### Mathematical Biosciences and Engineering

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

# 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

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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