Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: Community-based deworming in Kenya as a case study.

The World Health Organization has recommended the application of mass drug administration (MDA) in treating high prevalence neglected tropical diseases such as soil-transmitted helminths (STHs), schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. MDA-which is safe, effective and inexpensive-has been widely applied to eliminate or interrupt the transmission of STHs in particular and has been offered to people in endemic regions without requiring individual diagnosis. We propose two mathematical models to investigate the impact of MDA on the mean number of worms in both treated and untreated human subpopulations. By varying the efficay of drugs, initial conditions of the models, coverage and frequency of MDA (both annual and biannual), we examine the dynamic behaviour of both models and the possibility of interruption of transmission. Both models predict that the interruption of transmission is possible if the drug efficacy is sufficiently high, but STH infection remains endemic if the drug efficacy is sufficiently low. In between these two critical values, the two models produce different predictions. By applying an additional round of biannual and annual MDA, we find that interruption of transmission is likely to happen in both cases with lower drug efficacy. In order to interrupt the transmission of STH or eliminate the infection efficiently and effectively, it is crucial to identify the appropriate efficacy of drug, coverage, frequency, timing and number of rounds of MDA.

Introduction

More than one billion people worldwide are affected by neglected tropical diseases (NTDs) every year [1]. High prevalence NTDs such as onchocerciasis, soil-transmitted helminths (STHs), schistosomiasis and lymphatic filariasis lock people into poverty even though they are amenable to periodic deworming via the use of anthelmintic medicines, also known as preventive chemotherapy (PC) [2-5]. The World Health Organization (WHO) [6] has introduced three strategies of applying PC in controlling STH infections:

Mass drug administration (MDA), where PC is applied to the whole population of an endemic region at regular intervals, regardless of the infectious status of an individual.

Targeted chemotherapy, where anthelmintic medicines are given to specific risk groups of people (e.g., specified by age and gender) at regular intervals, regardless of the infectious status of an individual.

Selective chemotherapy, where anthelmintic medicines are given to infected individuals or individuals suspected to be infected.

In 2015, over 1.5 billion of doses of PC were administered to almost 1 billion individuals for at least one of the targeted infections: lymphatic filariasis, onchocerciasis, schistosomiasis, STHs and trachoma [4]. MDA strategies are not only safe and effective but also cost-effective in controlling these diseases [7, 8]; it costs between US $0.30 and US $0.50 per person treated in most settings [4]. To ensure the aim of MDA can be achieved successfully, improvements in water, sanitation and hygiene (WASH) infrastructure, hygiene education, training (such as planning, coordination, capacity building and data management and analysis) and human resources are crucial, including Social and Behaviour Change Communication (SBCC). Volunteers and experienced staff are needed to ensure that the drug-distribution strategy and implementation of MDA are carried out efficiently and effectively [4, 9–13].

The WHO recommends periodic MDA once a year if the prevalence of STH infections in the community is more than 20%—or twice a year if the prevalence exceeds 50%—in order to reduce the morbidity by reducing the worm burden [14]. To date, MDA, SBCC, WASH and hygiene education are the control strategies that have been widely implemented to reduce the rate of morbidity, especially in an endemic region with high prevalence of STH infections [9–11, 13, 15–21]. In addition, MDA is usually carried out annually or biannually by delivering anthelmintic medicines to the at-risk population of an endemic area via school-based or community-based programmes. The WHO aims to eliminate and control STH infections through MDA strategies by covering at least 75% of preschool and school-age children [4, 6]. Nevertheless, different countries apply different types of strategies in conducting MDA programmes, depending on the local or national policies [2, 12, 20, 22–24]. The WHO recommends a single dose of albendazole (400mg) or mebendazole (500mg) in MDA to treat soil-transmitted helminthiasis [25, 26]. Albendazole and mebendazole are highly effective in treating Ascaris lumbricoides and hookworm infections, but they are not as effective in treating Trichuris trichiura infection. The combination of albendazole and ivermectin is recommended for MDA of T. trichiura [22, 24, 27–30].

By treating children in school, a higher treatment coverage can be achieved because school-aged children in untreated communities are the carriers of the highest burden of STHs and consequently suffer the greatest setbacks to growth, health and cognition during their development. Nevertheless, treating children alone does not always reduce the transmission significantly; this is especially the case for hookworm, as adults are the major drivers of transmission [31]. Although scaling up the treatment to the whole community will lead to significant reduction in transmission, the main issue is the cost of treatment, which depends on demography, coverage level, the population that is going to be treated and the frequency and duration of treatment. If the interruption of transmission does not happen from treating children alone, treatment has to be continued indefinitely unless WASH programmes, health education and SBCC can change the underlying conditions [31, 32].

A handful of authors have modelled MDA strategies to interrupt STH transmission. Anderson et al. [33] investigated the possibility of eliminating soil-transmitted helminthiasis if MDA is the only control strategy that has been taken. They discovered that the STH infection persists if MDA is only targeting pre-school-aged and school-aged children, except for the case where the reproduction number is low (R0 ≤ 2) and transmission intensity is low to medium. However, by considering WASH intervention, the value of R0 decreases significantly, and hence the high-transmission setting can be reduced to a medium or low one. In addition, their model showed that, with higher coverage of MDA, it is possible to interrupt the transmission of STHs if MDA is targeted at both children and adults. Clarke et al. [34] conducted a systematic review and meta-analysis (searching via MEDLINE, Embase and Web of Science for articles published on or before November 5, 2015) to compare the effect of mass (community-wide) and targeted (children only) strategies on STH prevalence in school-aged children. Both regression models and meta-analysis showed that the prevalence of STHs in children would be significantly reduced if mass MDA is performed compared to targeted MDA. Bronzan et al. [35] assessed the impact of community-based integrated MDA on schistosomiasis and STH prevalence in Togo. They observed that the prevalence of both schistosomiasis and STHs in children aged 6 to 9 are significantly reduced compared to the baseline. Moreover, they noticed that there is a resurgence of hookworm infection in children who are living in areas with high prevalence and who did not receive treatment in the past half year. Hence they suggested that areas with high prevalence should not only continue with the MDA strategy but also require environmental improvements such as improvements in WASH infrastructure and practices in order to interrupt the transmission of STHs. Truscott et al. [36] examined heterogeneity in transmission parameters that play a major role in hookworm infection using the baseline data obtained from the TUMIKIA study in Kenya (which was a large, randomised trial). This study showed that prevalence is related to the R0 value in a nonlinear manner (due to the effect of density-dependent fecundity) and that there is a clear increasing linear trend in mean R0 values versus mean egg count. Moreover, they observed that the prevalence depends highly on the degree of parasite aggregation. As a result, they suggested different MDA approaches should be carried out, especially when prevalence is low; when prevalence is sufficiently low, the high degree of parasite aggregation indicates that STHs may concentrate at the household level or in a group of people who consistently fail to comply with treatment or who consistently do not or cannot adopt improved WASH practices. Although MDA has been shown to be safe and effective in controlling STH infections, MDA alone has yet to be proven an effective long-term solution. Issues of potential anthelmintic resistance and donor fatigue in particular have raised concerns around long-term sustainability in controlling the transmission of STHs. Vaz Nery et al. [37] thus highlighted the need to study the application of WASH intervention and behaviour change to sustainably control long-term STH infection alongside the implementation of MDA in order to maintain low prevalence or achieve the global target of infection elimination.

