Mathematical Biosciences and Engineering, 2012, 9(1): 111-122. doi: 10.3934/mbe.2012.9.111.

Primary: 34C12, 34C25; Secondary: 92D30.

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Threshold dynamics for a Tuberculosis model with seasonality

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

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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Keywords uniform persistence.; Basic reproductive number; periodic solution; seasonal fluctuation; global asymptotic stability

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


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