article: We study the geography of schistosomiasis across Burkina Faso by means of a spatially explicit model of water-based disease dynamics. The model quantitatively addresses the geographic stratification of disease burden in a novel framework by explicitly accounting for drivers and controls of the disease, including spatial information on the distributions of population and infrastructure, jointly with a general description of human mobility and climatic/ecological drivers. Spatial patterns of disease are analysed by the extraction and the mapping of suitable eigenvectors of the Jacobian matrix subsuming the stability of the disease-free equilibrium. The relevance of the work lies in the novel mapping of disease burden, a byproduct of the parametrization induced by regional upscaling, by model-guided field validations and in the predictive scenarios allowed by exploiting the range of possible parameters and processes. Human mobility is found to be a primary control at regional scales both for pathogen invasion success and the overall distribution of disease burden. The effects of water resources development highlighted by systematic reviews are accounted for by the average distances of human settlements from water bodies that are habitats for the parasite’s intermediate host. Our results confirm the empirical findings about the role of water resources development on disease spread into regions previously nearly disease-free also by inspection of empirical prevalence patterns. We conclude that while the model still needs refinements based on field and epidemiological evidence, the proposed framework provides a powerful tool for large-scale public health planning and schistosomiasis management.
  National programs for schistosomiasis control and elimination require appraising spatial patterns of endemic disease under variable conditions accounting for changing epidemiological drivers and controls inclusive of varying exposure rates, human mobility, habitat ranges for the intermediate host and the complexities of the parasite’s life cycle. Patterns of waterborne disease are unique in their spatial complexity which arise from pathogen reproduction, transport and transmission through waterways and human mobility networks, and for the corresponding challenges to morbidity and transmission control. Indeed both micro- and macro-parasitic waterborne diseases are conditioned by spatially varying natural (environmental or climatic [1–3]) and anthropogenic factors (water resources, [4–6] habitat availability and suitability [7], pathogen dispersal by river networks [8–11], and human mobility [12–16]. Here we focus on the transmission cycle of schistosomiasis, a parasitic disease, which is emblematic of the interplay among spatially varying drivers and controls. Schistosomiasis, or bilharzia, is a chronic debilitating disease caused by parasitic worms of genus Schistosoma that affected an estimated 249 million people around the world in 2012. A crushing 93% of these people live in Sub-Saharian Africa [17], where both the urinary and intestinal forms of the disease, caused by S. haematobium and S. mansoni respectively, are present. This figure has grown from 77% in 2006 [18]. Both forms of schistosomiasis have been reported in Burkina Faso since the early fifties, with measured prevalences prior to the implementation of Mass Drug Administration Campaigns (MDAs) within the Schistosomiasis Control Initiative (SCI) [19] systematically higher than 30% [20,21]. A North-to-South decreasing gradient was observed for the urinary form of the disease and an opposite trend for the intestinal one [21]. The MDAs had a important impact on prevalence with immediate post-MDA prevalence levels ten times lower than pre-treatment baseline, but levels of infection have in some cases risen again in recent years, with some villages back to pre-treatment conditions [22]. Challenges to the successful control of the disease are manifold due to the complexity of the transmission cycle, which requires freshwater aquatic snails (Bulinus spp. or Biomphalaria spp. for S. haematobium and S. mansoni respectively) as obligate intermediate hosts. The transmission cycle consists of the excretion of parasite eggs from human to water bodies where they hatch into miracidia, the first larval stage, which infect the aquatic snail intermediate host. Asexual reproduction therein produces second-stage larvae called cercariae which infect humans through skin penetration. Once in the human host, they migrate in the system, mature into adult schistosomes and mate in the capillary surrounding the bladder or the intestine depending on the parasite genus leading to egg production and excretion. Environmental, climatic, ecological and socio-economic factors drive the transmission cycle by conditioning both snail and human probability of infection [12]. Dynamical models of schistosomiasis [23,24], and their spatial extension to connected environments [12], provide the opportunity to show the applicability of a general mathematical framework for analysing the disease invasion conditions and the resulting spatial patterns of human schistosomiasis which could inform control and elimination programs. With this goal, we study schistosomiasis spread and persistence in the context of Burkina Faso with an emphasis on the roles of