Mathematical models can provide key insights into the course of an ongoing epidemic, potentially aiding real-time emergency management in allocating health care resources and by anticipating the impact of alternative interventions. We study the ex post reliability of predictions of the 2010-2011 Haiti cholera outbreak from four independent modeling studies that appeared almost simultaneously during the unfolding epidemic. We consider the impact of different approaches to the modeling of spatial spread of Vibrio cholerae and mechanisms of cholera transmission, accounting for the dynamics of susceptible and infected individuals within different local human communities. To explain resurgences of the epidemic, we go on to include waning immunity and a mechanism explicitly accounting for rainfall as a driver of enhanced disease transmission. The formal comparative analysis is carried out via the Akaike information criterion (AIC) to measure the added information provided by each process modeled, discounting for the added parameters. A generalized model for Haitian epidemic cholera and the related uncertainty is thus proposed and applied to the year-long dataset of reported cases now available. The model allows us to draw predictions on longer-term epidemic cholera in Haiti from multiseason Monte Carlo runs, carried out up to January 2014 by using suitable rainfall fields forecasts. Lessons learned and open issues are discussed and placed in perspective. We conclude that, despite differences in methods that can be tested through model-guided field validation, mathematical modeling of large-scale outbreaks emerges as an essential component of future cholera epidemic control.waterborne diseases | epidemiology | ecohydrology | human mobility |

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.

[1] Here we propose spatially explicit predictions of the residual progression of the current Haiti cholera outbreak accounting for the dynamics of susceptible and infected individuals within different local human communities, and for the redistribution among them of Vibrio cholerae, the causative agent of the disease. Spreading mechanisms include the diffusion of pathogens in the aquatic environment and their dissemination due to the movement of human carriers. The model reproduces the spatiotemporal features of the outbreak to date, thus suggesting the robustness of predicted future developments of the epidemic. We estimate that, under unchanged conditions, the number of new cases in the whole country should start to decrease in January. During this month the epidemic should mainly involve the Ouest department (Port-au-Prince) while fading out in northern regions. Our spatially explicit model allows also the analysis of the effectiveness of alternative intervention strategies. To that end our results show that mass vaccinations would have a negligible impact at this stage of the epidemic. We also show that targeted sanitation strategies, providing clean drinking water supply and/or staging educational campaigns aimed at reducing exposure, may weaken the strength of the residual evolution of the infection. Citation: Bertuzzo, E., L. Mari, L. Righetto, M. Gatto, R. Casagrandi, M. Blokesch, I. RodriguezIturbe, and A. Rinaldo (2011), Prediction of the spatial evolution and effects of control measures for the unfolding Haiti cholera outbreak, Geophys. Res. Lett., 38, L06403,

Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R 0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G 0 , explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number Λ 0 (the dominant eigenvalue of G 0 ) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G 0 . Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G 0 provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections.ecohydrology | aquatic ecosystems | invasion | bifurcations W aterborne diseases, mainly due to protozoa or bacteria and often resulting in profuse diarrhea (cholera is a prominent example), are one of the leading causes of death and especially strike infants and children in low-income countries (1). Therefore, it is fundamental to develop realistic dynamical models that can provide insights into the course of past and ongoing epidemics, assist in emergency management, and allocate health-care resources via an assessment of alternative intervention strategies (2-7). These models must properly account for the relevant disease and transport timescales (8-10). Whereas some diarrheal infections, like Rotavirus, have basically a fecal-oral transmission and their spread can thus be modeled as susceptible-infected-recovered (SIR) systems (11), traditional waterborne disease models (12, 13) include, in addition to susceptibles (S) and infectives (I) (14), the population dynamics of bacteria (B) in water reservoirs. More recent modeling has considered hyperinfectivity of newly excreted vibrios (15), prey-predator interactions with phages (16), and seasonal and climate forcings (17)(18)(19)(20)(21)(22). All these models, however, have not considered explicitly the ...

Waterborne pathogens cause many possibly lethal human diseases. We derive the condition for pathogen invasion and subsequent disease outbreak in a territory with specific, space-inhomogeneous characteristics (hydrological, ecological, demographic, and epidemiological). The criterion relies on a spatially explicit model accounting for the density of susceptible and infected individuals and the pathogen concentration in a network of communities linked by human mobility and the water system. Pathogen invasion requires that a dimensionless parameter, the dominant eigenvalue of a generalized reproductive matrix J 0 , be larger than unity. Conditions for invasion are studied while crucial parameters (population density distribution, contact and water contamination rates, pathogen growth rates) and the characteristics of the networks (connectivity, directional transport, water retention times, mobility patterns) are varied. We analyze both simple, prototypical test cases and realistic landscapes, in which optimal channel networks mimic the water systems and gravitational models describe human mobility. Also, we show that the dominant eigenvector of J 0 effectively portrays the geography of epidemic outbreaks, that is, the areas of the studied territory that will be initially affected by an epidemic. This is important for planning an efficient spatial allocation of interventions (e.g., improving sanitation and providing emergency aid and medicines).