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

In this paper, an SEIR epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited 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.