized by microscopy [19]. Therefore, infants who are tested after one month of birth or test negative are retested using serology when they are 9-12 months old [2]. Treatment options include Benznidazole or Nifurtimox [4]. Treatment during pregnancy is not currently recommended because of a lack of data on safety [16]. However, since the treatment options are highly effective for newborns, treatment should begin as soon as the diagnosis is made [2].

A few articles have been published on using mathematical models to explore Chagas disease dynamics, including [20–23]. Raimundo et al. in [24] focused on the congenital transmission of Chagas disease in populations where vectorial transmission has been eliminated. By considering both vertical transmission and the presence of vectorial transmission, our study expanded on this work. Furthermore, we also incorporated vector control measures into the model. Coffield et al. in [25] used a mathematical model to explore Chagas disease transmission by including congenital and oral transmission modes in humans and domestic mammals. The research concluded that while congenital transmission has a limited impact on infection, oral transmission in domestic mammals significantly contributes to the disease’s spread, highlighting the importance of considering alternative transmission modes in disease control strategies [25]. None of these published papers explored the impact of congenital transmission and newborn therapy in controlling the disease. Our study addresses this gap by investigating the impact of congenital transmission and newborn therapy on controlling Chagas disease. The main question guiding our research is: how do congenital transmission and newborn therapy influence Chagas disease’s dynamics, particularly in controlling its spread?

Materials and methods

In this section, we develop a compartmental model that reflects the dynamics of Chagas disease in both human and vector populations. The vector population is divided into two classes at time t: susceptible vectors (Sv) and infected vectors (Iv). The human population is divided into four classes at time t: infected acute humans (Ia), infected chronic humans (Ic), susceptible humans (Sh), and newborn babies from infected mothers (M). The natural death rate of vectors is denoted by μv, and the model assumes all newborns from non-infected mothers are susceptible. If a susceptible vector feeds on an infected acute or infected chronic human, the rate of disease transmission from the human to the vector is represented by βhv, and the susceptible vector moves to the infected vector class and stays there for life. When an infected vector bites a susceptible human, the disease is transmitted at a rate of βvh, and the susceptible human is moved to the infected acute stage. From there, the infected acute human can progress to the infected chronic human class; this progression rate is denoted by k. Individuals in the infected chronic class remain in that class for life unless they leave the population through natural death at rate μh or the death rate from Chagas given by δh. The birth rate of infected acute and infected chronic mothers combined, represented by bh(Ic + Ia), is what comprises the M class. Newborns to infected mothers in the M class progress to either the Sh or Ia class at rate p; the progression could be due to treatment or aging. In [15], the authors demonstrated that the treatment of newborns is effective, with a 90–95% efficacy. We incorporate newborn therapy and let 0 ≤ α ≤ 1 represent the proportion of newborns (to infected mothers) who receive successful therapy and move to the class Sh. The remaining proportion, 1 − α, undergo unsuccessful treatment or do not receive any treatment and are classified as infected acute individuals. Values of α close to unity imply that almost all newborns receive or undergo perfect therapy, while a low level of α implies that no newborn receives treatment therapy. A diagram depicting the dynamics explained in this section is shown in Fig 1; the parameters and their meanings are presented in Table 1.

10.1371/journal.pone.0308136.g001 Fig 1 Schematic diagram of the model.

See Table 1 for meanings of parameters/variables.

10.1371/journal.pone.0308136.t001 Table 1 Parameters of the disease model and their meanings.

Parameter	Meaning	
β vh	The transmission rate from infected vectors to a susceptible human	
β hv	The transmission rate from infected human to susceptible vectors	
μ h	Death from unrelated causes rate of human	
μ v	Death rate of vectors	
δ h	Death rate from the disease of humans in the chronic stage	
b h	Birth rate of humans	
b v	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 rate from M to Sh or Ia class	
α	Proportion of newborns that undergo treatment therapy	

Under the assumptions described above and the diagram, we obtain the following system of nonlinear ordinary differential equations. dSvdt=bv-λvSv-μvSvdIvdt=λvSv-μvIvdShdt=bh+αpM-λhSh-μhShdIadt=λhSh+(1-α)pM-(k+μh)IadIcdt=kIa-(μh+δh)IcdMdt=bh(Ia+Ic)-(p+μh)M (1)

Where λv=βhv(Ia+IcNh),λh=(βvhIvNv),Nv=Sv+Iv,Nh=Sh+Ia+Ic+M.

The disease-free equilibrium (DFE) is given as: DFE=(bvμv,0,bhμh,0,0,0). (2)

A next-generation approach is defined as the dominant eigenvalue (spectral radius) of the matrix FV−1 [26–28], where F and V−1 are matrices determined as: F=[∂Fi(x0)∂xj] and V=[∂Vi(x0)∂xj]. Here, xj is the number of infested units, x0 is the disease-free equilibrium, Fi is the rate of appearance of new infection in the infected compartments, Vi=Vi--Vi+ with Vi- denoting the rate at which infected individuals are transferred out of the infected compartments and Vi+ denoting the rate at which individuals are transferred into the infected compartments.

