Global stability of an age-structured cholera model.

In this paper, an age-structured epidemic model is formulated to describe the transmission dynamics of cholera. The PDE model incorporates direct and indirect transmission pathways, infection-age-dependent infectivity and variable periods of infectiousness. Under some suitable assumptions, the PDE model can be reduced to the multi-stage models investigated in the literature. By using the method of Lyapunov function, we established the dynamical properties of the PDE model, and the results show that the global dynamics of the model is completely determined by the basic reproduction number R0: if R0<1 the cholera dies out, and if R0>1 the disease will persist at the endemic equilibrium. Then the global results obtained for multi-stage models are extended to the general continuous age model.