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

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
2. School of Mathematics and Computer Science, Guizhou Education University, Guiyang 550018, China

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.

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Copyright Info: © 2017, Shanjing Ren, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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