We will use the next-generation method to compute the control reproduction number Rc. Fi=[FIvFIaFIcFM]=[λvSvλhSh0bh(Ia+Ic)]

and Vi=[VIvVIaVIcVM]=[μvIv-(1-α)pM+(k+μh)Ia-kIa+(μh+δh)Ic(p+μh)M].

Therefore F=[0βhvSv*Nh*βhvSv*Nh*0βvhSh*Nv*00000000bhbh0].

and V=[μv0000k+μh0-(1-α)p0-kμh+δh0000p+μh],

where Sh*=bhμh=Nh* and Sv*=bvμv=Nv*.

By the next generation method, the control reproduction number is the spectral radius FV−1. That is, Rc=Ψ1+(k+μh+δh)Ψ2+Ψ122(μh+k)(μh+p)(μh+δh),

where Ψ1=bhp(1-α)(k+μh+δh)Ψ2=4βhvβvh(μh+k)(μh+p)2(μh+δh)/μv.

Let us consider a scenario that allows a perfect treatment that is α = 1. RL=(limα⟶1Rc)2=βhvβvh(k+μh+δh)μv(k+μh)(μh+δh). (3)

Eq 3 shows that perfect treatment of newborns is insufficient to exterminate the infection if RL>1. In addition to the newborn therapy, control measures that would reduce RL below unity are required to eradicate the disease.

Let us consider the existence of an endemic equilibrium of the system. The endemic equilibrium levels are the steady-state solutions where the Chagas infection persists in the population. So, at the Chagas disease persistence equilibrium, EE=(Sv*,Iv*,Sh*,Ia*,Ic*,M*), the following equations are satisfied: 0=bv-λv*Sv*-μvSv*,0=λv*Sv*-μvIv*,0=bh+αpM*-λh*Sh*-μhSh*,0=λhSh*+(1-α)pM*-(k+μh)Ia*,0=kIa*-(μh+δh)Ic*,0=bh(Ia*+Ic*)-(p+μh)M*. (4)

Also, at the endemic equilibrium, the force of infections are λv*=βhv(Ia*+Ic*Nh*)≤βhv,λh*=(βvhIv*Nv*)≤βvh. To explore the effects of α on the infected individuals at equilibrium theoretically, we consider when λv*=βhv and λh*=βvh to obtain explicit equations for the endemic levels of the state variables. By the first, second, third, fifth, and sixth lines of (4), we have Sv*=bvβhv+μv,Iv*=βhvbvμv(βhv+μv),Ic⋆=kIa⋆μh+δh,M⋆=bh(Ia*+Ic*)p+μh=bh(μh+δh+k)Ia⋆(p+μh)(μh+δh),Sh*=bhβvh+μh+αpMa⋆βvh+μh=bhβvh+μh+αpbh(μh+δh+k)Ia⋆(μh+δh)(μh+p)(βvh+μh).

Also, by the fourth line of (4), we have Ia*=βvhSh*+(1-α)pM*k+μh. (5)

Substituting the expressions of Sh* and M* into (5) and solving for Ia* gives Ia⋆=bhβvh(k+μh)(βvh+μh)(1-Φ),

where Φ=bhp(μh+δh+k)(βvh+(1-α)μh)(k+μh)(βvh+μh)(μh+δh)(p+μh).

Hence, an endemic equilibrium exists when Φ < 1. The parameter α is our control parameter; let us describe how it influences the endemic equilibrium. The ∂Ia⋆∂α<0; indicating that I* is always decreasing with respect to α. Observe that Ic* and M* also decrease with respect to α, as they are directly proportional to Ia*. This implies that treating many infants can significantly lower the endemic prevalence.

Stability analysis of the disease-free equilibrium

In this section, we determine the local and global stability of the disease-free equilibrium.

First, we determine the local stability of the disease-free equilibrium by computing the eigenvalues of the linearized Jacobian matrix at the disease-free equilibrium and obtain J0(DFE)=(-μv00-βhvSv⋆Nh⋆-βhvSv⋆Nh⋆00-μv0βhvSv⋆Nh⋆βhvSv⋆Nh⋆00-βvhSh⋆Nv⋆-μh00αp0βvhSh⋆Nv⋆0-(k+μh)0(1-α)p000k-(μh+δh)0000bhbh-(μh+p)).

The eigenvalues of the Jacobian matrix, J0(DFE) are, ϱ1 = −μv, ϱ2 = −μh, ϱ3 = −μv, ϱ4 = −(μh + p), ϱ5 = −(μh + δh), and ϱ6=μv(p+μh)(k+μh)(μh+δh)(p+μh)B1B2+μvbh(1-α)p(ε-1)

where ε=((p+μh)B1B2+μvbh(1-α)p)(μh+δh+k)μv(p+μh)(k+μh)(μh+δh).

The disease-free state of the system is locally asymptotically stable when ε < 1.

Observe that for α = 1, we have ϱ6=μv(k+μh)(μh+δh)B1B2(RL-1),

leading to the following result.

Theorem 1. For α = 1, the disease-free equilibrium of the system is locally asymptotically stable if RL<1 and unstable if RL>1. For 0 ≤ α < 1, the disease-free equilibrium of the system is locally asymptotically stable if ε < 1 and unstable if ε > 1.

