Rainfall mediations in the spreading of epidemic cholera
Introduction
The recent, still ongoing cholera outbreak that has struck Haiti has brought to broad public attention the magnitude of the loss of human lives and of the social and economic disruption caused, even to date, by epidemics of the disease. The global relevance of the problem and the need for a preventive assessment and control of cholera spreading is manifest also in view of other recent or ongoing outbreaks in the Congo river basin, Cuba, Sierra Leon and the Sahel region [3], [30], [35], [40].
While the role of climatic conditions, and rainfall in particular, on patterns of waterborne infections have long been studied especially in empirical frameworks [5], [19], [20], [31], [34], [42], hydrologically-driven, spatially explicit mathematical models of cholera epidemics have only recently been developed [8], [9]. They have been applied to study the course of the Haitian epidemic, starting from the very first months after its insurgence in late 2010 [10], [13], [53], and following disease resurgence occurred in May 2011 in connection with unusually intense tropical rains [46]. Even though concerns for correct surveillance, monitoring and intervention planning have been on the rise in international institutions debate, regarding cholera in particular (e.g. [57]), none of these models have been utilized to date to test their effectiveness as predictive and control tools. Such models could be in principle applied, for instance, to deploy medical staff and life-saving supplies through projections of the patterns of cholera infections, and to implement pro-active rather than reactive policies as commonplace in epidemiological control strategies.
The Haitian epidemic represents more than just another test case. In fact, cholera had never been reported in Haiti before 2010 and therefore it is likely that the population had no significant prior exposure or acquired immunity to the disease, suggesting that the entire population was initially susceptible to infection. Moreover, once a cholera epidemic starts, infected patients excrete huge numbers of Vibrio cholerae bacteria which spread either through water pathways (via active and passive dispersal; [8], [9], [13], [36], [45]) or through human mobility networks involving both susceptibles and infected individuals [13], [37], [53]. Thus, the poor sanitation conditions, experienced especially after the disastrous 2010 earthquake that struck the island, facilitated both types of spread and fostered the abundance of microorganisms in the water system, thus rendering the Haitian outbreak exemplary [46].
The Haiti epidemic also provided direct and compelling evidence relating cholera resurgence to environmental drivers, specifically to rainfall patterns. Little insight could be gained, in fact, from past empirical studies correlating rainfall to cholera cases because most, if not all, previous studies were carried out in contexts where cholera is endemic (see e.g. [20], [34]). In fact, reported correlations between rainfall events and resurgences – both in their sign and time lag – have been rather disparate [2], [28], [35], [49]. This reflects the range of potential mechanisms through which rainfall may affect increased exposure to risk of infections (e.g. crowding effects due to flooding; raw sewage contamination of water sources; increased availability of compounds boosting V. cholerae survival or toxins diminishing it; increased contamination due to over-exploitation of the water reservoirs, to name a few). Rinaldo et al. [46] have shown how such correlation could be implemented in epidemiological models by forcing the contamination of the local water reservoir through rainfall-runoff transfer of V. cholerae from waste- to drinking-water. In the spatially explicit framework presented in [46] – which includes a family of models encompassing different epidemiological and hydrological assumptions – Haiti is depicted as a network of human communities (the nodes) connected by both hydrology and human mobility (the edges). Each community is represented by a system of Ordinary Differential Equations (ODE), in which the population is divided into Susceptible (S), Infected (I) and Recovered (R) individuals. The evolution of the concentration of V. cholerae in the environmental water reservoir is also considered. Here we further extend that approach, generating scenarios of precipitation to perform epidemiological predictions and to evaluate a priori the impact of intervention policies.
Unlike cholera, rainfall predictions are an established endeavour [14], [47] and rainfall stochastic generators have recently been widely considered for studying precipitation patterns [33], also in the light of the inclusion of a description of superstatistics of interannual variability [44]. Here we use a Poisson generator that takes into account both the inter-annual and the spatial variabilities of rainfall intensity in order to preserve space/time correlations while generating rainfall at local scale. The identification of statistically equivalent spatio-temporal aggregates is carried out using suitable clustering techniques. This approach allows to generate a large number of precipitation scenarios, naturally preserving the statistical properties of the rainfall dataset.
