Global stability of an age-structured cholera model

Abstract

In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE modelcan be reduced to the multi-stage models investigated in theliterature. By using the method of Lyapunov function, we establishedthe dynamical properties of the PDE model, and the results show thatthe global dynamics of the model is completely determined by thebasic reproduction number $\mathcal R_0$: if $\mathcal R_0 1$ the disease will persist at the endemicequilibrium. Then the global results obtained for multi-stage modelsare extended to the general continuous age model.

Keywords

• age of infection
• global stability
• lyapunov function.
• cholera