Threshold dynamics for a Tuberculosis model with seasonality

Xinli Hu; Xinli Hu

doi:10.3934/mbe.2012.9.111

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 1: 111-122. doi: 10.3934/mbe.2012.9.111

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Threshold dynamics for a Tuberculosis model with seasonality

Xinli Hu

1.
Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049

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.
- uniform persistence.,
- Basic reproductive number,
- periodic solution,
- seasonal fluctuation,
- global asymptotic stability
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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Abstract

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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