We make use of these synthetic rainfall fields to force our epidemiological model and to obtain, as a result, estimates of the strength of the disease resurgence. It should be noted that our attempt differs substantially from, say, classical hydrological predictions, as several epidemiological and social processes are acting simultaneously on top of the rainfall dynamics we try to reproduce. As the magnitude of many of these processes is often uncertain (sometimes being even difficult to identify correctly the whole set of intervening processes), epidemiological predictions are particularly challenging. Here, we perform two types of analysis: (i) an a posteriori evaluation, in which calibration, validation and prediction all belong to the past course of the outbreak; (ii) multi-seasonal projections, from the current state of the epidemic to the next few years in which cholera is speculated to become endemic in the region [39]. The first analysis simulates real-time conditions in which short-term (a few month) scenarios of cholera resurgence are used to evaluate the performance of the model as a predictive and control tool during the very course of an epidemic. We then analyze the effect of different, alternative scenarios of intervention (sanitation and vaccination, possibly differing in timing and in spatial distribution) on the evolution of the outbreak to mimic model-guided intervention policies. We study whether the inference of the most effective policy – say, that aiming at the maximum reduction of the total number of reported cases in a given time frame – may still hold in the face of the actual development of disease resurgence. In the long-term case, the study of correlations of cyclic resurgence of the disease with the seasonal rainfall cycle matters, as the particular initial conditions that have favored the appearance of cholera in Haiti – i.e. a high number of susceptibles – will no longer apply in the future. The epidemic, in fact, can be expected to revamp in particular conditions of stress (e.g. extreme rainfall events) with an intensity that depends on the rate at which recovered individuals lose their temporary acquired immunity to the disease. This kind of analysis allows also to estimate the amount of sanitation or the extent of a vaccination campaign aimed at eradicating the disease from the region, and is deeply rooted in hydrologic sciences.
Section snippets
Spatially explicit epidemiological models for the Haitian epidemic
We make use here of some of the models presented in [46], who have constructed a spatially explicit framework for the description of the Haitian epidemic and whose approach evolved from the first Haiti application by Bertuzzo et al. [10]. In particular, we restrict here our analysis to the two models which emerged as best performing under absorbing or diffusive boundary conditions [46], see Fig. S8 therein). The first model accounts for the baseline hydro-epidemiological dynamics relevant to
Rainfall generation patterns
In the hydrological literature, stochastic rainfall generation is often modeled as a marked Poisson process, where rainfall events are treated as a series of point events in continuous time where the associated mark represents the rainfall depth of the event (see e.g. [33], [48]). This implies that no temporal evolution of a single event is taken into account, such that the amount of rainfall falling at a given time scale – which is usually assumed as daily, as in this paper – is modeled by a
Rainfall scenarios
We first analyse the performance of the stochastic model for rainfall generation. Fig. 5 shows the cumulative probability distributions and the probability density functions of the whole ensemble of inter-arrival times and of rainfall depths for the observed rainfall and for the multivariate Poisson generator, for both the global and the local scale. As in [44], the so-called “super-statistics” generator shows a good agreement with data. Moreover, we run an exercise to illustrate the
Conclusions
The following conclusions are worth mentioning:
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spatially explicit mathematical models provide a tool to predict and control the course of ongoing cholera epidemics. The relevance of this new class of models relates to the fact that inappropriate responses can be avoided by providing adequate and timely information to policy-makers, decision-makers, the media and the public. While several issues remain open, like the field validation of parameters defined node-by-node, major public health policy
Acknowledgements
This article is dedicated to the caring memory of Erika Schild, formerly MS student at EPFL, who passed away during a stage in Haiti dedicated to her thesis on modeling cholera epidemics. The authors wish to express their deepest regret. LR, EB, LM and AR acknowledge the support provided by ERC Advanced Grant program through the project RINEC-227612 and by the SFN/FNS projects 200021 124930/1 and CR2312 138104/1. MG and AR acknowledge the support from the SFN/FNS project IZK0Z2 139537/1 for
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