Modelling cholera epidemics: the role of waterways, human mobility and sanitation

Abstract

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000 -2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.

Mean Field Approximation of Uncertain Stochastic Models

“…Furthermore, as we will see in the next section, under a proper scaling, the behaviour of an imprecise Markov chain is closely related to the one of a differential inclusion corresponding to Equation (3). In this section, we provide a quick introduction to DI, recalling some classical definitions.…”

“…Moreover, the infection rate itself may depend on environmental factors, which can change arbitrarily in time. For instance, in cholera spreading [3], the level of rainfall impacts on the diffusion of the bacterium among nearby water reservoirs, leading to infection rates which can vary unpredictably in time.…”

Efficient Stochastic Simulation of Systems with Multiple Time Scales via Statistical Abstraction

“…In order to tame such complexity, a common practice is to rely on abstraction techniques, simplifying some scales of the model, yet still capturing relevant features of the dynamics. Examples are the abstraction of the complex intra-cellular state as a finite state automaton, a typical approach to build cell population models, the abstraction of the local dynamics of epidemic spreading in country-level models [12], or the averaging of fast dynamics in enzyme kinetics [13,6]. The downside of such approaches is that the abstractions that are constructed are non-trivial and model-specific, and often require considerable efforts from the modellers.…”

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

“…In just a few years, the DREAM algorithm has found widespread application and use in numerous different fields, including (among others) atmospheric chemistry (Partridge et al, 2011(Partridge et al, , 2012, biogeosciences (Scharnagl et al, 2010;Braakhekke et al, 2013;Ahrens and Reichstein, 2014;Dumont et al, 2014;Starrfelt and Kaste, 2014), biology (Coelho et al, 2011;Zaoli et al, 2014), chemistry (Owejan et al, 2012;Tarasevich et al, 2013;DeCaluwe et al, 2014;Gentsch et al, 2014), ecohydrology (Dekker et al, 2010), ecology (Barthel et al, 2011;Gentsch et al, 2014;Iizumi et al, 2014;Zilliox and Goselin, 2014), economics and quantitative finance (Bauwens et al, 2011;Lise et al, 2012;Lise, 2013), epidemiology (Mari et al, 2011;Rinaldo et al, 2012;Leventhal et al, 2013), geophysics (Bikowski et al, 2012;Linde and Vrugt, 2013;Carbajal et al, 2014;Lochbühler et al, 2014Lochbühler et al, , 2015, geostatistics (Minasny et al, 2011;Sun et al, 2013), hydrogeophysics (Hinnell et al, 2011), hydrologeology (Keating et al, 2010;Laloy et al, 2013;Malama et al, 2013), hydrology (Vrugt et al, 2008a(Vrugt et al, , 2009a…”