Here, we would like to examine the impact of MDA on the mean number of worms in a human population and the possibility of interrupting the transmission of STHs if MDA is implemented. Two mathematical models are proposed in this study:

an impulsive mean-worm model to examine the effect of MDA on the mean number of worms in a human population of size N;

a modified form of the impulsive mean-worm model to examine the dynamics of the mean number of untreated worms due to lack of treatment or inefficacy of drug in the host population after the application of MDA.

This paper is organized as follows. First, we introduce our impulsive mathematical models and determine approximate analytical solutions. We then discuss the dynamics of the mean number of worms in host populations for community-based MDA of the TUMIKIA project in Kenya by applying both proposed models. We conclude with a discussion.

Mathematical models

A set of nonlinear ordinary differential equations depicting the dynamics of the approximate mean number of worms M(t) in a human population of size N (i.e., the total number of worms in a human population divided by N) and the infectious reservoir L(t) in the habitat of a human host at time t, proposed by Anderson and May [38], is defined as follows: where the associated parameters are defined in Table 1.

Table 1

Variables and parameters in model (1).

Variable/ Parameter	Description
M(t)	Mean number of worms in a human population of size N at time t
L(t)	The infectious reservoir in the habitat of human host at time t
β	The transmission rate between human and reservoir
μ 1	The human death rate
μ 0	The parasite mortality rate
μ	The worm death rate
λ	The within-host rate of egg production by female worms
k	The clumping parameter of the negative binomial distribution
γ	The strength of density-dependent effects on fecundity
z	e −γ

Since the observed pattern of worm numbers per host is well described empirically by a negative binomial distribution [38], the density-dependent constraints on adult worm fecundity can be described by and the mating probability of adult worms is given by where k is the clumping parameter of the negative binomial distribution (where the degree of worm clumping is measured inversely by k), γ is the strength of density-dependent constraints, z = e− measures the strength of the density-dependent effects on adult worm fecundity and . For a negative binomial probability distribution of worms per host, the prevalence of infection, y, is defined as

By taking into account the fact that the lifespan of the infectious reservoir (about one month or less) is much shorter than the adult worm in the host (1–2 years), we expect the dynamics of L(t) will reach equilibrium much faster than the mean number of worms, M(t). We can thus rewrite model (1) as where is the reproduction number of this model in the absence of density-dependent effects in adult worm fecundity.

Clearly, M = 0 is an equilibrium point for model (2). Endemic equilibria, M, of model (2) exist whenever we solve . The numerical solution of M (using bisection method) is depicted in Fig 1. The stable solution of M is denoted by the solid line, whereas the unstable solution of M is represented by the dashed line. To avoid confusion, we denote the stable endemic equilibrium by M* and the unstable endemic equilibrium by M*. A bifurcation point, M, exists in model (2) (denoted by the filled circle in Fig 1), defined as follows:

Fig 1

Numerical solutions of the endemic equilibria M as a function of R0 with different k values, fixing z = 0.96.

The corresponding reproduction number of M [38, 39] is given as follows:

The aggregation of STH parasites in the human host population is one of the key parameters in determining the prevalence of infection, y. Fig 1 shows that the endemic equilibrium and breakpoint of model (2) become smaller whenever k is decreasing. In this case, we may have fewer individuals in the population who carry a higher burden of parasites if the probability distribution of STH parasites within the human host population becomes highly aggregated (i.e., when k is small).

Next, we investigate the stability of the equilibrium point of model (2). An equilibrium occurs when there is no change in the rate of change of M, and the stability of an equilibrium point describes the effect of small perturbations near the equilibrium. If small deviations return to the equilibrium (or remain close), then the equilibrium is stable and is hence robust to noise and other random factors; if the equilibrium is unstable, then even very small perturbations will deviate from it over time. Since model (2) is one-dimensional, the stability of the equilibrium is determined by the sign of the derivative at the equilibrium.

Theorem. Let M(2). The disease-free equilibrium of model(2)is always locally asymptotically stable. The endemic equilibrium of model(2)is locally asymptotically stable if M > M and unstable if M < M. A local bifurcation occurs at M.

Proof. Differentiating model (2) with respect to M, we have

In the absence of infection, since all associated parameters are positive. Hence the disease-free equilibrium (M = 0) of model (2) is locally asymptotically stable. Moreover, the endemic equilibrium of model (2) is locally asymptotically stable whenever where since all associated parameters are positive.

Therefore M* is locally asymptotically stable if M > M (the infection will remain whenever the endemic equilibrium is larger than the breakpoint). Similarly, M* is unstable if M < M. Moreover, a local bifurcation occurs at M, where . This completes the proof.

Thus a separatrix exists, which splits the phase portrait of this model into two regions: trajectories that start above this separatrix tend to M*, whereas trajectories with initial conditions below this separatrix will converge to M = 0.