Next, we will apply the approach of Castillo-Chavez et al [29] to prove the global stability of the disease-free equilibrium. The approach is defined in the theorem below.

Theorem 2. If a model system can be written in the form: dXdt=F(X,0),dIdt=G(X,I),G(X,0)=0,

where X ∈ ℜm denotes the number of uninfected compartments and I ∈ ℜn, denotes the number of infected compartments, including latent, exposed, and acute individuals. U(X⋆, 0) denotes the disease-free equilibrium of the system. Then the conditions (H1) and (H2) must be satisfied to guarantee local asymptotic stability.

H1 : For dXdt=F(X,0), X⋆ is globally asymptotically stable.

H2 : G(X,I)=AI-G^(X,0)≥0 for (X, I) ∈ Δ, where A = DiG(X⋆, 0) is a Metzler matrix (the off-diagonal elements of A are non-negative) and Δ is the region where the model makes biological sense and mathematically well-posed. Then the fixed point U0 = (X⋆, 0) is globally asymptotically stable equilibrium of the Chagas infection model provided Rc<1.

Theorem 3. The disease-free equilibrium DFE=(bvμv,0,bhμh,0,0,0)

is globally asymptotically stable if the conditions (H1) and (H2) are satisfied.

Proof. From the model system, we have X∈ℜ2=(Sv⋆,Sh⋆) and I∈ℜ4=(Iv⋆,Ia⋆,Ic⋆,M⋆). Hence, for condition (H1), we have dXdt=F(X,0)=(bv-βhvSvIaNv-βhvSvIcNv-μvSvbh+αpM-βvhShIvNh-μhSh)

and dIdt=G(X,I)=(βhvSvIaNv+βhvSvIcNv-μvIvβvhShIvNh+(1-α)pM-(k+μh)IakIa-(μh+δh)IcbhIa+bhIc-(p+μh)M).

It follows that F(X,0)=(-μv00-μh).

The eigenvaules from the matrix F(X, 0) are obtained to be π1=-μv<0,π2=-μh<0.

Since all the eigenvalues of the matrix F(X, 0) are negative, it follows that X⋆ is always globally asymptotically stable. Also, applying Theorem (2) to the Chagas disease model system gives G^(X,I)=AI-G(X,I)=(0βhvSv⋆Nv⋆βhvSv⋆Nv⋆0βvhSh⋆Nh⋆-(k+μh)0-(1-α)p0k-(μh+δh)00bhbh-(p+μh))(IvIaIcM)-(βhvSvIaNv+βhvSvIcNv-μvIvβvhShIvNh+(1-α)pM-(k+μh)IakIa-(μh+δh)IcbhIa+bhIc-(p+μh)M)

Hence, G^(X,I)=(βhvSv⋆IaNv⋆+βhvSv⋆IcNv⋆βvhSh⋆IvNh⋆-(k+μh)Ia-(1-α)pMkIa-(μh+δh)IcbhIa+bhIc-(p+μh)M)-(βhvSvIaNv+βhvSvIcNv-μvIvβvhShIvNh+(1-α)pM-(k+μh)IakIa-(μh+δh)IcbhIa+bhIc-(p+μh)M)

Therefore, G^0(X,I)=([βhvSv⋆IaNv⋆-βhvSvIaNv]+[βhvSv⋆IcNv⋆-βhvSvIcNv]+μvIvβvhSh⋆IvNh⋆-βvhShIvNh00)=(βhvIaNv⋆[Sv⋆-Sv]+βhvIcNv⋆[Sv⋆-Sv]βvhIvNh⋆[Sh⋆-Sh]00).

So, A is a Metzler matrix with non-negative off-diagonal elements. We observed that G^0(X,I)=(βhvIaNv⋆[Sv⋆-Sv]+βhvIcNv⋆[Sv⋆-Sv]βvhIvNh⋆[Sh⋆-Sh]00)≥0,

because βhvIaNv⋆[Sv⋆-Sv]+βhvIcNv⋆[Sv⋆-Sv]≥0 and βvhIvNh⋆[Sh⋆-Sh]≥0. Therefore, the disease-free equilibrium DFE is globally asymptotically stable.

Numerical simulation results

In this section, we analyzed the numerical simulation of the proposed model. We used literature values and MATLAB to explore the control reproduction number, the endemic and disease-free equilibrium, and the spread of the Chagas disease. The initial conditions of the state variables are given to be Sh(0) = 20000, Ia(0) = 2000, Ic(0) = 4000, M(0) = 0, Sv(0) = 500000, and Iv(0) = 100000. The baseline parameter values are in Table 2.

10.1371/journal.pone.0308136.t002 Table 2 Baseline parameter values of the disease model and their sources.

Parameter	Value	Source	
β vh	0.000032–0.0000096 per day	[23]	
β hv	0.000012–0.0000036 per day	[23]	
μ v	0.005 per day	[30]	
μ h	0.000042 per day	[30]	
δ h	0.00013–0.00018 per day	[30]	
b h	70/365 per day	[31]	
b v	183.68–551.04 per day	[32]	
k	0.02675	[30]	
p	0.0125	Assumed	

Exploring impact of α on the control reproduction number

First, we examined how varying α affects the reproduction number and the infected population. Essentially, α represents the proportion of infants born to infected mothers that undergo successful treatment.

