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

Kazuo Yamazaki; Xueying  Wang

doi:10.3934/dcdsb.2016.21.1297

Article Contents

2016, Volume 21, Issue 4: 1297-1316. Doi: 10.3934/dcdsb.2016.21.1297

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

Kazuo Yamazaki^1, and
Xueying Wang^2,

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

Received: May 2015

Revised: December 2015

Published: June 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B65, 35K57; Secondary: 47H20.

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