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.

Figure 1.

Epidemiology of the 2000–2001 KZN cholera epidemics. (a) Spatial patterns of recorded cholera cases, (b) population densities and (c) yearly cholera incidence (defined as the ratio between the total number of recorded cases and local population abundances) in each health subdistrict. Temporal evolution of the epidemic outbreak through the whole KZN province, shown as the weekly count of reported cases (d) (cumulated cases (e)). Data from the KZN Health Department and the 2001 South African Census.

Figure 2.

Hygienic conditions of the KZN province. Spatial patterns of availability of (a) piped water and (b) toilet facilities. Data from the 2001 South African Census.

Figure 3.

Two-layer network model. (a) River systems of the KZN province, with the three most populated basins (uMngeni, Thukela and Mfolozi) highlighted. (b) Human mobility patterns. For each node only the three most important outbound connections (as computed from the gravity model detailed in the text) are shown. Note the role played by Durban, the most populated town in the KZN province, in organizing the southmost part of the mobility network. Data from (a) the South African Department of Water Affairs and Forestry and (b) the 2001 South African Census.

Figure 4.

Functional relationships used in the epidemiological model. (a) Probability of infection f as a function of exposure to a given concentration of V. cholerae cells. (b) Water availability W as a function of local community size (c = 1, H_T = max(H)/4). (c) Rate of exposure to contaminated water β as a function of piped water availability (ɛ = 2). (d) Contamination rate p as a function of access to toilet facilities (ϕ = 2).

Figure 5.

Simulation of the KZN cholera outbreak. Comparison between (a) observed and (b) generated spatial patterns of cumulated cholera cases (best-fit full model). Spatial linear interpolation of the node values has been performed in both panels. White dots in (a) show the location of the cases recorded during the first week of the epidemics, used as initial condition for model simulations. (c) Temporal evolution of the epidemic as recorded from field data (red) and simulated by the best-fit full model (blue). The shaded area shows the uncertainty of model simulations evaluated as the envelope of a set S of 200 randomly selected runs corresponding to parameter settings explored by the DREAM_ZS algorithm after convergence. (d) Comparison between observed and generated epidemic records catchment by catchment (best-fit full model). Dot size is proportional to catchment population (log scale). Error bars show the variability found within S. Inset: yearly cholera incidence versus local community size, as evaluated from data (red) and the best-fit full model simulation (blue). Incidence values for each network node have been grouped via a logarithmic binning based on local population size. Bins and error bars represent the mean value for the best-fit simulation and minimum/maximum values among the simulations in S. Parameter values as in tables 1 and 2 (full model).

Figure 6.

Effects of parameter variations on the simulation of the best-fit full model. (a) Variations of total yearly cholera incidence produced by ±20% variations of the parameters reported in table 1. (b) As in (a), with reference to the tuning parameters reported in table 2 (±20% of the best-fit values obtained with the full model). Black (grey) refers to simulations in which the value of the relevant parameter has been increased (decreased) by 20%.

Figure 7.

The role of human mobility in the spread of cholera. (a) Temporal evolution of the epidemic as recorded from field data (red) and simulated by the best-fit model without human mobility (m = 0, blue line). The shaded area shows the uncertainty of model simulations and is evaluated as the envelope of a set S′ of 200 randomly selected runs corresponding to parameter settings explored by the DREAM_ZS algorithm after convergence. (b) Comparison between observed and generated epidemic records catchment by catchment (best-fit model without human mobility). Dot size is proportional to catchment population (log scale). Error bars show the variability found within S′. Inset: spatial distribution of cumulated cholera cases as predicted by the best-fit full model with m = 0.

Figure 8.

Effects of preventive interventions on sanitation conditions. (a) Total yearly cholera incidence versus population involved in sanitation efforts aimed at improving access to piped water. Solid, dashed and dotted lines, respectively, represent spatially homogeneous interventions, interventions targeted to poorly sanitated communities (ω ≥ 0.5) and interventions targeted to large communities (H_i > 10 000). (b) As in (a), with reference to efforts aimed at improving access to toilet facilities.