Global stability of an age-structured cholera model
Jianxin Yang Zhipeng Qiu Xue-Zhi Li
Mathematical Biosciences & Engineering 2014, 11(3): 641-665 doi: 10.3934/mbe.2014.11.641
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 $\mathcal R_0$: if $\mathcal R_0 < 1$ the cholera dies out, and if $\mathcal R_0 >1$ 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.
keywords: Age of infection global stability Lyapunov function. cholera

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