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Keywords:

  • SIR-like models;
  • travelling waves;
  • scaling laws;
  • human movement

Abstract

We propose an important extension of a previously studied, spatially explicit and hydrology-driven, model of cholera spreading. Our reformulation concerns the role of different modelizations of human movement on the overall dynamics of the epidemics, which were previously expressed synthetically by bacterial diffusion. The system is composed of three compartments: susceptible and infected components, Vibrio cholerae dispersion and reaction dynamics. The underlying spatial framework is based on a reaction-diffusion scheme, which is applied, for simplicity, to ecological corridors modelled as one-dimensional lattices mimicking river reaches. In this geometry, we are able to predict important features of disease propagation, like the analytical evaluation of the spreading celerity of travelling fronts of epidemics. The explicit mechanism of human movement presented here leads to a comparison with previous approaches, revealing notable differences in how cholera spreads in space and time along the system. Studying human movement allows the analysis of specific quantities useful to policy makers and epidemiologists, such as the value of human diffusion which can generate upstream propagation of the disease. A robust relationship among key parameters, which links together diffusion mechanism, drift speed and resulting epidemic intensity, is also shown. Copyright © 2010 John Wiley & Sons, Ltd.