
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.
Keywords: Agestructure; Liapunov function; tuberculosis; infection equilibrium; global stability
Citation: Shanjing Ren. Global stability in a tuberculosis model of imperfect treatment with agedependent latency and relapse. Mathematical Biosciences and Engineering, 2017, 14(5&6): 13371360. doi: 10.3934/mbe.2017069
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This article has been cited by:
 1. Y. Ma, C. R. Horsburgh, L. F. White, H. E. Jenkins, Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis, Epidemiology and Infection, 2018, 1, 10.1017/S0950268818001760
 2. Lili Liu, Xiaomei Feng, A multigroup SEIR epidemic model with agedependent latency and relapse, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.5193
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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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