We generated a contour plot to analyze the control reproduction number (Rc) of the model as a function of the proportion of newborns that undergo successful treatment, α, and the progression rate, p, as displayed in Fig 2. Based on the contour plot result, the Rc decreases as more newborns to infected individuals are given the therapy. Thus, higher values of α correspond to lower control reproduction numbers. When α is at its minimum (0), the reproduction number is approximately 3.5. On the other hand, when α is at its maximum (1), the reproduction number decreases to below 1.4. This indicates that the control reproduction number decreases as the proportion of newborns that undergo successful treatment increases, resulting in less disease spread. However, this control measure alone cannot eradicate the disease since the control reproduction is above unity.

10.1371/journal.pone.0308136.g002 Fig 2 Contour plot of the control reproduction number (Rc) of the model as a function of the proportion of newborns that undergo successful treatment, α, and the progression rate, p.

Also, we considered the control reproduction number (Rc) as a function of the proportion of newborns that undergo successful treatment, α, and the transmission rate, βvh, as shown in Fig 3, to examine combinations of the two parameters that are capable of reducing the reproduction number to a desired level. Essentially, effective vector controls lower the βvh and reduce the transmission of the infection to susceptible humans. As shown in Fig 3, high values of α and βvh cannot reduce the reproduction to below unity. A low βvh and a high α are required to control Chagas disease transmission effectively. When βvh is set to zero or relatively small, and at least 55% of the newborns successfully receive treatment, the reproduction number drops below unity, emphasizing the importance of vector control and successful newborn therapy measures in reducing the spread and impact of Chagas disease.

10.1371/journal.pone.0308136.g003 Fig 3 Contour plot of the control reproduction number (Rc) of the model as a function of the proportion of newborns that undergo successful treatment, α, and the transmission rate, βvh.

Exploring impact of α on the disease spread

In this section, we used the model to conduct numerical simulations depicting Chagas disease’s dynamics. We considered when the system approaches an endemic and disease-free equilibrium, allowing us to observe how the proportion, α, of newborns that undergo successful therapy influences the Chagas disease dynamics. We examined how varying α affects the acutely infected population. Again, a low α implies a small proportion of newborns receive successful treatment, and a high α indicates that a significant portion or even all newborns receive successful therapy. The results provided valuable insights for optimizing control strategies for the disease.

Firstly, we considered the impact of α on the infected individuals at an endemic equilibrium. We set α = 0.5 (the baseline scenario) and then modified it by increasing and decreasing its value by 25%, 50%, and 75% to examine how varying α values affected the spread, particularly when the system approaches an endemic equilibrium. This led to seven different α values: the baseline α of 0.5, a 25% increase (α = 0.625), a 25% decrease (α = 0.375), a 50% increase (α = 0.75), a 50% decrease (α = 0.25), a 75% increase (α = 0.875), and a 75% decrease (α = 0.125). We also looked at the scenarios where α was set to 1 (universal treatment) and 0 (no newborn receives treatment). Fig 4 illustrates the population of acutely infected individuals over the time interval [0, 3000], given these α values. We calculated the area under the curve (AUC), providing a measure of the acutely infected population over time for each α value. This analysis assumes an endemic equilibrium, where the disease remains consistently present in the population over a long period. The calculated percentage changes represent the difference in the infected population compared to the baseline scenario, illustrating the impact of adjusting α values on disease dynamics. The respective AUC values for the different scenarios and percentage change values are presented in Table 3.

10.1371/journal.pone.0308136.g004 Fig 4 The acutely infected population at an endemic equilibrium, for different α values.

The figure illustrates the impact of varying α (proportion of newborns receiving treatment) on disease spread, ranging from baseline (α = 0.5) to 25%, 50%, and 75% increases and decreases. It also shows scenarios of universal treatment (α = 1) and no treatment (α = 0).

10.1371/journal.pone.0308136.t003 Table 3 Impact of varying α on the acutely infected population at an endemic equilibrium.

α value	AUC	Percentage Change	
0.5 (baseline)	19,155,646.82	-	
0.625 (25% increase)	18,238,085.57	-4.79	
0.375 (25% decrease)	20,101,943.08	4.94	
0.75 (50% increase)	17,348,644.31	-9.43	
0.25 (50% decrease)	21,077,599.61	10.03	
0.875 (75% increase)	16,486,718.12	-13.93	
0.125 (75% decrease)	22,083,252.08	15.28	
0 (100% decrease)	23,119,546.64	20.69	
1 (100% increase)	15,651,712.072	-18.29	

Interpreting these results, a 25% increase in α correlated with a 4.79% decrease in the acutely infected population relative to the baseline. Conversely, a 25% decrease in α corresponded to a 4.94% increase in the infected population. Similarly, a 50% increase in α resulted in a 9.43% reduction in the infected population, signifying significant progress in disease management. Meanwhile, a 50% decrease in α led to a 10.03% increase in the infected population. A 75% increase in α correlated with a 13.93% reduction in the infected population, while a 75% decrease in α resulted in a 15.28% increase in infections. When α was set to 1 (100% increase, universal treatment), there was an 18.29% reduction in the acutely infected population, whereas setting α to 0 (100% decrease, no newborn receives treatment) resulted in a 20.69% increase in the acutely infected population. These results underscore how α, representing the proportion of newborns that receive treatment, influences the disease spread. Higher α values lead to reduced endemic levels, while lower values indicate higher endemic levels due to a smaller proportion of newborns receiving treatment.