A standard mean-worm model with impulsive effect

WHO-recommended MDA is one of the most effective treatments to combat STH infection in endemic regions, and it is used to prevent morbidity caused by STH infection. By treating worms, the morbidity of STH can be reduced [15, 25, 38, 40–42]. We thus examine the impact of MDA on the dynamics of the mean number of worms in a human population of size N by adding an impulsive effect into model (2). Hence our impulsive model, one that is governed by a set of impulsive differential equations, is defined as follows: where t is the time when MDA is implemented, n is an arbitrary positive integer, ω is the coverage of MDA and ϵ is the efficacy of drug. Impulsive differential equations generally lead to semi-continuous periodic orbits whose endpoints describe the local maxima and minima during each cycle. The endpoints of the impulsive orbit at time t = t are and , where is the mean number of worms in a human population immediately before applying MDA, while is the mean number of worms immediately after applying MDA.

Throughout this manuscript, we choose z = 0.96, μ = 0.5 per year and per year in performing the numerical simulations, unless otherwise stated. To examine the impact of MDA, numerical simulations that consider the application of one round of MDA at time t = 1 versus no treatment are compared, and the results are shown in Fig 2. For arbitrary k, ω and ϵ values, all trajectories of model (3) and (4) as in Fig 2a and 2b are converging to zero if M0, the initial value of M, is below the unstable endemic equilibrium M*. However, with the application of one round of MDA at t = 1 (black and red solid curves), elimination of STH transmission can be achieved faster if ω and ϵ are sufficiently high compared to no treatment (blue solid curve). For sufficiently large M0 (i.e., M0 = M* as in Fig 2e and 2f), all solutions eventually approach the stable endemic equilibrium M*, but trajectories with higher ω and ϵ values (red solid curves) take the longest time to reach M*. This shows that the control strategy has reduced the mean number of worms and prolonged the time for the disease to achieve its endemic steady state. In addition, for arbitrary M* < M0 < M*, eradication is possible if we could successfully interrupt the transmission (for instance, by applying treatment) and reduce the mean number of worms such that it is less than M* (see Fig 2c and 2d). Hence the solution of model (2) will converge to zero, and interruption of transmission is likely. Therefore, in order to achieve the target of transmission interruption, the application of the control strategy is crucial when the mean number of worms is greater than the transmission breakpoint, M*.

Fig 2

Transmission dynamics of model (3) and (4) considering no application of MDA and one round of MDA at time t = 1 with k = 0.05 and R0 = 2.

(a) M0 < M*. (b) M* < M0 < M*. (c) M0 = M*. (d) M0 > M*.

Next, we examine the effect of applying biannual and annual MDA on STH transmission. By varying ϵ while selecting ω = 0.5, R0 = 2 and M* < M0 < M* in Fig 3, treatment is again unnecessary if M < M*. From Fig 3, we observe that, for k = 0.05, six and three rounds of biannual MDA (respectively, seven and three rounds of annual MDA) are needed in order to eliminate STH infection if the efficacies of drug are 0.4 (i.e., 40% of the mean number of worms in the human population are removed if MDA is taken) and 0.8, respectively. Conversely, for k = 0.5, eight and three rounds of biannual MDA (respectively, eleven and four rounds of annual MDA) are required, with the aim of disease eradication, if ϵ = 0.4 and 0.8, respectively. These results show that more rounds of MDA are needed to eradicate the disease if k is large, the drug efficacy is low and MDA is applied less frequently. The value of M* varies greatly if k and R0 values are increasing, but the value of M* does not vary much in this case, as shown in Fig 1.

Fig 3

Transmission dynamics of model (3) and (4) by considering the implementation of biannual and annual MDA, M0 > M*, varying ϵ and choosing z = 0.96, R0 = 2 and ω = 0.5.

Top row: biannual MDA. Bottom row: annual MDA. Left column: k = 0.05. Right column: k = 0.5.

Overestimates

We have shown that the STH infection will eventually decline (even without treatment) if M < M*. Thus we examine the case M0 > M* by using an overestimate of model (3) and (4) to estimate the number of rounds of MDA required to reduce the mean number of worms to less than the transmission breakpoint and hence interrupt STH transmission.

For arbitrary M(t)>M* and t ≠ t such that , Eq (3) is bounded by

Hence, for arbitrary and M(t)>M*, the solution of (3) is bounded by where the mean number of worms in a human population of density N decays exponentially if (respectively, grows if ). After undergoing an impulse, the solution is bounded by where Δt = t − t is assumed fixed in our study since the MDA is usually applied at fixed intervals.

By considering for arbitrary M, we expect that the analytical solution (5) with (6) may overestimate the solution of model (3) and (4). Thus, to determine whether (5) and (6) provide a good approximation to the solution of model (3) and (4), we compare these two solutions for arbitrary M(t)>M* by taking into consideration both biannual and annual MDA control strategies in Figs 4 and 5, respectively. Moreover, by choosing ω = 0.5, ϵ = 0.4 and varying k and R0 values, the mean squared error (MSE) of these two solutions can be used to identify the magnitude of differences between these two solutions. Given any two functions, g1(t) and g2(t), where i = 0, 1, 2, …, m − 1, the MSE is defined as follows [43, 44]:

Fig 4

The comparison of the overestimate (5) and (6) and original model (3) and (4) by considering the implementation of biannual MDA with ϵ = 0.4 and ω = 0.5 and varying k and R0 values.

(a) R0 = 2, k = 0.05, n > 5.83 and MSE = 0.1258 × 10−4. (b) R0 = 2, k = 0.5, n > 8.34 and MSE = 0.2167 × 10−2. (c) R0 = 1.8, k = 0.05, n > 2.86 and MSE = 0.5217 × 10−6. (d) R0 = 1.8, k = 0.5, n > 5.38 and MSE = 0.6392 × 10−3.

Fig 5

The comparison of solutions (5) and (6) and numerical solutions of model (3) and (4) by considering the implementation of annual MDA with ϵ = 0.4 and ω = 0.5 and varying k and R0 values.

(a) R0 = 2, k = 0.05, n > 7.29 and MSE = 0.6333 × 10−4. (b) R0 = 2, k = 0.5, n > 13.14 and MSE = 0.0156. (c) R0 = 1.8, k = 0.05, n > 2.96 and MSE = 0.2106 × 10−5. (d) R0 = 1.8, k = 0.5, n > 6.29 and MSE = 0.2264 × 10−2.

To find the endpoints of an impulsive orbit, first let us suppose that . Then we obtain

The impulsive orbit is bounded above by an orbit with endpoints

Knowing the endpoints, we are able to find the estimated number of rounds of MDA such that with fixed ω and ϵ; i.e., or with fixed n (and ϵ or ω), the estimated values of ω and ϵ such that disease elimination is possible are given by and respectively.

