In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in , 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.
|Number of pages||20|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|State||Published - Jun 2016|
- Cholera dynamics
- Disease threshold dynamics
- Principal eigenvalues
- The basic reproduction number