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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

  • 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.

    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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  • This article has been cited by:

    1. Zuiyuan Guo, Dan Xiao, Xiuhong Wang, Yayu Wang, Tiecheng Yan, Epidemiological characteristics of pulmonary tuberculosis in mainland China from 2004 to 2015: a model-based analysis, 2019, 19, 1471-2458, 10.1186/s12889-019-6544-4
    2. Joshua Kiddy K. Asamoah, Zhen Jin, Gui-Quan Sun, Non-seasonal and seasonal relapse model for Q fever disease with comprehensive cost-effectiveness analysis, 2021, 22, 22113797, 103889, 10.1016/j.rinp.2021.103889
    3. Consolato Sergi, Nicola Serra, Claudia Colomba, Ayansina Ayanlade, Paola Di Carlo, Tuberculosis evolution and climate change: How much work is ahead?, 2019, 190, 0001706X, 157, 10.1016/j.actatropica.2018.11.016
    4. Xin-Xu Li, Li-Xia Wang, Hui Zhang, Xin Du, Shi-Wen Jiang, Tao Shen, Yan-Ping Zhang, Guang Zeng, Shabir Ahmed Madhi, Seasonal Variations in Notification of Active Tuberculosis Cases in China, 2005–2012, 2013, 8, 1932-6203, e68102, 10.1371/journal.pone.0068102
    5. Tamer Oraby, Olga Vasilyeva, Daniel Krewski, Frithjof Lutscher, Modeling seasonal behavior changes and disease transmission with application to chronic wasting disease, 2014, 340, 00225193, 50, 10.1016/j.jtbi.2013.09.003
    6. Y. Ma, C. R. Horsburgh, L. F. White, H. E. Jenkins, Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis, 2018, 146, 0950-2688, 1478, 10.1017/S0950268818001760
    7. Jiaxuan Ding, Lei Shi, Ziang Chen, Liping Wang, A novel pulmonary tuberculosis infectious disease model with piecewise periodic transmission rate for epidemic analysis in Zhejiang province, China, 2024, 0924-090X, 10.1007/s11071-024-10596-w
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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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