GLOBAL STABILITY IN A TUBERCULOSIS MODEL OF IMPERFECT TREATMENT WITH AGE-DEPENDENT LATENCY

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 R-0 is calculated. We obtain the global behavior of the model in terms of R-0. If R-0 < 1, the disease-free equilibrium is globally asymptotically stable, whereas if 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.