Threshold Kinetic Analysis Of A Degenerate Reaction-diffusion Cholera Model In A Heterogeneous Environment

The prevalence of cholera has an enormous impact on the physical and mental health of the population and has also caused significant social,economic and polit-ical burdens.The purpose of this paper is to establish a mathematical model with biological significance and explore the transmission mechanism of cholera.We sys-tematically analyze two types of reaction-diffusion cholera models with degenerated terms.At first,we perform a complete analysis on a degenerate reaction-diffusion cholera model with stabilizing total humans and non-mobility of cholera bacteria in a spatially heterogeneous bounded domain.The existence of a global attractor is established.The basic reproduction number and its equivalent characterizations,the dispersal rate of infected humans and local basic reproduction number have been used to analyze the threshold-type results.Moreover,we compare the basic reproduction number for the models without and with considering the mobility of cholera bacteria.In order to make the model more universal,we use the general nonlinear func-tions to represent the intrinsic growth rate of susceptible humans and incidence functions,so as to construct a degenerated reaction-diffusion cholera model with bacterial hyperinfectivity and spatial heterogeneity.Then the well-posedness of the model is verified and its basic reproduction number(?)₀is defined.The epidemic of cholera and the global attractivity of corresponding disease free steady state under critical condition are analyzed with(?)₀as the threshold.In the homogeneous case,the global asymptotic stability of the corresponding unique positive equilibrium is achieved by the new Lyapunov functions for the above two models.Numerical simulations support our analytical results.