Threshold dynamics for a Tuberculosis model with seasonality

  • Received: 01 February 2011 Accepted: 29 June 2018 Published: 01 December 2011
  • MSC : Primary: 34C12, 34C25; Secondary: 92D30.

  • In this paper, we investigate a SEILR tuberculosis model incorporating the effect of seasonal fluctuation, where the loss of sight class is considered. The basic reproduction number $R_{0}$ is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if $R_{0}<1$, and there exists at least one positive periodic solution and the disease is uniformly persistent if $R_{0}>1$. Numerical simulations are provided to illustrate analytical results.

    Citation: Xinli Hu. Threshold dynamics for a Tuberculosis model with seasonality[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 111-122. doi: 10.3934/mbe.2012.9.111

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  • In this paper, we investigate a SEILR tuberculosis model incorporating the effect of seasonal fluctuation, where the loss of sight class is considered. The basic reproduction number $R_{0}$ is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if $R_{0}<1$, and there exists at least one positive periodic solution and the disease is uniformly persistent if $R_{0}>1$. Numerical simulations are provided to illustrate analytical results.
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    © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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