From Figs 4 and 5, we discover that numerical solutions of both the overestimate (5) and (6) and the original model (3) and (4) are compatible if k and R0 values are sufficiently small. Moreover, both solutions have a better agreement for the case study of biannual MDA compared to annual MDA, where we can see that the MSE values for the biannual MDA are smaller than the annual MDA for arbitrary initial conditions, k and R0 values. Using Eq (7), the estimated number of rounds of biannual MDA such that interruption of STH transmission is feasible is well-matched with the numerical prediction for arbitrary k and R0 values, but it only has good agreement if k and R0 values are sufficiently small for annual MDA.

A modified form of the impulsive mean worm model

In this section, we examine the behaviour of the mean number of untreated worms due to no treatment as well as inefficacy of drug in the host population after the application of MDA. Suppose that the mean number of worms in a human population of size N before the application of any control strategy is M. By applying MDA, the human population of size N can be divided into two subpopulations: treated and untreated, denoted N and N, respectively.

Next, assume that there are ωN treated people and (1 − ω)N untreated people, where ω is the coverage of MDA, and the total human population is N = N + N. Let M represent the mean number of untreated worms due to inefficacy of drug in the treated population and M represent the mean number of worms in the untreated population. For t ≠ t, the dynamics of M(t), M(t) and L(t) can be described by the following differential equations:

Since the lifespan of adult worms in human hosts is much longer than the lifespan of larvae or eggs, the rate of change of L(t) is expected to move much faster than M and M; hence we can rewrite model (8) using the equilibrium state of L as follows: with impulse conditions

The disease-free equilibrium for model (9) is (M, M) = (0, 0), and the endemic equilibrium is , since . can be found by solving numerically, similar to the result obtained in Fig 1.

Theorem. The disease-free equilibrium of model(9)is always locally asymptotically stable. The endemic equilibrium of model(9)is locally asymptotically stable ifand unstable if.

Proof. Let represent the eigenvalue of model (9). Then the characteristic equation is

In the absence of infection, with multiplicity 2, since all associated parameters are positive. Hence the DFE is locally asymptotically stable. For the endemic equilibrium, , we have

Therefore is locally asymptotically stable if . Otherwise, is unstable. This completes the proof.

To avoid confusion, we denote the stable endemic equilibrium by , the unstable endemic equilibrium by and the initial value of (M, M) by .

When there is no implementation of any control strategy, we have N = 0 and N = N. Thus the transmission dynamics of M (model (9)) is similar to M (model (3)), which is illustrated in Fig 6 for arbitrary initial conditions. STH infection remains endemic whenever the initial values of M and M are greater than the unstable equilibrium M* or (in this case, these two models have similar equilibrium points; i.e., and ); see Fig 6a and 6b. Conversely, disease elimination is always possible if M0 and M are below the unstable equilibrium (see Fig 6c). We can thus infer that control strategies may not be necessary if M(t)

Fig 6

The comparison of models (3) and (9) when no control strategy has been applied.

Both models have the same outcomes for arbitrary initial points, R0 = 2 and k = 0.05. (a) M0 > M* and . (b) M* < M0 < M* and . (c) M0 < M* and .

To investigate the impact of MDA in disease transmission, the transmission dynamics of M and M with and without treatment are compared. By selecting k = 0.05, R0 = 2 and the implementation of MDA at t = 1, the transmission dynamics of model (9) with impulse (10) for arbitrary , ω and ϵ is depicted in Fig 7. There is a decrease in the mean number of worms in both treated and untreated human subpopulations if treatment is taken compared to no application of MDA. However, if M and M are still sufficiently large after treatment, this will increase the likelihood of disease spread, and hence STH infection will persist and remain endemic (see Fig 7a and 7b). The effects of ω and ϵ are more pronounced if is close to the neighbourhood of the unstable endemic equilibrium, , in particular. From Fig 7c, we observe that disease elimination is likely to happen whenever ω and/or ϵ are sufficiently high, but STH infection persists if no control strategy is taken or if ω and ϵ are sufficiently low. Hence the application of MDA with appropriate ω and ϵ may hasten the elimination of STH infection.

Fig 7

The transmission dynamics of model (9) and (10) for a range of , ϵ and ω values, with k = 0.05 and R0 = 2.

(a) ω = ϵ = 0.6 and . (b) ω = ϵ = 0.6 and . (c) around the neighbourhood of .

Approximate analytical solution of (9) and (10)

In this subsection, we will focus on finding the approximate analytical solution of model (9) and (10) to estimate the required number of rounds of MDA in order to interrupt STH transmission for arbitrary .

Eq (9) is bounded by

Thus, for arbitrary , the analytical solution of (11) satisfies and, at impulse t = t, by applying (10), we have

We can compare numerical solutions of model (12) and (13) and model (9) and (10) with ω = ϵ = 0.6 and calculate the MSE to determine the magnitude of error between these two solutions. Fig 8 illustrates biannual MDA for both models, whereas Fig 9 compares annual MDA for these two solutions. By varying k and R0 values, the analytical and numerical solutions of M and M in the case of biannual MDA demonstrate a better agreement compared to annual MDA. Moreover, we observe that analytical solutions forecast slightly higher values of M and M and that more rounds of MDA are needed in order to achieve disease eradication compared to numerical solutions of model (9) and (10). This may be due to the approximations and for arbitrary M and M. Nevertheless, both analytical and numerical solutions of M and M lead to a good agreement if k and R0 are sufficiently small and there is a higher frequency of MDA (biannual MDA in our case).

Fig 8

Numerical comparison of model (12) and (13) and model (9) and (10) by considering the implementation of biannual MDA with ϵ = ω = 0.6 and varying k and R0 values.

(a) k = 0.05, R0 = 1.8 and MSE for M and M are 5.9377 × 10−5 and 1.1881 × 10−5, respectively. (b) k = 0.2, R0 = 1.8 and MSE for M and M are 1.5909 × 10−3 and 2.2534 × 10−4, respectively. (c) k = 0.05, R0 = 2 and MSE for M and M are 2.6274 × 10−4 and 2.9925 × 10−5, respectively. (d) k = 0.2, R0 = 2 and MSE for M and M are 4.5018 × 10−3 and 4.7219 × 10−4, respectively.

