
Mathematical Biosciences and Engineering, 2017, 14(5&6): 13371360. doi: 10.3934/mbe.2017069
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Global stability in a tuberculosis model of imperfect treatment with agedependent 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
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In this paper, an $SEIR$ epidemic model for an imperfect treatment disease with agedependent latency and relapse is proposed. The model is wellsuited 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 diseasefree 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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