human mobility and water resources development. The biological pace imposed by the pathogen’s life cycle makes the role of the obligate intermediate host key in disease spread on longer time scales than micro-parasitic waterborne diseases such as epidemic cholera, typically demonstrating outbreak waves [9,16] and showing forest fire-like revamping behaviour [25]. In Burkina Faso, the spatial distribution of the snail host is determined by the strong South-to-North climatic gradient of the transition from sudanian to sahelian regimes [26]. An extensive study of the ecology of both Bulinus spp. and Biomphalaria pfeifferi in Burkina Faso revealed both the importance of climatic zones and habitat type (including natural and man-made) on snail presence or absence [27]. Indeed B. pfeifferi was seldom found North of the 12th parallel and absent North of the 14th [28], matching the observed historical range of intestinal schistosomiasis in the country [21]. Furthermore, a marked climatic seasonality in Burkina Faso determines the ephemerality of waterbodies and hydrological networks, hence of potential transmission, thus strongly conditioning several epidemiological characteristics of the disease [20]. Not only do climatic and environmental conditions greatly limit the ecological ranges of the intermediate hosts of the disease, but they also underpin the patterns of human-water contacts during socio-economic and domestic activities through which both exposure to infection and contamination of waterbodies occur [29–32]. In Burkina Faso agricultural activities (market gardening or maraîchage, rice culture) and fishing (in reservoirs or rivers) are the main causes of male human-water contacts, whereas domestic activities (laundry, dish washing, water collection) are the main factors of exposure to infection for women [32,33]. Contamination and exposure for children are known to be mainly associated with recreational bathing in streams, temporary ponds and reservoirs, and participation in parental agricultural activities [29,33]. Seasonal variation of human-water contacts has not yet been addressed Burkina Faso to our knowledge. Even rudimentary notions of disease transmission mechanisms and prevention have been reported to be poor in most of the settings that have been investigated [21,29,32]. Human mobility is known to play a major role in the persistence and the expansion of the disease within and from endemic areas in Africa [34–37] and Brazil [38]. Indeed people may become infected while performing their livelihood tasks away from home and importing the disease back in their home village. Furthermore infected migrants coming form endemic regions can introduce schistosomiasis in disease-free villages. This type of medium-to-long range contamination is indeed compatible with the successive focal transmission of the disease at the local level suggested by recent landscape genetics studies [39]. The socio-ecological and epidemiological specificities of the transmission of intestinal schistosomiasis in sub-Saharan Africa and Brazil may explain the different roles played by human mobility, a topic to be elucidated by future research. Given its importance for transmission in the African context, data regarding mobility patterns, possibly directly via cellular phone displacements, will be necessary to produce reliable predictive tools for disease elimination both in terms of re-appearance and of prioritization of directed interventions in Burkina Faso. As observed in many other schistosomiasis-affected countries, agricultural development and the construction of large-scale irrigation schemes have induced anthropogenic perturbations of the underlying natural matrix affecting schistosomiasis distribution [37,40–44]. This fact is well illustrated in Burkina Faso by the construction of the Sourou valley dam at the northern border with Mali in the late 1980’s (Fig 1), which resulted in the expansion of the ecological range of Biomphalaria pfeifferi along the Mouhoun river from the Bobo-Dioulasso region to the north [21,42]. Arrival of intestinal bilharzia followed shortly, possibly brought in by migrants coming from the endemic South of the country to work in the rice paddies, yielding an increase in prevalence from virtually zero to more than 60% among school-aged children in villages located around the Sourou dam in about 10 years. With a 5-fold increase in the number of small reservoirs in Burkina Faso in the past 60 years, and in the perspective of further constructions of large dams [45], these observations highlight the need to explicitly address the impact of water resources development on schistosomiasis transmission [43,46]. The interwoven complexity of economic development, water management, and ecology make the need for appropriate prediction tools to attain an integrated control of schistosomiasis [47] addressesing the inherent contradiction between water resources development and livelihood preservation [48,49] linked to the emergence and persistence of waterborne diseases [44]. Under this viewpoint large improvements can be made in terms of both model adequacy to local contexts, in this case that of the country of Burkina Faso, and knowledge of the processes related to disease transmission, specifically human mobility and snail ecology. Mathematical models have proved useful