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 R0 is calculated. For R0 < 1, the disease-free equilibrium is globally asymptotically stable. For R0 > 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.
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C. Connell McCluskey (2012) studied this question.
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