Fig 9

Numerical comparison of model (12) and (13) and model (9) and (10) for annual MDA with ϵ = ω = 0.6 and varying k and R0 values.

(a) k = 0.05, R0 = 1.8 and MSE for M and M are 1.4241 × 10−4 and 4.9371 × 10−5, respectively. (b) k = 0.2, R0 = 1.8 and MSE for M and M are 3.2954 × 10−3 and 9.5671 × 10−4, respectively. (c) k = 0.05, R0 = 2 and MSE for M and M are 4.3739 × 10−4 and 1.1943 × 10−4, respectively. (d) k = 0.2, R0 = 2 and MSE for M and M are 8.6585 × 10−3 and 2.1309 × 10−3, respectively.

Applications to the TUMIKIA project in Kenya

The Global Atlas of Helminth Infections [45] reported that approximately 15 million Kenyans are infected with STHs. The TUMIKIA project has the objective to assess which strategy is more efficient and effective in both controlling and eliminating soil-transmitted helminthiasis in Kenya: the combination of school- and community-based MDA versus school-based MDA alone. There were 120 community clusters in Kwale County, Kenya, that had been selected to participate in this project over two years, and 40 community clusters had been randomized to take part in one of the following three strategies [45-48]:

Annual school-based MDA programme, involving pre-school and school-aged children.

Annual community-based MDA programme, involving children and adults.

Biannual community-based MDA programme.

In this section, we focus on the impact of TUMIKIA community-based biannual and annual deworming strategies on the dynamics of M, M and M. A total of two (four) rounds of MDA had been implemented for a two-year community-based annual (biannual) MDA programme in Kenya. Moreover, the possibility of controlling STH infection in Kenya after the application of MDA for two years will be investigated. Model (3) and (4) will be employed to study the dynamics of M, whereas model (9) and (10) will be applied to study the dynamics of M and M. Since approximately 15 million Kenyans are infected with STHs [45], out of an estimated 43 million Kenyans [49], the initial prevalence value of STH infection in Kenya is about 0.3488. Thus, the estimated k and R0 values are 0.1624 and 1.8, respectively [36]. By taking the average of ω for all community clusters that had participated in each round of biannual and annual MDA programmes, the numerical simulations of model (3) and (4) and model (9) and (10) are demonstrated in Figs 10 and 11. The overall mean number of worms in both treated and untreated human populations is given by

Fig 10

Numerical results of model (3) and (4) and model (9) and (10) by varying ϵ and applying the coverage of MDA data from the TUMIKIA community-based biannual deworming control strategy.

(a) Disease persistence if ϵ < 0.44. (b) Disease extinction is possible if ϵ ≥ 0.61. (c) Disease extinction is possible for model (3) and (4) if ϵ ≥ 0.44, but the disease will remain in endemic state for model (9) and (10) if ϵ < 0.61.

Fig 11

The numerical results of model (3) and (4) and model (9) and (10) by varying ϵ and applying the coverage of MDA data from the TUMIKIA community-based annual deworming control strategy.

(a) Disease persistence if ϵ < 0.73. (b) Disease extinction if ϵ ≥ 0.85. (c) Disease elimination is possible for model (3) and (4) if ϵ ≥ 0.73, but the disease will remain in endemic state for model (9) and (10) if ϵ < 0.85.

From Fig 10, we see that, by implementing the TUMIKIA community-based biannual MDA strategy for two years, STH infection remains endemic for both models (3) and (4) and (9) and (10) if ϵ < 0.44, but the infection dies off if ϵ ≥ 0.61 (see Fig 10a and 10b, respectively). However, Fig 10c shows that multiple outcomes are possible, depending on the model. That is, model (3) and (4) predicts interruption of transmission is possible if ϵ ≥ 0.44, but model (9) and (10) forecasts that STH infection persists if ϵ < 0.61. By considering an additional round of TUMIKIA community-based biannual MDA at time t = 2.5 or t = 7, where the coverage of MDA is increased to 0.72, we notice that, in Fig 12, interruption of STH transmission is possible even though ϵ = 0.44.

Fig 12

Numerical solutions of model (9) and (10) with an additional round of TUMIKIA community-based biannual deworming strategy.

For the TUMIKIA community-based annual MDA strategy, we notice that in Fig 11a and 11b, both models predict disease persistence whenever ϵ < 0.73 and disease extinction if ϵ ≥ 0.85, respectively. Nevertheless, we can see that there are multiple possible outcomes in Fig 11c: model (3) and (4) forecasts disease eradication if ϵ ≥ 0.73, but model (9) and (10) predicts that disease eradication is unlikely if ϵ < 0.85.

From Fig 11, we observe that a sufficiently high efficacy of drug is needed (ϵ ≥ 0.85) in order to eliminate STH infection for the TUMIKIA community-based annual MDA programme using model (9) and (10). Thus we investigated the possibility of transmission interruption by considering the application of an additional round of MDA. Two cases are examined: an additional round of MDA is employed in the third and seventh years after the last round of TUMIKIA community-based annual deworming (i.e., at times t = 3 and 7, respectively) with coverage ω = 0.6. From Fig 13, we see that the STH infection in both cases will decline if ϵ ≥ 0.77. However, the infection is eliminated faster than in Fig 11. Since the rates of change of M and M are very small around the unstable endemic equilibrium , the interruption of STH infection in Fig 11 takes a long time to reach a disease-free state. Hence it is crucial for us to assess the appropriate coverage of MDA, efficacy of the drug and timing of the deworming strategy if we aim to achieve interruption of transmission quickly and effectively.

Fig 13

Numerical solutions of model (9) and (10) with an additional round of TUMIKIA community-based annual deworming strategy.

Discussion

To examine the impact of MDA on the dynamics of STH infection in host populations and the feasibility of interrupting the transmission, two novel impulsive mathematical models were proposed: 1) a standard mean-worm model (3) and (4) to describe the effect of deworming strategy on the mean number of worms in a host population of size N, and 2) a modified form of the standard mean-worm model (9) and (10) to describe the dynamics of the mean number of worms in treated and untreated human subpopulations undergoing MDA.

