A reaction-convection-diffusion model for cholera spatial dynamics

Xueying  Wang; Drew  Posny; Jin  Wang

doi:10.3934/dcdsb.2016073

Article Contents

2016, Volume 21, Issue 8: 2785-2809. Doi: 10.3934/dcdsb.2016073

This issue Previous Article On the Rayleigh-Taylor instability for the compressible non-isentropic inviscid fluids with a free interface Next Article Spatial degeneracy vs functional response

A reaction-convection-diffusion model for cholera spatial dynamics

1.
Washington State University, Department of Mathematics and Statistics, Pullman, WA 99164-3113
2.
NSF Center for Integrated Pest Management, North Carolina State University, Raleigh, NC 27606
3.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403

Received: August 31, 2015

Revised: October 31, 2015

Published: September 2016

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Abstract

In this paper, we propose a general partial differential equation (PDE) model of cholera epidemics that extends previous mathematical cholera studies. Our new formation concerns the impact of the bacterial and human diffusion, bacterial convection, and their interaction with the intrinsic bacterial growth and multiple disease transmission pathways. A sensitivity analysis for a few key model parameters indicates the significance of diffusion and convection in shaping cholera epidemics. We then investigate the traveling wave solutions of our PDE model based on analytical derivation and numerical simulation, with a focus on the interplay of different biological, environmental and physical factors that determines the spatial spreading speeds of cholera. In addition, disease threshold dynamics are studied by computing the basic reproduction number associated with the PDE model, using both asymptotic analysis and numerical calculation.

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Mathematics Subject Classification: 35K57, 35C07, 37N25, 92D30.

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