Global dynamics of a hybrid Cholera model with phage–bacteria interaction

Abstract

We propose, in this paper, a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment, which is coupled with some reaction–diffusion equations and first-order partial differential equations. The precise formulation of basic reproduction number ([Formula: see text]) is deduced, which characterizes the elimination or prevalence of this disease. Specifically, the disease-free steady state is globally asymptotically stable for [Formula: see text] but unstable for [Formula: see text]. Further, the phage invasion reproduction number [Formula: see text] is also obtained, which portrays the impact of phages on Vibrio cholerae in the environment. That is, for [Formula: see text], the phage-free endemic steady state is globally asymptotically stable if [Formula: see text], and the phage-present endemic steady state is globally asymptotically stable if [Formula: see text]. Numerical simulations are introduced for the purpose of verifying the main results.