Both models forecast that the application of MDA is unnecessary if the initial conditions are below the transmission breakpoint. If the initial number of worms is greater than the transmission breakpoint, then the mean number of worms in the host population can be suppressed using sufficient control strategies. Otherwise, there will be recrudescence in the community. Moreover, we found that fewer rounds of MDA are required to interrupt STH transmission if the clumping parameter (k) and basic reproduction number (R0) are sufficiently small or if the efficacy of drug, coverage and frequency of MDA are sufficiently high.

We also used both models to investigate worm dynamics for community-based MDA in the TUMIKIA project in Kenya. Both models predicted interruption of transmission was possible if the efficacy of drug was suffiently high (greater than 61% for the biannual programme or greater than 85% for the annual programme), whereas persistence was guaranteed if the efficacy was sufficiently low (less than 44% or 73%, respectively). The two models had different predictions when the efficacies were between these values. However, we showed that an additional round of MDA significantly improved the possibility of transmission interruption.

Our models have some limitations, which should be acknowledged. We set the infectious reservoir to steady state, due to the different timescales, although this may not apply perfectly. Impulsive differential equations assume the time-to-peak of MDA is negligible, which is only valid so long as the time between drug administrations is sufficiently large. STH eggs remain viable in soil for many years, so recrudescence of STH is inevitable without improvements in access to WASH and the adoption of new behaviours by the communities affected. We did not validate how long before STH recrudescence occurs if there is no WASH strategy or Social and Behaviour Change Communication. Finally, it is also crucial that the strategy implementation is respectful of the local context, traditional authorities, customs and belief systems.

Future work will consider age structure in human hosts, the effect of stochastic perturbations on disease transmission and assess the effectiveness of different potential interventions. We will also include a cost–benefit analysis of the MDA schedules. Implementing MDA programs takes time, coordination and costs, with volunteers increasingly expected to be paid for their services. More effective drugs delivered less frequently might be significantly cheaper for a health service than a cheaper drug requiring more rounds of MDA.

5 Mar 2021

Dear Dr. Smith?,

Thank you very much for submitting your manuscript "Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: community-based deworming in Kenya as a case study" for consideration at PLOS Neglected Tropical Diseases. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments, especially please try to translate your results into public health sense so that more audience and understand your performance well. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

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[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

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Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

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Guo-Jing Yang

Associate Editor

PLOS Neglected Tropical Diseases

Banchob Sripa

Deputy Editor

PLOS Neglected Tropical Diseases

***********************

Reviewer's Responses to Questions

Key Review Criteria Required for Acceptance?

As you describe the new analyses required for acceptance, please consider the following:

Methods

-Are the objectives of the study clearly articulated with a clear testable hypothesis stated?

-Is the study design appropriate to address the stated objectives?

-Is the population clearly described and appropriate for the hypothesis being tested?

-Is the sample size sufficient to ensure adequate power to address the hypothesis being tested?

-Were correct statistical analysis used to support conclusions?

-Are there concerns about ethical or regulatory requirements being met?

Reviewer #1: Methods

I am unable to make any comment about the mathematical modelling, but if you are treating worms and of equal importance to public health across species it is flawed as 100 eggs of hookworm cause more morbidity than 100 of T. Trichuria v 100 of Acscaris.

Reviewer #2: (No Response)

Reviewer #3: I think my answer to the above questions is positive. By the way I dont have remarks about.

--------------------

Results

-Does the analysis presented match the analysis plan?

-Are the results clearly and completely presented?

-Are the figures (Tables, Images) of sufficient quality for clarity?

Reviewer #1: Application to the Tumikia project in Kenya

L 269: Is this project aiming to control or to eliminate?

L 274: This sounds as if after 2 years you expect the problem to have been solved without potential recrudescence. Within 2 years you may get reduction or even control (<10% prevalence with <1% moderate/heavy infections) but recrudescence is inevitable of behaviours and WASH resources are not addressed no matter how many rounds of effective drugs are used.

Reviewer #2: (No Response)

Reviewer #3: Yes

--------------------

Conclusions

-Are the conclusions supported by the data presented?

-Are the limitations of analysis clearly described?

-Do the authors discuss how these data can be helpful to advance our understanding of the topic under study?

-Is public health relevance addressed?

Reviewer #1: Discussion

L 335: You do not take into consideration that STH eggs remain viable in soil for many years, hence this interruption is only temporary.

L 341 Eradication is a completely new term and not appropriate here. Even elimination is inappropriate. I believe you are aiming for control whilst, WASH and human behavioral changes are strengthened.

Reviewer #2: (No Response)

Reviewer #3: Yes

--------------------

Editorial and Data Presentation Modifications?

Use this section for editorial suggestions as well as relatively minor modifications of existing data that would enhance clarity. If the only modifications needed are minor and/or editorial, you may wish to recommend “Minor Revision” or “Accept”.

Reviewer #1: Author Summary

L 2: I suggest 'control' rather than 'tackle'

L 3: Can you make any comment regarding the cost of using an additional round of weaker drugs vs cost of using stronger drugs and fewer rounds?

Abstract

Responsive to ‘preventive chemotherapy’.

Is the mean number of worms the best way of perceiving the effort to reduce STH to ‘no longer of public health significant’ (<10% prevalence of any STH and <1% moderate/heavy infections) Do you actually mean worms of eggs per gram of faces?

There is such enormous variance in the morbidity of epg by species that you cannot compare 100epg for hookworm with 100epg for Ascaris: the morbidity is grossly different.

Reviewer #2: (No Response)

Reviewer #3: The paper can be published in the present form.

--------------------

Summary and General Comments

Use this section to provide overall comments, discuss strengths/weaknesses of the study, novelty, significance, general execution and scholarship. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. If requesting major revision, please articulate the new experiments that are needed.

Reviewer #1: Introduction

L 12: I suggest 'preventive chemotherapy (PC)' is more appropriate than 'deworming' as one doesn't know if the individual has actually been de-wormed the worm burden will have reduced but whether it gets to zero will depend upon mostly the worm burden before treatment as well as the type of medicine used (more v less effective)

L 18: I don't think 'only' is helpful here as targeted chemo and selective chemo and mass chemo often coexist in a community.

L 19: I don't think you need 'after a regular screening test'. Persons can self-refer for selective chemotherapy and be treated by clinicians/pharmacists without tests and/or buy over the counter medicines without consultations

L 21: Of doses of PC rather than 'treatments'

L 25: This brings be back to my comment about the costs of providing another round of MDA with a less effective agent versus the cost of less rounds of MDA with more effective agents.