Next, we explored the effect of α at the disease-free equilibrium. In this case, the disease is absent in the population. To accomplish disease-free equilibrium for our simulations, we modified the values of the transmission rates, βvh (transmission rate from infected vectors to susceptible humans) and βhv (transmission rate from infected humans to susceptible vectors. Vector-human interactions are linked to these parameters, and implementing efficient vector control measures can reduce their values. The values tested for α were 0.5 (baseline), 0 (100% decrease), and 1 (100% increase). Again, an α of 0 means no newborns receive treatment, while an α of 1 means all newborns receive treatment. Fig 5 shows the population of the acutely infected individuals over a given time interval. We calculated the area under the curve for each α value and determined the percent change from the baseline, as shown in Table 4.

10.1371/journal.pone.0308136.g005 Fig 5 The number of acutely infected individuals under the disease-free equilibrium scenario of Chagas disease dynamics.

The figure illustrates the impact of varying α values on Chagas disease incidence: baseline (α = 0.5), no treatment (α = 0), and universal treatment (α = 1). In this case, disease-free equilibrium is achieved with a low vector transmission rate.

10.1371/journal.pone.0308136.t004 Table 4 Impact of varying α on the acutely infected population at a disease-free equilibrium.

α value	AUC	Percentage Change	
0.5 (baseline)	302,553.67	-	
0 (100% decrease)	318,903.40	5.40	
1 (100% increase)	287,632.49	-4.93	

The results show a 5.40% increase in the acutely infected population when α = 0 compared to the baseline (α = 0.5), whereas there is a 4.93% decrease when α = 1. This reduction from the baseline suggests that increasing the proportion of newborns receiving treatment effectively reduces the burden of Chagas disease. Thus, a disease-free equilibrium is achievable with both effective vector and newborn therapy control measures.

To explore the impact of α further, we considered the scenario where the system approached a disease-free equilibrium with a specific α value. We compared it to a scenario where α is not introduced, that is, α = 0, and the system grows within the comparison period. The results are graphically represented in Fig 6, and values for the AUC and percentage changes from the baseline can be found in Table 5. The graph shows that introducing newborn treatment creates disease-free conditions. Specifically, treating half of the newborns (α = 0.5) is sufficient to achieve disease-free equilibrium. But, without any newborn treatment (α = 0), the disease continues to grow, which suggests that newborn treatment control is necessary. Additionally, at α = 0.5, the system slowly approaches disease-free equilibrium. Increasing α to 1 accelerates this transition, as shown by the smaller AUC (340,787.08) compared to the α = 0 (4,522,769.21). This underscores the importance of increasing the number of newborns receiving treatment to control disease spread effectively.

10.1371/journal.pone.0308136.g006 Fig 6 The number of acutely infected individuals under the disease-free equilibrium with newborn therapy and the disease spread without newborn therapy.

10.1371/journal.pone.0308136.t005 Table 5 Impact of α on the acutely infected population at a disease-free equilibrium, and the disease spread without newborn therapy.

α value	AUC	Percentage Change (from Baseline AUC)	
0.5 (baseline)	943,004.29	-	
0 (100% decrease)	4,522,769.21	379.61	
1 (100% increase)	340,787.08	-63.86	

Discussion

In this paper, we constructed and analyzed a deterministic Chagas disease model that accounted for the proportion of newborns to infected mothers who undergo treatment therapy. This section discusses the implications of our findings and their significance for strengthening control strategies for Chagas disease. The theoretical and numerical results highlighted that treating a reasonable proportion (or even implementing a universal therapy) of newborns to infected mothers significantly impacts the spread of the disease.

We analyzed the control reproduction number of the model using contour plots. The contour plots showed that the control reproduction number decreases as the proportion of newborns that undergo successful treatment increases, which will result in less disease spread. However, this control measure alone is insufficient to eliminate the Chagas disease. A low vectorial transmission and a high newborn therapy are required to control Chagas disease transmission effectively. It was also observed that if vector transmission can be managed, at least 55% of the babies must receive treatment to eradicate the disease.

In a scenario where endemic equilibrium exists, increasing α from a baseline value 0.5 results in a reduction in the infected population by 4.79%, 9.43%, and 13.93% for 25%, 50%, and 75% increases in α, respectively. Conversely, decreasing α by the same percentages leads to an increase in the infected population by 4.94%, 10.03%, and 15.28%. These findings highlight the importance of treating newborns as it can substantially reduce the burden of Chagas disease. Additionally, the results show the impact of minimizing (α = 0) and maximizing (α = 1) the proportion of newborns that receive treatment. Minimizing α, implying no newborns receive treatment, led to a 20.69% increase in the infected population. On the other hand, maximizing α led to an 18.29% reduction in the acutely infected population.