in analysing the spread of both micro- and macro- parasitic waterborne diseases in spatially explicit settings e. g. [11–15]. Furthermore social and hydrological connectivity for schistosomiasis have been discussed in the context of distributed human-snail contact sites [50,51], and formally developed in agent-based [52] and connected metapopulation models, building on the seminal Macdonald schistosomiasis model [23]. Gurarie and Seto specifically highlighted the potential importance of both hydrological and social connectivity in small-scale environments [12]. Similar in their approach, spatially explicit metapopulation models have been developed for waterborne diseases such as cholera for which a generalized framework has been developed for determining spatially explicit invasion conditions and predicting spatial patterns of disease spread [53–55]. The exploration of invasion conditions could be of relevance in the perspective of sustainable elimination of schistosomiasis, and the inference of the spatial scale of the deployment of control measures in changing conditions of endemicity. The transition between morbidity-centred control programs and transmission-based elimination strategies would ideally require the deployment of surveillance-response mechanism entailing a higher degree of planning and decision-making than traditional mass drug administration campaigns [56], thus calling for new tools to support them [57]. The design of improved sampling protocols for surveillance, and the investigation of transmission breakpoints have been recently highlighted as research priorities for helminth diseases modelling [57]. In line with such priorities, we propose a novel mathematical exploration of an established model [12] and an application of the geography of the disease to the context of Burkina Faso. Special emphasis is placed on linking disease spread and human mobility and water resource development as a proof of concept for the usefulness of the implementation of these kind of tools for macroparasitic waterborne diseases like schistosomiasis.
  The mechanistic process model proposed by [12] expanded the seminal spatially implicit model of schistosomiasis by [23]. The extension proposes a connected metapopulation network of n villages. The system of differential equations is expressed in terms of the mean worm burden in human populations, Wi, the prevalence of infection in the snail intermediate hosts, Yi, and the densities of cercariae and miracidia, Ci and Mi, the two intermediate larval stages of the parasite. Connectivity is accounted for by human mobility and hydrologic transport of larvae (while neglecting snail mobility). The parameters of this model are explained in Table 1. With our notation, the model of [12] can be written as: d W i d t = a [ (1 - m i) θ i C i + m i ∑ j = 1 n Q i j θ j C j ] - γ W i d Y i d t = b M i (1 - Y i) - ν Y i d C i d t = Π C V i N i Y i - μ C C i - l i C C i + ∑ j = 1 n l j C P j i S j i C V j V i C j d M i d t = Π M V i θ i ′ [ (1 - m i) H i W i 2 + ∑ j = 1 n m j H j W j 2 Q j i ] - μ M M i - l i M M i + ∑ j = 1 n l j M P j i S j i M V j V i M j (1) Here at each node i, the rate of change in the mean worm burden is given by the difference between the intensity of cercarial infection expressed as a probability of infection upon contact a times the exposure to contaminated water θi and cercarial density, and worm mortality at given rate γ. Density of cercariae is dynamically determined by the per-capita cercarial output from infected snails ΠC and the number of infected snails Ni Yi at time t, and limited by cercarial mortality μC. The rate of change in the prevalence of infected snails is given by the probability of infection of a susceptible snail b (1 − Yi) times miracidial density and limited by snail mortality ν. Finally, miracidial density is determined by the rate of miracidial output from humans ΠM, the contamination rate θ i ′ and the number of pairs of adult schistosomes, given by half of the mean worm burden times the number of human hosts Hi, divided by the volume of water Vi in which they are released (to obtain larval concentration in water). Human mobility is included by specific contact distribution fractions Qij. In the original version of [12], the connectivity matrix is set to be proportional to distance between nodes, i. e. Qij ∝ e−αdij with α being a measure of zonal social connectivity. Hydrologic connectivity is implemented through a distance-dependent transport survival rate Sij = e−βdij for each larval stage from upstream to downstream settlements with different volumes of contaminated water Vi. Model 1 differs slightly from the one proposed by [12] in the way it treats larval densities and human connectivity. Indeed, we explicitly introduce the volume of water Vi in which larvae are released in order have the state variable expressed as a concentration per unit volume (rather than general unit habitat as expressed by [12]). However, in our analysis we set all Vi to 1 so as restrain the analysis on the connectivity parameters. Regarding human connectivity, we choose to keep traveller contacts and local contacts distinct by the mobility parameter m instead of distributing the whole local contact parameters θi as a function of population and distance as proposed by [12] in their formulation of a social