L 26: PC should have been introduced earlier and then the abbreviation can be used throughout the manuscript.

L 30: I would add that the strategy needs to be respectful of the local context, traditional authorities, customs and belief systems if the last mile toward STH control is to be effective and that control to be maintained. I suggest that STH recrudesce is almost inevitable if these are not taken into consideration: if personal and environment hygiene are not considered.

L 33: This is a different definition to that used by the WHO 'no-longer of public health significance'

L 34: Important to also mention other important control strategies: improved water and sanitation (WASH).

L 38: Or community-based

L 41: Rather than use the word 'treating' I would use PC

L 44: Trichuris trichiura. The combination of ALB and IVM is recommended for LF-PC.

L 45: T. trichiura

L 48: Only strategy? No health education on WASH and/or efforts to improve safe water and improved sanitation?

L 53: Did this study continue to validate how long before STH recrudesce occurred if there truly was no strategy for WASH?

L 63: Areas with high baseline prevalence are especially in need of health education on personal hygiene and improved sanitation at household, community and school-level. MDA alone will be insufficient to eliminate and prevent resurgence. Rebound STH infection after mass MDA and apparent ‘control’ has been well documented for over 30 years.

L 73: Or consistently don't or cannot adopt improved WASH practices.

L 76: Again you could consider the cost-benefit of this approach, identifying monitoring and treating groups of individual versus improving WASH resources for a community/ or a vulnerable subgroup within a community.

Reviewer #2: The paper presents two mathematical models to guide strategy for MDA as an intervention for STH. The models have been thoroughly investigated, and forecasts for the mean number of worms in the population over time, for different drug efficacies, are presented. The authors investigated different levels of coverage.

The paper does not suit a public health journal. The focus is on the mathematics, and the paper is written with inadequate translation to real life circumstances. The paper reads like an excellent mathematical exercise, but there is a lack of motivation that suits public health readers. For example,

- What is the mean number of worms in a population? The mean of the estimate? The number of worms in a population is a scalar, not a distribution.

- Figure 1 shows the mean value of worms for different R0. There are three lines to correspond to three values of k, without any explanation as to why these values were chosen. The relation of k to the real life is lacking, i.e. it is impossible to interpret what different "clumping parameters of the negative binomial distribution" mean in the real world. What different settings would have a low/high k?

- Why provide the eigenvalues of the models? What does the eigenvalue tell us?

- Lines 116, "Moreover, the endemic equilibrium of model (2) is locally asymptotically stable whenever [an eqn where any relationships between parameters are too complicated to make the eqn easily interpretable] since all associated parameters are positive." What real world information does this tell us about the endemic equilibrium? Similarly on line 216

- L 177 "To find the endpoints of an impulsive orbit..." What is an impulsive orbit? Why do we need to calculate them?

- There is regular mention of choosing arbitrary parameter values. Why? Are real life values impossible to obtain? In which case, why? Because the don't relate to real life or because the data is difficult to obtain?

- How is the drug efficacy interpreted? Is it assuming perfect adherence? Is it the clearance rate?

With regards to writing style - it is unclear what parts of the model are new and the authors contribution to the field.

The application to Kenya data is underwhelming. The prevalence is averaged over the whole country, making the application very broad. It is not shown methodically that only (b) and (c) strategies are considered in this paper. There is a lack of clarity with regards to how many MDA rounds are used in (b) compared to (c). Results are converted from decimals to percentages in an inconsistent manner. The plots are provided without explanation as to the meaning of \\hat{M} etc (plots should be intepretable without having to read the paper).

Abstract

- Don't include parameter notation in the abstract.

- The acronym STH is introduced early on, and then throughout the paper the authors switch from writing out soil-transmitted helminthiasis in full, and using STH.

Main text

- Line 38. The idea of focusing on children is alluded to, but not formally addressed.

- Line 52 How low for R0?

- Line 53 Did Clark et al. [10] use data? This is unclear.

- Line 64 Is MDA the deworming strategy?

- Line 68 states that there is variation in R0. In what sense? Under different settings? This statement doesn't provide enough information to make the reader feel that the work had a conclusion.

- Line 81 to 86 Use the same wording where possible, so that the differences between the two models are immediately clear. Similarly for lines 275-280.

- Line 87-91 and line 212 are missing references to Sections.

- Line 97 needs a reference to justify using a negative binomial distn.

- Table 1 would benefit from z being added, even if stating exp(-\\gamma), to make the introduction to the model smoother.

- The notation M_eq M^* M_* is unclear, and I'm not sure whether the authors interchange parts of these. In general, M^* and M_* are not distinctly different enough.

- Line 125, n is a positive arbitrary integer. What are the units?

- Line 155 states that if k is large. From Fig 1 can you relate this to R0, and instead state that when R0 is large. This is a better reference point because R0 has real life meaning.

- Line 176 What are these functions!?

- For a public health journal, like the abstract, the discussion should avoid use of referring to parameters with their notation (i.e., k).

Reviewer #3: The problem that this manuscript takes in consideration is of great importance in some regions of the world. The authors carry on their analises with the help of some Mathematical models described by ODEs systems. Of special interest is the carefulness that the author put in the derivation of the form of constitutive functions. The numerical results are carefully compared with real data. The author discuss about some possible restrictions on the applicability of their study.The paper is clear and well organized, in my opinion it can be published in the present form.

--------------------

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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4 Jun 2021

Submitted filename: ResponsesToReviewersComments.pdf

Click here for additional data file.

23 Jun 2021

Dear Dr. Smith?,

Thank you very much for submitting your manuscript "Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: community-based deworming in Kenya as a case study" for consideration at PLOS Neglected Tropical Diseases. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Guo-Jing Yang

Associate Editor

PLOS Neglected Tropical Diseases

Banchob Sripa

Deputy Editor

PLOS Neglected Tropical Diseases

***********************

Reviewer's Responses to Questions

Key Review Criteria Required for Acceptance?

As you describe the new analyses required for acceptance, please consider the following:

Methods

-Are the objectives of the study clearly articulated with a clear testable hypothesis stated?

-Is the study design appropriate to address the stated objectives?

-Is the population clearly described and appropriate for the hypothesis being tested?

-Is the sample size sufficient to ensure adequate power to address the hypothesis being tested?

-Were correct statistical analysis used to support conclusions?