While our results underscore the significant impact of α in influencing the spread of Chagas disease, it is crucial to recognize that these factors alone are necessary but insufficient for eliminating the disease burden. A more comprehensive approach that includes newborn therapy and vector control strategies, such as insecticide spraying, addressing poor housing conditions, and initiating educational programs to reduce human-vector contact, is crucial to combat Chagas disease effectively. This is important because Chagas disease primarily spreads through the triatomine bugs, which serve as vectors for the Trypanosoma cruzi parasite. These vectors play a pivotal role in disease transmission, and their control is essential for reducing vectorial transmission. Our simulations demonstrate the impact of vector control by considering disease-free equilibrium scenarios. In these cases, the values of βvh and βhv are reduced to smaller values. When no newborn receives treatment (α = 0), there was a 5.40% rise in acutely infected individuals, whereas treating all newborns (α = 1) resulted in a 4.93% reduction in the acutely infected population. These results underscore how essential vector control measures are to reduce human-vector interactions and their transmission rates.

Based on our results, it is clear that a multifaceted approach, including increasing newborn treatment and implementing vector control measures, is imperative for managing Chagas disease. Treating newborns is very important for controlling and reducing the burden of Chagas disease; however, that does not address vector-borne transmission. Hence, it becomes clear that vector control has to be part of the multifaceted approach to mitigate Chagas disease transmission. Public health interventions should consider these varied disease control methods to develop exhaustive strategies regulating both congenital and vector-to-human transmission routes. 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.

Our study has some limitations that should be acknowledged. This model did not incorporate the impacts of treating Chagas disease-infected individuals, particularly potential mothers. However, including treatment for infected potential mothers may prevent transmission to their progeny. Additionally, our model relied on existing data for parameter values, including the transmission rates. The availability of comprehensive data could help estimate the parameter values and validate the model. Also, Chagas disease transmission is complex; our model is simplified and does not account for other transmission routes and domestic animals that contribute to the disease. Despite these limitations, our study has many strengths. We provide essential insights into the congenital transmission of Chagas disease, highlighting the importance of therapy to newborns of infected mothers. These results are significant as they inform policy decisions for enhancing Chagas disease control.

10.1371/journal.pone.0308136.r001
Decision Letter 0
Rychtář Jan Academic Editor
© 2024 Jan Rychtář
2024
Jan Rychtář
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version0
12 Apr 2024

PONE-D-24-06545Congenital transmission of Chagas disease: The role of newborn therapy on the disease’s dynamicsPLOS ONE

Dear Dr. Chataa,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

The paper have been reviewer by two reviewers and both suggest a number of important changes. I agree with their recommendations and hope the authors can address the reviewer's concerns and suggestions in their major revision.

==============================

Please submit your revised manuscript by May 27 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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Jan Rychtář

Academic Editor

PLOS ONE

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Additional Editor Comments:

The paper have been reviewer by two reviewers and both suggest a number of important changes. I agree with their recommendations and hope the authors can address the reviewer's concerns and suggestions in their major revision.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: I Don't Know

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This is a relatively standard ODE model of a disease. The model is appropriate for Chagas disease and the analysis is sound.

The biggest issue with this paper lies in the result section. The results and the figures are presented in a cumbersome manner. Results on the effect of alpha should be presented in a table and also a figure (with change of alpha on the x axis and the effect on the y axis)

An even more important issue is that the authors consider only DFE and not endemic equilibrium. Their proofs for stability of DFE are standard and can perhaps be streamlined. The formulas for EE are missing completely and should be added.

The validation of the model is missing, i.e., there is no clear reason to believe that the model fits reality. In fact, the model most likely does not fit the reality as it predicts an exponential growth. I would be inclined to believe that in most regions with Chagas, the disease is already endemic and more or less on a stable levels (or fluctuating due to environmental and other changes) but not exponentially growing.

Due to the above issue, the EE should be evaluated, the model validated, perhaps compared to EE and then the sensitivity to alpha reconsidered (i.e. describe how alpha influences the EE, not the growth)

Reviewer #2: Dear authors, this is a study highlighting the importance of adressing the importance of newborn therapy for Chagas Disease control. The methods are sound and the results interesting. There are but a few comments I would like to do.

1. I would recommend abbreviating the introduction.

2. I would add abbreviation definitions to the footnote of figure 1.

3. I would end the introduction section stating the study question.

4. My biggest concern, however, is the fact that treatment of infected humans with Chronic Chagas Disease has not been included in the model. I would think this is very likely to have an important impact on the congenital transmission for two reasons, more infected mothers will be treated and thus would not transmit the disease and because as less infected humans are present less infections of the bugs would occur. I believe this is an important caveat and should be addressed in the discussion.

