Global dynamics of a reaction-diffusion waterborne pathogen model with general incidence rate

In this paper, we first propose a reaction-diffusion waterborne pathogen model with general incidence rate, incorporating both direct and indirect transmission pathways. Then, using the basic reproduction number we investigate the global dynamical behaviors of the continuous model. By nonstandard finite difference scheme, we derive a discrete counterpart of the continuous model. Then, the global properties of the discretized model are investigated. Finally, we conclude the paper by an example and numerical simulations.