# American Institute of Mathematical Sciences

June  2016, 21(4): 1297-1316. doi: 10.3934/dcdsb.2016.21.1297

## Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model

 1 Department of Mathematics, Washington State University, Pullman, WA 99164-3113 2 Washington State University, Department of Mathematics and Statistics, Pullman, WA 99164-3113, United States

Received  May 2015 Revised  December 2015 Published  March 2016

In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the special structure of the system and continuation of local theory argument, we show that in fact this problem is globally well-posed. Secondly, we analyze the local asymptotic stability of the solutions based on the basic reproduction number associated with this model.
Citation: Kazuo Yamazaki, Xueying Wang. Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1297-1316. doi: 10.3934/dcdsb.2016.21.1297
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