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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

## Abstract    Full Text(HTML)    Figure/Table    Related pages

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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