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

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


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