contact matrix. Indeed in their approach mi is implicitly considered to be constant and proportional to Hi/ ∑j Hje−αdij for local contamination and exposure rates. By distinguishing between travellers and non-travellers we assume that contamination and exposure rates depend only on the physical characteristics of the site, and not on the traveller origin (captured by θi). This is reasonable when analysing patterns on a national scale where the physical characteristics of human settlements are heterogeneous (cites vs. towns vs. villages), and thus the contact rate at a visited location θj depends mainly on j. The main features of Model 1 are (1) well-mixed and stationary human and snail populations at each village i (2) miracidial dispersal and cercarial uptake through human movement matrix Qij modulated by the fraction of moving people mi, and (3) miracidial and cercarial dispersal through hydrologic connectivity matrices P j i S j i C and P j i S j i M modulated by the hydrologic transport rates l j C, M. By setting { m i, l j C, M } = 0 ∀ i, j Model 1 collapses to the local model of [23] expressed for each individual settlement, for which the local basic reproduction numbers are derived as R 0, i = (a b θ θ ′ Π C Π M H i N i) / (2 γ ν μ C μ M V i 2) (see S1 Text). In this simple case, parasite invasion of the disease-free system depends locally on the condition R0, i > 1. The above-mentioned model [12] does not include detailed biological controls (worm mating probability, negative density feedback on within-host worm population) nor immunological ones (acquired immunity of human hosts). Although this could prove inadequate for the study of a particular village close to endemic equilibrium, we deem these factors of secondary importance in the analysis of pathogen invasion conditions at the national level. The stability analysis of the model is carried out here for our reformulated version and extended to explore the spatial patterns of disease spread. Sensitivity analysis of model assumptions can be found in [12]. Despite the complexity given by the spatially explicit formulation of Model 1, a rigorous stability analysis can be used to determine spatially explicit conditions for pathogen invasion. As the system is positive and the disease-free equilibrium is characterized by null values of the state variables, the bifurcation can only occur via an exchange of stability. Specifically, the disease-free equilibrium switches from stable node to saddle through a transcritical bifurcation, at which the Jacobian has one zero eigenvalue [12,53,58,59]. Parasite invasion is determined by the unstability of the disease-free equilibrium (DFE) X0 = [0n, 0n, 0n, 0n]T, with 0n a 1 × n null vector, n being the number of settlements. The stability properties of the DFE can be studied by analysing the Jacobian linearised at the DFE, J 0 *, which reads: J 0 * = [ A B C D ], (2) where A = [ - γ I 0 0 - ν I ] B = [ a (I - m + m Q) θ 0 0 b I ] C = [ 0 Π C V - 1 N Π M 2 V - 1 θ ′ (I - m + Q T m) H 0 ] D = [ - μ C I + T C 0 0 - μ M I + T M ]. where: I is the identity matrix; m, θ, V, N, θ′ and H are diagonal matrices whose non-zero elements are made up by the parameters mi, θi, Vi, Ni, θ i ′ and Hi, respectively; Q = [Qij] is the connectivity matrix for human mobility; TC = (V−1 PCT V − I) lC and TM = (V−1 PMT V − I) lM, while P C = [ P i j S i j C ] = P ∘ S C (where ∘ is the Hadamard product) and P M = [ P i j S i j M ] = P ∘ S M are the transport matrices accounting for hydrologic connectivity and larval survival during transport, and l C and l M are diagonal matrices whose non-zero elements are the local values of l i C and l i M, respectively. After some manipulations (see S1 Text), the bifurcation condition det (J 0 *) = 0 can be reformulated as: det (I - (I - m) 2 R 0 + R 0 M (m, Q) + T (μ C, T C, μ M, T M) ) = 0 (3) We can define a generalized reproduction matrix (GRM) for our model of schistosomiasis transmission as the sum of three matrices. One depends on local dynamics only; the other two (non-linearly) on spatial coupling mechanisms, reading, G 0 = (I - m) 2 R 0 + R 0 M (m, Q) + T (μ C, T C, μ M, T M). (4) Parasite invasion conditions can therefore be decomposed into spatially explicit local conditions, R0, and connectivity-induced conditions R 0 M and T for mobility and hydrologic transport respectively. R0 is a diagonal matrix, whose non-zero elements are the local values R0i of the basic reproduction number. R 0 M is a matrix depending on human mobility structure and magnitude, i. e. R 0 M (m, Q) = a b Π C Π M 2 γ ν μ C μ M N V - 1 θ ′ [ (I - m) m H Q + Q T H m (I - m) + Q T m 2 H Q ] θ V - 1. T is another matrix depending on larval death rates and transport through the hydrologic network T (μ C, T C, μ M, T M) = 1 μ C V T C V - 1 + 1 μ M N T M N - 1 - 1 μ C μ M N T M V N - 1 T C V - 1. Ensuing from Eqs 3 and 4 the condition for parasite invasion can be stated in terms of the dominant eigenvalue g0 of matrix G0, i. e. g0 = maxk (λk (G0) ), with disease spread occurring if g0 > 1. Bearing the operational use of this condition in mind, it is important to note that control measures that successfully lead to a stable DFE (driving g0 below 1, for instance by improving sanitation or through snail control [60]) do not imply immediate transmission interruption, i. e. non-zero