Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse

Abstract

In this paper, an SEIR epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is wellsuited to model tuberculosis. The basic reproduction number R0 is calculated. We obtain the global behavior of the model in terms of R0. If R0 < 1, the disease-free equilibrium is globally asymptotically stable, whereas if R0 > 1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.