A partially diffusive cholera model based on a general second-order differential operator

We propose a new mathematical model for cholera transmission dynamics using a system of reaction-convection-diffusion equations. The model differs from previously published partial differential equations (PDEs) based cholera models in that the diffusion and convection processes are only incorporated into the bacterial dynamics, which are described by a general second-order differential operator. This feature allows us to perform a careful study on the movement and dispersal of the pathogenic bacteria in a heterogeneous aquatic environment and its impact on cholera transmission among human hosts. We rigorously analyze the well-posedness and stability of this partially diffusive system, and establish threshold results characterizing cholera transmission dynamics.