parasite loads in the population and in the environment persist for some time. In ecological terms, the time to reach pathogen extinction corresponds to the relaxation time of the system [61–63], t R, which is determined by the characteristic timescale of system trajectories approaching the DFE. The relaxation time of schistosomiasis transmission is therefore set by the dominant eigenvalue g0 as t R = 1 / | log (g 0) |. If g0 < 1 parasite transmission decreases exponentially in time. Therefore, transient dynamics can safely be assumed to be over after 5 t R time units. Based on this relation it is possible to associate a given socio-ecological setting in the country (i. e. a given value of g0) to an estimate of the time for transmission to effectively die out once conditions for pathogen extinction are met (g0 < 1). Eigenvector analysis, here carried out for the first time on spatially explicit modes of schistosomiasis, proves capable of capturing key features of the spatial pattern of empirically reported infections/prevalences (see e. g. [54]). The dominant eigenvector g0 of the GRM can be used to study the geography of disease spread close to the transcritical bifurcation. Here, g0 corresponds to the cercarial component C of the vector of state variables for trajectories diverging from the (unstable) DFE (see S1 Text). This is of particular interest in the study of spatial patterns of disease spread. In fact, close to an unstable DFE the dominant eigenvector of matrix J0*, λ max (J 0 *), pinpoints the directions in the state space along which the system trajectories will diverge from the equilibrium. In other words, computing λ max (J 0 *) enables not only the quantitative analysis of conditions for the parasite to invade a connected set of spatial locations, but also to predict the direction of disease spread geographically in the time close to the onset. Of particular interest in the dominant eigenvector analysis is the mean worm burden compartment, W, which in the case of schistosomiasis is an important measure of infection severity and the natural target of control interventions through antischistosomal treatments [64,65]. At the bifurcation through which the DFE loses stability, spatial distribution of the mean worm burden can be computed in terms of g0 as W = (a/γ) (I − m + mQ) θg0 (see S1 Text). Schistosomiasis control and elimination programs are implemented on the national scales by centralized national institutions [56]. We apply the dominant eigenvalue and eigenvector analysis to the context of Burkina Faso, a landlocked country in the transition zone from the sudanian to the sahelian climatic zones [26], emblematic of the intertwined ecological, climatic and soci-economic drivers of schistosomiasis transmission and persistence [21]. Schistosomiasis has been known in the country since the first demographic surveys in the 1950’s [21] and has yet to be eliminated despite national-scale control measures from 2004–2008 by the Schistosomiasis Control Initiative [19,66,67]. Both urinary and intestinal forms of the disease are present with very different historical geographical coverages, governed by the ecological ranges of their respective intermediate hosts [21]. The intestinal form of the disease will be used for the subsequent analysis given the proven importance of human mobility in its geographical expansion in the country [20]. The parameters of Model 1 and the values used for its implementation are detailed in Table 1. Sources and references of the spatial data used in the analysis are given in S1 Table.
  Because the real magnitude of human mobility in Burkina Faso is currently unknown, we explore a wide range of possible scenarios. We assume that the structure of the human mobility network is accurately captured by the radiation model, thus we explore only the intensity of mobility fluxes. In order to encompass all possible behaviours in real large scale mobility patterns (although extremes are unlikely) values of the fraction of mobile population in the range m ∈ [0,1] are considered. The relation between contamination and exposure rates and population density dependence also lacks ground-truthed data, and therefore it is explored through sigmoid contact functions (Eq 5) with α ∈ {0. 0001,0. 001,0. 01,0. 1}. Increasing α can be seen as increasing urban contamination and exposure rates. Not surprisingly, human mobility is found to strongly condition successful parasitic invasion of the system. Two opposite effects are illustrated in Fig 2 with a dilution effect for fractions of mobile people increasing from m = 0 to m ≈ 0. 3; and an increase in the risk of disease spread for m > 0. 3. Indeed for all investigated levels of urban contamination and exposure rates the dominant eigenvalue g0 of the GRM falls below 1 for intermediate ranges of the fraction of mobile people and low values of θMAX. Beyond the specificities of Model 1, these results are consistent with the conclusions of [12], at least close to the bifurcation and for the parameter region where m < 0. 5. The parameter region in which the DFE is stable (gray shaded area in Fig 2), thus preventing parasite invasion, is of similar sizes for all values of α, except for high levels of urban contact rates (α = 0. 