Dynamical analysis of spatial heterogeneous cholera models with convection and different infectivities

In this paper, we develop a new model to analyze the global dynamics of spatially heterogeneous cholera models with different infectivities. We first show the model admits globally positive solutions. Second, the dynamic problem of a single environmental model without shedding rate is studied. In order to discuss the extinction and persistence of the disease, we will also study the global dynamics of Vibrio cholera controlled by both the basic reproduction number of the environment and the basic reproduction number of the infection. Finally, for the models with different nonlinear reaction terms in homogeneous environments, we demonstrated the global stability of steady-state through appropriate Lyapunov functionals.