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

  • Received: 04 June 2016 Revised: 30 December 2016 Published: 01 October 2017
  • MSC : Primary: 35L60, 92C37; Secondary: 34K20

  • 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.

    Citation: Shanjing Ren. Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1337-1360. doi: 10.3934/mbe.2017069

    Related Papers:

  • 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.


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