1) for which pathogen invasion is observed for a wider range in the parameter space. This can be seen as the effect of coupling locations with high mobility (densely populated areas) with locations with high transmission potential (high contamination and exposure rates). For all subsequent analysis we therefore focused on the case that seemed the most realistic, namely intermediate urban contamination and exposure rates (α = 0. 01). In addition to the stability of the DFE, the dominant eigenvalue of the GRM contains information on the average time for transmission to fade out in the case of unfavourable conditions for pathogen spread. The relaxation time isolines (constant t R) follow the shape of the stability boundary, with a logarithmic decrease of extinction time as a function of distance to the boundary g0 = 1. The time to extinction is of the order of a century close to the stability line, and decreases sharply for small modifications of human mobility and contamination/exposure rates. Similarly to the stability conditions, the relaxation time is minimal at intermediate mobility levels for a given θMAX. Furthermore the shape of the time to extinction isolines suggests that above the mobility threshold, say m ≈ 0. 3, reducing contamination/exposure rates would have a larger marginal reduction on the time to extinction than acting on mobility. Water resources development directly impacts large-scale schistosomiasis transmission by altering the probability of presence of the intermediate snail host in the environment. This is explicitly accounted for in our approach through the distance to water, D w a t e r, of a human settlement. To investigate the side-effects of water resources development on schistosomiasis in the country, B. pfeifferi probability of presence was re-evaluated using MaxEnt for alternative scenarios of water resources development by randomly removing existing reservoirs to consider different numbers of built dams expressed as a fraction ϵ of the existing ones, and the stability of the DFE recomputed for parameter combinations used in Fig 2. The evolution of water resources development in Burkina Faso (a 5-fold increase in the number of reservoirs in the past 60 years [46]) was explored by varying ϵ in the set {0. 25,0. 5,0. 75} of existing reservoirs, which represents increasing numbers of built reservoirs. An illustration of the predicted changes in the ecological range of the intermediate host due to water resources development, in comparison with the current scenario, is given in Fig 6. Uncertainty in the stability predictions induced by random removal of reservoirs was assessed by repeating the procedure 10 times for each value of ϵ and taking the 95% confidence intervals of the realizations of the resulting stability lines. The effect of water resources development on pathogen invasion is illustrated in Fig 7 for the case of ϵ = 0. 5, results for the other two scenarios are similar and reported in S5 Fig. For all the reduced water resources development scenarios, the DFE tends to be stable for a wider set of mobility and contact parameters, for all levels of urban contamination and exposure rates. Examining the stability diagrams in Fig 7, it becomes evident that human mobility plays an important role in the stability of the DFE, thus of pathogen invasion conditions, in these alternative scenarios. Indeed the interplay between human mobility and water resources development is greatly conditioned by the level of urban contamination/exposure rates. For α < 0. 1 the effect of building dams is most detrimental for low levels of human mobility (m < 0. 25), while the bifurcation lines tend to be close to the invasion condition of the current scenario for m > 0. 8. On the other hand, for high levels of urban transmission of schistosomiasis (α = 0. 1) human mobility accentuates the negative impact of the increasing number of dams by augmenting the gap between the bifurcations curves of the alternative and current scenarios m > 0. 6. Furthermore, uncertainty in the stability of the DFE increases with the fraction of mobile people for all α’s. These observations can be seen as the contribution of less connected settlements, where contamination and exposure are high, to the overall (in) stability condition of the DFE. By increasing urban contamination and exposure rates, nodes with high connectivity also present high transmission, thus having a large impact on the stability of the system. When removing reservoirs that determine the number of snails in these key nodes, the stability region of the DFE expands. In other words, the system is more dependent on a small set of highly connected nodes, thus the construction of dams close to these points has a much larger effect on stability. The uncertainty associated to the location of the stability line is thus directly related to the random removal of the reservoirs influencing snail abundance in these key nodes. Human mobility therefore exacerbates the effect of water resources development on risk of pathogen invasion in the case of high urban contamination and exposure rates. Although preliminary, these results illustrate the use of the proposed eigenvector analysis of the GRM to quantify the potential impacts of water resources development in a spatially explicit framework that includes connectivity mechanisms such as human mobility. In particular, we concur with previous studies suggesting