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Received June 5, 2018; Accepted September 18, 2018; Published October 1, 2018
Abstract. In this paper, a model structured in vaccination and infection ages with a general class of nonlinear incidence is introduced and investigated. The resulting model is a system of two age-structured PDEs and an ODE with a non local term. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic reproduction number. Further, by constructing a new Lyapunov functional, we show the global asymptotic stability of the endemic equilibrium whenever it exists. Finally, a discussion about controlling the spread of the disease is provided.
How to Cite this Article:
Ismail Boudjema, Tarik Mohammed Touaoula, Global stability of an infection and vaccination age-structured model with general nonlinear incidence, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 33, pp. 1-21.