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Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control

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Listed:
  • Xiying Wang
  • Wei Xu
  • Yujun Cui
  • Xiaomei Wang

Abstract

This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time‐varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward.

Suggested Citation

  • Xiying Wang & Wei Xu & Yujun Cui & Xiaomei Wang, 2014. "Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:853960
    DOI: 10.1155/2014/853960
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    References listed on IDEAS

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    1. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Li, Ping & Zhong, Shou-Ming & Cui, Jin-Zhong, 2009. "Stability analysis of linear switching systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 474-480.
    3. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, April.
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