that strategies to mitigate negative effects on human health should become integral parts in the planning, implementation, and operation of future water resources development projects [44]. In particular the interplay between the water resources development and connectivity induced by human mobility are deemed to be important in the risk of re-emergence of the disease if elimination is attained. Although the main focus of this work is on the system conditions requiring deployment of intervention measures in the perspective of elimination, thus far from the endemic equilibrium, an appropriate calibration would need to be validated against historical data for the specific context of Burkina Faso. The first step in this direction would require the availability of comprehensive historical and national scale data on disease prevalence and infection intensity currently unavailable in a standardized accessible form. These data would also allow quantification of the associated uncertainty of the predictions. The second step could consist in the relaxation of simplifying assumptions of the model by [12]. Namely the assumptions are: (1) constant, although spatially heterogeneous, human and (2) snail populations, (3) population-dependent contamination and exposure rates, (4) no hydrologic transport of parasite larvae (5) nor of the snail intermediate host, and finally (6) mobility patterns modulated by population density. To that end, Burkina Faso seems uniquely positioned in Africa for capitalizing on existing field and epidemiological data [21,27]. Here, parameter values were taken from previously investigated configurations, but field data collection would be needed to strengthen the use of the results presented here. If assumptions (1) and (4) are deemed to be reasonable for studying schistosomiasis at the country-level, the remaining points still need to be addressed. Snail population dynamics (2) needs to be explicitly modelled with respect to local environmental conditions governing its habitat and its population dynamics, mainly driven by hydrology [28,84,85]. Furthermore, the seasonal variation of eco-hydrologic parameters would need to be properly addressed and incorporated in the modelling framework [55]. For both of these aspects of particular use would be local hydro-climatic data at suitable temporal and spatial resolutions in Burkina Faso, to be assimilated along with remotely sensed data with of bridging the existing gaps in their use for schistosomiasis risk profiling [86]. Contact and contamination rates (3) strongly depend on human-water contacts driven by local socio-economic realities [32,47,87], and are of particular importance to quantify the success of control measures through education and access to clean water, sanitation and hygiene (WASH). A generalizable framework would need to be developed for the specific context of Burkina Faso where detailed geo-referenced data are increasingly available especially on improved water sources, sanitation infrastructure and natural or man-made waterbodies, complemented by surveys and participatory-observant methods in distinct climatic, water resource availability and socio-economic contexts [31,32]. This would reduce the uncertainty introduced with the population-density based approach presented here for estimating water-contact rates, with a particular focus on the seasonal dynamics of water contacts across the territory. Hydrologic transport of the intermediate host (4) regarding transport rates, variability, snail species specificities and seasonality is also in need of an assessment regarding its possible inclusion in large-scale modelling frameworks. Finally, increasing access to human mobility data such as cell phone records would not only remove the necessity for modelling mobility patterns (6) [75,88], but would also permit the validation of existing mobility models that are generally based on data from highly motorized countries [74,76] against the specific mobility characteristics of Sub-Saharan Africa for their use in the context of schistosomiasis study. Indeed we note that other mobility models such as the gravity model imply different underlying assumptions. A detailed study of the relative merits of radiation versus gravity-like models has been the subject of recent attention. A relevant point for the work we present here is that the radiation model was found to systematically under-estimate long-range mobility fluxes, whereas the gravity model overestimated them [89]. In other words, the radiation model produces conservative estimates of mobility with respect to a gravity model and potentially to real mobility patterns. This implies that our conclusions are a lower bound on the effects of mobility on schistosomiasis transmission in the country. Nevertheless workers reported in the same study that both models failed to capture short-range mobility in rural areas, which could be of great importance for local schistosomiasis transmission. In light of these considerations the radiation model was chosen to investigate the impact of human mobility on schistosomiasis in Burkina Faso at this stage. Needless to say, the availability of real mobility data would overcome the need for modelling, as observed mobility fluxes could be used directly (see e. g. [74]), and would permit a thorough assessment of