-Are there concerns about ethical or regulatory requirements being met?

Reviewer #1: Yes, objectives are clearly articulated and the study design is appropriate with clearly described population and hypothesis. the sample is sufficient and no concerns about ethical regulatory requirements

--------------------

Results

-Does the analysis presented match the analysis plan?

-Are the results clearly and completely presented?

-Are the figures (Tables, Images) of sufficient quality for clarity?

Reviewer #1: Yes

--------------------

Conclusions

-Are the conclusions supported by the data presented?

-Are the limitations of analysis clearly described?

-Do the authors discuss how these data can be helpful to advance our understanding of the topic under study?

-Is public health relevance addressed?

Reviewer #1: I think the imitations paragraph needs a little editing:

392: ‘so human-induced interruptions are only temporary; hence our results have less viability in the long term’ could you phrase this. Perhaps something like ‘recrudescence of STH is inevitable without improvements in access to WASH and the adoption of new behaviors by the communities affected’.

L394: and SBCC

L 396-398: could you also include a cost-benefit analysis of these various schedules of MDA. Implementing MDAs takes time, coordination and costs. Volunteers are increasingly expecting to be paid for their services so a more effective drugs delivered less frequently might be significantly cheaper for a health service than a cheaper drug requiring more rounds of MDA.

--------------------

Editorial and Data Presentation Modifications?

Use this section for editorial suggestions as well as relatively minor modifications of existing data that would enhance clarity. If the only modifications needed are minor and/or editorial, you may wish to recommend “Minor Revision” or “Accept”.

Reviewer #1: (No Response)

--------------------

Summary and General Comments

Use this section to provide overall comments, discuss strengths/weaknesses of the study, novelty, significance, general execution and scholarship. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. If requesting major revision, please articulate the new experiments that are needed.

Reviewer #1: This is much improved and now fits better into the reality of programming in SSA. I still have a few comments:

Introduction

L22: ‘deworming’ use instead of ‘PC’ or MDA which is used more often going forward

L24-27: you have omitted the human-element: the change in behavior usually addressed by Social and Behavior Change Communication (SBCC)

L29: you have used PC here but almost everywhere else you have used MDA, please be consistent unless you are trying to differentiate between MDA and PC?

L31: ‘deworming’

L34: and SBCC

L39: now MDA is used instead of PC, please choose on or the other but don’t switch back and forth

L47: Trichuris trichiura has been introduced in full on L46 so it can be abbreviated to T. trichiura form then onwards

L48-49: Schools are not targeted because of cost-efficiencies but because the SAC are, in untreated communities the carriers of the highest burden of STHs and whilst growing suffer the greatest set-backs to growth, health and cognition.

L56: and BCCC (which is different from just health education)

L58: MDA (or PC) but not ‘deworming’

L89: ‘deworming’

L98: presumable also of SBBC?

Discussion:

L373: ‘appropriate’ what is meant by that?

L375: ‘greater than’ or less than?

L375 ‘Otherwise, the infection may persist’ This sounds odd do you mean the infection in that individual or the risk of recrudescence within the community?

--------------------

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Reviewer #1: Yes: Dr Mary H, Hodges

Figure 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. 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 us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

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To enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article's retracted status in the References list and also include a citation and full reference for the retraction notice.

25 Jun 2021

Submitted filename: ResponsesToReviewersComments.pdf

Click here for additional data file.

5 Jul 2021

Dear Dr. Smith?,

We are pleased to inform you that your manuscript 'Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: community-based deworming in Kenya as a case study' has been provisionally accepted for publication in PLOS Neglected Tropical Diseases.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Neglected Tropical Diseases.

Best regards,

Guo-Jing Yang

Associate Editor

PLOS Neglected Tropical Diseases

Banchob Sripa

Deputy Editor

PLOS Neglected Tropical Diseases

***********************************************************

Reviewer's Responses to Questions

Key Review Criteria Required for Acceptance?

As you describe the new analyses required for acceptance, please consider the following:

Methods

-Are the objectives of the study clearly articulated with a clear testable hypothesis stated?

-Is the study design appropriate to address the stated objectives?

-Is the population clearly described and appropriate for the hypothesis being tested?

-Is the sample size sufficient to ensure adequate power to address the hypothesis being tested?

-Were correct statistical analysis used to support conclusions?

-Are there concerns about ethical or regulatory requirements being met?

Reviewer #1: (No Response)

**********

Results

-Does the analysis presented match the analysis plan?

-Are the results clearly and completely presented?

-Are the figures (Tables, Images) of sufficient quality for clarity?

Reviewer #1: (No Response)

**********

Conclusions

-Are the conclusions supported by the data presented?

-Are the limitations of analysis clearly described?

-Do the authors discuss how these data can be helpful to advance our understanding of the topic under study?

-Is public health relevance addressed?

Reviewer #1: (No Response)

**********

Editorial and Data Presentation Modifications?

Use this section for editorial suggestions as well as relatively minor modifications of existing data that would enhance clarity. If the only modifications needed are minor and/or editorial, you may wish to recommend “Minor Revision” or “Accept”.

Reviewer #1: Line 82 and 369 deworming strategy still there (rather than MDA). In 369 especially it is potentially confusing as the second section specifically refers to MDA.

Line 392 you are now using the term drug administration rather than MDA

**********

Summary and General Comments

Use this section to provide overall comments, discuss strengths/weaknesses of the study, novelty, significance, general execution and scholarship. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. If requesting major revision, please articulate the new experiments that are needed.

Reviewer #1: (No Response)

**********

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Reviewer #1: Yes: Mary H Hodges

28 Jul 2021

Dear Dr. Smith?,

We are delighted to inform you that your manuscript, "Modelling the ability of mass drug administration to interrupt soil-transmitted helminth transmission: community-based deworming in Kenya as a case study," has been formally accepted for publication in PLOS Neglected Tropical Diseases.

We have now passed your article onto the PLOS Production Department who will complete the rest of the publication process. All authors will receive a confirmation email upon publication.

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Thank you again for supporting open-access publishing; we are looking forward to publishing your work in PLOS Neglected Tropical Diseases.

Best regards,

Shaden Kamhawi

co-Editor-in-Chief

PLOS Neglected Tropical Diseases

Paul Brindley

co-Editor-in-Chief

PLOS Neglected Tropical Diseases