Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse - Shanjing Ren (Mathematical Biosciences and Engineering)
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 $R_{0} \lt 1$, the disease-free equilibrium is globally asymptotically stable, whereas if $R_{0} \gt 1$, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.