existing mobility models in the context of Burkina Faso. In fact, the mobility matrix Qij and the mobile fraction mi of the Hi inhabitants in each location could be inserted directly into our mathematical framework. By implementing dynamical system analysis techniques recently developed for waterborne diseases, we have highlighted the roles of human mobility and water resources development in the spread of intestinal schistosomiasis in Burkina Faso. Human mobility was shown to play a role not only in the degree of success of invasion of the network of human settlements by the pathogen, but also in the spatial patterns of disease spread. For small fractions of mobile people mobility induced a dilution effect of the parasite concentration in accessible waters leading to an effective prevention of parasite invasions, in agreement with previous results derived at much smaller spatial scales. Even in settings unfavourable to pathogen invasion, human mobility had a large effect on the time delay of transmission interruption. Above a threshold value, mobility prompted a systematic exacerbation of the disease by shifting its hotspots from the most populated areas (even where local conditions warrant local reproduction numbers larger than one) to more transmission-prone areas with higher contamination and exposure rates and snail abundance. Predicting the spread of the disease based on water resources development was also investigated, specifically by quantifying the modification of the stability conditions of the disease-free equilibrium resulting from anthropogenic expansions of suitable habitats for B. pfeifferi, the snail acting as intermediate host in the life cycle of the parasite S. mansoni. By considering theoretical scenarios representative of pre-existing levels of water resources development in the country, we showed that the marked increase in the number of dams prompted by water development projects favoured pathogen invasion. For low urban schistosomiasis transmission, the greatest effects of water resources development were found to occur for low levels of human mobility, thus favouring localized transmission which maximizes the effect of each additional dam built. Interestingly, intense human mobility was also shown to exacerbate the impact of the building of the dams in the case of high levels of urban contamination and exposure rates. We conclude that insight from the tools we develop here could directly inform national and regional control measures in the perspective of elimination in terms of pathogen invasion conditions and initial spatial spread, thus contributing to two of the points brought to the fore as research priorities for helminth modelling efforts [57]. Both prevention and intervention at regional scales, in fact, need to address the central role of human mobility in the perspective of the deployment of surveillance-response mechanisms and the localization of treatment measures. Controls of urban contamination and exposure rates, say by reducing contamination rates by control programs like WASH, could be measured against predicted disease burden reductions. Even at the current state of development, results of management alternatives obtained from mathematical models are potentially informative for epidemiological decisions in conditions of close-to-threshold transmission that will hopefully be the rule in the near future thanks to elimination programs in sub-Saharan Africa and Burkina Faso. The proposed theoretical framework provides opportunities for the design of control indicators based on stability, possibly also taking into account the timescales of pathogen extinction. Overall, our work supports the key role that mathematical toolboxes built on spatially explicit models of disease dynamics play for the prediction of the spatial patterns of schistosomiasis at regional scales.
summary: Dynamical models of schistosomiasis infections, even spatially explicit ones, have so far only addressed spatial scales encompassing at best a few villages and the disease transmission impacts of related short-range human mobility. Here, we build from existing models of disease dynamics and spread, including a proxy of the ecology of the intermediate host of the parasite, and from generalized reproduction numbers of SIR-type systems developed for epidemics of waterborne disease, to set up large-scale projections of spatial patterns of the disease at whole country level. We ground our study in Burkina Faso in sub-Saharan Africa, and its model of social and economic development including the infrastructure built to exploit water resources, especially irrigation schemes, which have been empirically linked to enhanced disease burden. We make extensive use of remotely sensed and field data, and capitalize on ecohydrological insight. We suggest that reliable nationwide patterns of disease burden can be projected in relation to the key roles of human mobility and water resources development subsuming exposure, and claim that the case at hand provides an insightful example towards the integration of development and environmental thinking not confined to ad-hoc indicators of human development.
title: A Theoretical Analysis of the Geography of Schistosomiasis in Burkina Faso Highlights the Roles of Human Mobility and Water Resources Development in Disease Transmission