5. I also miss a section evaluating the limitations and strengths of the conclusions reached.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

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10.1371/journal.pone.0308136.r002
Author response to Decision Letter 0
Submission Version1
20 May 2024

Dear Editor:

The authors would like to thank you for the opportunity to revise our manuscript. We also want to thank both reviewers and the Handling Editor for thoughtful comments and suggestions on the previous version of this manuscript. We have thoroughly revised it and addressed their comments. Below, please find our response to the reviewers' comments.

REVIEWER 1:

We appreciate the reviewer's feedback and do address the concerns below.

This is a relatively standard ODE model of a disease. The model is appropriate for Chagas disease and the analysis is sound.

The biggest issue with this paper lies in the result section. The results and the figures are presented in a cumbersome manner. Results on the effect of alpha should be presented in a table and also a figure (with change of alpha on the x axis and the effect on the y axis)

We thank the reviewer for this comment. We have summarized the impact of the alpha on the infected individual's compartment of the model in Table 3. Furthermore, we have added two new plots: Figure 2(a) (contour plot), and Figure 2(b) (I^*-vs alpha) to further demonstrate the effect of alpha on the model dynamics.

An even more important issue is that the authors consider only DFE and not endemic equilibrium. Their proofs for stability of DFE are standard and can perhaps be streamlined. The formulas for EE are missing completely and should be added.

We thank the reviewer for this comment. We have streamlined the local stability proof of DFE.

The validation of the model is missing, i.e., there is no clear reason to believe that the model fits reality. In fact, the model most likely does not fit the reality as it predicts an exponential growth. I would be inclined to believe that in most regions with Chagas, the disease is already endemic and more or less on a stable levels (or fluctuating due to environmental and other changes) but not exponentially growing.

Due to the above issue, the EE should be evaluated, the model validated, perhaps compared to EE and then the sensitivity to alpha reconsidered (i.e. describe how alpha influences the EE, not the growth)

We thank the reviewer for this comment. This is an ODE model that grows, decays, and reaches an equilibrium under certain conditions. We have evaluated and derived conditions for which the EE exists. We have also analyzed the impact of the alpha on the EE both numerically and theoretically. Figure 5(b) (I^*-vs alpha) demonstrates the effect of alpha on the EE and these results collaborate.

REVIEWER 2:

We thank the reviewer for carefully reading the manuscript and for valuable suggestions. We have incorporated the suggestions in the revised version.

Dear authors, this is a study highlighting the importance of adressing the importance of newborn therapy for Chagas Disease control. The methods are sound and the results interesting. There are but a few comments I would like to do.

1. I would recommend abbreviating the introduction.

We thank the reviewer for this comment. We agree with the reviewer that the introduction was long and have reduced it by one paragraph.

2. I would add abbreviation definitions to the footnote of figure 1.

We thank the reviewer for this comment. However, the comment is not clear to us. Figure I is the schematic diagram of the model. The model parameters are defined in Table 1 and the variables are defined in the first paragraph of the materials and methods section.

3. I would end the introduction section stating the study question.

We thank the reviewer for this comment. We have rephrased the last paragraph of the introduction and added the research question.

4. My biggest concern, however, is the fact that treatment of infected humans with Chronic Chagas Disease has not been included in the model. I would think this is very likely to have an important impact on the congenital transmission for two reasons, more infected mothers will be treated and thus would not transmit the disease and because as less infected humans are present less infections of the bugs would occur. I believe this is an important caveat and should be addressed in the discussion.

We thank the reviewer for this comment. Several studies have confirmed the effectiveness of acutely infected individuals and are less effective for chronic Chagas disease patients. Nevertheless, we have addressed this comment as a limitation.

5. I also miss a section evaluating the limitations and strengths of the conclusions reached

We thank the reviewer for this comment. We have added a paragraph addressing limitations and strengths.

Attachment Submitted filename: Response to Reviewers.docx

10.1371/journal.pone.0308136.r003
Decision Letter 1
Rychtář Jan Academic Editor
© 2024 Jan Rychtář
2024
Jan Rychtář
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
29 May 2024

PONE-D-24-06545R1Congenital transmission of Chagas disease: The role of newborn therapy on the disease’s dynamicsPLOS ONE

Dear Dr. Chataa,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

The reviewer still finds several major issues that need to be fixed. All of the raised points are important and need to be addresses, starting with point #3 that identifies a problem with the model setup, point #1 that asks for more formulas so that readers can follow the calculations for the endemic equilibrium (plus a fact that R0 should most likely pop up in the formulas), and finally point #2 about simulating the appropriate scenarios instead of starting near disease-free equilibrium.

==============================

Please submit your revised manuscript by Jul 13 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Jan Rychtář

Academic Editor

PLOS ONE

Additional Editor Comments:

The reviewer still finds several major issues that need to be fixed. All of the raised points are important and need to be addresses, starting with point #3 that identifies a problem with the model setup, point #1 that asks for more formulas so that readers can follow the calculations for the endemic equilibrium (plus a fact that R0 should most likely pop up in the formulas), and finally point #2 about simulating the appropriate scenarios instead of starting near disease-free equilibrium.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: (No Response)

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Thank you for revising the manuscript. There are still several issues that should be addressed

1) The authors provide formulas for the endemic equilibrium but not the derivation. Some calculations should be provided that would indicate that the formulas are correct. It is common that the formulas for EE contains basic reproduction number and that one needs the reproduction number to be greater than 1 for the formulas to be biologically reasonable. The provided formulas are sort of along the lines, but it is really not clear that they are correct. So, my suggestion is to a) include the calculations and b) look for the reproduction number in the formulas.

