Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 08, pp. 1-38.

Title: Dynamics of a partially degenerate reaction-diffusion cholera model with
horizontal transmission and phage-bacteria interaction
       
Authors: Zhenxiang Hu (Xinjiang Univ., Urumqi, China)
         Shengfu Wang (Xinjiang Univ., Urumqi, China)
         Linfei Nie   (Xinjiang Univ., Urumqi, China)
         
Abstract:
We propose a cholera model with coupled reaction-diffusion equations and ordinary
differential equations for discussing the effects of spatial heterogeneity,
horizontal transmission, environmental viruses and phages on the spread of
vibrio cholerae.
We establish the well-posedness of this model which includes the existence of unique global
positive solution, asymptotic smoothness of semiflow, and existence of a global attractor.
The basic reproduction number R<sub>0</sub> is obtained to describe the persistence
and extinction of the disease. That is, the disease-free steady state is globally
asymptotically stable for R<sub>0</sub>&le;1, while it is unstable for
R<sub>0</sub>&gt;1. And, the disease is persistence and the model has the phage-free
and phage-present endemic steady states in this case.
Further, the global asymptotic stability of phage-free and phage-present endemic
steady states are discussed for spatially homogeneous model.
Finally, some numerical examples are displayed in order to illustrate the main
theoretical results and our opening questions.

Submitted June 30, 2022. Published January 24, 2023.
Math Subject Classifications: 35B35, 35K57, 35Q92, 37N25, 92D30.
Key Words: Cholera model; environmental and horizontal transmission;
           spatial heterogeneity and phages; basic reproduction number;
           global asymptotic stability.