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Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes

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MBE2012,4,819doi:10.3934/mbe.2012.9.819

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number $\mathcal{R}_{0}$ is calculated. For $\mathcal{R}_{0}<1$, the disease-free equilibrium is globally asymptotically stable. For $\mathcal{R}_{0}>1$, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present. Finally, some special cases are considered.