2) The figures still show exponential growth (i.e. what happens when one varies alpha in the DFE). As mentioned earlier, the diseases is endemic. So it would make more sense to investigate what happens when one varies alpha in EE

in light of the point 3 below, if the authors indeed change the model, this point be addressed by varying r rather than alpha (assuming omega is more or less given by the nature of the treatment).

3) upon closer reading of the model description, there appears to be a very important and significant inconsistency in how authors treat alpha and p and r. They introduce alpha as omega times r where omega is treatment efficacy and r is a treatment rate. That means that alpha is a rate. The term alpha times p times M for the transmission from M to Sh does not make much sense (one cannot multiply rate with a rate to get a rate). Similarly, the term (1-alpha) in the flow from M to Ia does not make much sense either (on its own and definitely not when multiplied again by a rate p). It seems that much more natural rates from M to Sh would be omega times r and from M to Ia to be (1-omega) times r. There is also probably another process (such as aging) during which the untreated newborns from M become Ia. This is likely why authors used p in the model (and the overall rate from M to Ia would then be p+(1-omega)r).

So, my suggestions is for the authors to revise the model appropriately (or if they do not agree with the above interpretation, explain the model properly)

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

10.1371/journal.pone.0308136.r004
Author response to Decision Letter 1
Submission Version2
5 Jul 2024

Dear Editor:

The authors would like to thank you again for the opportunity to revise our manuscript. We also want to thank the reviewer for thoughtful comments and suggestions on the previous version of this manuscript. We have thoroughly revised it and addressed their comments. Below (in blue), please find our response to the reviewers' comments.

REVIEWER 1:

Reviewer #1: Thank you for revising the manuscript. There are still several issues that should be addressed

1) The authors provide formulas for the endemic equilibrium but not the derivation. Some calculations should be provided that would indicate that the formulas are correct. It is common that the formulas for EE contains basic reproduction number and that one needs the reproduction number to be greater than 1 for the formulas to be biologically reasonable. The provided formulas are sort of along the lines, but it is really not clear that they are correct. So, my suggestion is to a) include the calculations and b) look for the reproduction number in the formulas.

We thank the reviewer for this comment and suggestion. We have added some details and streamlined the derivation of the EE. We also agree with the reviewer that the EE of some models can be expressed in terms of the reproduction number; unfortunately, our EE cannot be written in terms of our R_c/R_L.

2) The figures still show exponential growth (i.e. what happens when one varies alpha in the DFE). As mentioned earlier, the diseases is endemic. So it would make more sense to investigate what happens when one varies alpha in EE.

We thank the reviewer for the comment. We have provided simulations showing the effects of alpha on the system at EE (Figure 4) and DFE (Figure 5).

in light of the point 3 below, if the authors indeed change the model, this point be addressed by varying r rather than alpha (assuming omega is more or less given by the nature of the treatment).

3) upon closer reading of the model description, there appears to be a very important and significant inconsistency in how authors treat alpha and p and r. They introduce alpha as omega times r where omega is treatment efficacy and r is a treatment rate. That means that alpha is a rate. The term alpha times p times M for the transmission from M to Sh does not make much sense (one cannot multiply rate with a rate to get a rate). Similarly, the term (1-alpha) in the flow from M to Ia does not make much sense either (on its own and definitely not when multiplied again by a rate p). It seems that much more natural rates from M to Sh would be omega times r and from M to Ia to be (1-omega) times r. There is also probably another process (such as aging) during which the untreated newborns from M become Ia. This is likely why authors used p in the model (and the overall rate from M to Ia would then be p+(1-omega)r).

So, my suggestions is for the authors to revise the model appropriately (or if they do not agree with the above interpretation, explain the model properly)

We thank the reviewer for this comment. This is important feedback, and we agree that the parameter alpha was not well-defined. We have redefined and explained alpha. We also thank the reviewer for the suggested model. It is a great idea, and we thoroughly explored it. However, we observed some concerns and caveats in this version of the model. For example, while I_a decreases with respect to omega (efficacy), it increases with respect to the treatment rate, r, with a fixed omega.

Attachment Submitted filename: Response to Reviewers_2.docx

10.1371/journal.pone.0308136.r005
Decision Letter 2
Rychtář Jan Academic Editor
© 2024 Jan Rychtář
2024
Jan Rychtář
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version2
16 Jul 2024

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

PONE-D-24-06545R2

Dear Dr. Chataa,

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10.1371/journal.pone.0308136.r006
Acceptance letter
Rychtář Jan Academic Editor
© 2024 Jan Rychtář
2024
Jan Rychtář
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
23 Jul 2024

PONE-D-24-06545R2

PLOS ONE

Dear Dr. Chataa,

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on behalf of

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Academic Editor

PLOS ONE
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