Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 1297 - 1316, Volume 21, Issue 4, June 2016      doi:10.3934/dcdsb.2016.21.1297

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Kazuo Yamazaki - Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States (email)
Xueying Wang - Washington State University, Department of Mathematics and Statistics, Pullman, WA 99164-3113, United States (email)

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.

Keywords:  Cholera dynamics, well-posedness, the basic reproduction number, principal eigenvalues, disease threshold dynamics, stability.
Mathematics Subject Classification:  Primary: 35B65, 35K57; Secondary: 47H20.

Received: May 2015;      Revised: December 2015;      Available Online: March 2016.