Global dynamics of cholera models with differential infectivity.

A general compartmental model for cholera is formulated that incorporates two pathways of transmission, namely direct and indirect via contaminated water. Non-linear incidence, multiple stages of infection and multiple states of the pathogen are included, thus the model includes and extends cholera models in the literature. The model is analyzed by determining a basic reproduction number R0 and proving, by using Lyapunov functions and a graph-theoretic result based on Kirchhoff's Matrix Tree Theorem, that it determines a sharp threshold. If R0≤1, then cholera dies out; whereas if R0>1, then the disease tends to a unique endemic equilibrium. When input and death are neglected, the model is used to determine a final size equation or inequality, and simulations illustrate how assumptions on cholera transmission affect the final size of an epidemic.