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Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects

Nonlinear Dynamics volume 59, pages 503–513 (2010)Cite this article

Abstract

In this paper, the propagation of a nonlinear delay SIR epidemic using the double epidemic hypothesis is modeled. In the model, a system of impulsive functional differential equations is studied and the sufficient conditions for the global attractivity of the semi-trivial periodic solution are drawn. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination, and nonlinear incidence have significant effects on the dynamics behaviors of the model. The conditions for the control of the infection caused by viruses A and B are given.

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Author information

Affiliations

  1. State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China

    Xinzhu Meng & Zhenqing Li

  2. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266510, People’s Republic of China

    Xinzhu Meng

  3. College of Agronomy, Henan University of Science and Technology, Luoyang, 471003, People’s Republic of China

    Xiaoling Wang

Authors
  1. Xinzhu Meng
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  2. Zhenqing Li
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  3. Xiaoling Wang
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Corresponding author

Correspondence to Zhenqing Li.

Additional information

This project was supported by the National Natural Science Foundation of China (No. 30870397) and National Basic Research Program of China (973 Program) (No. 2006CB403207-4).

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Meng, X., Li, Z. & Wang, X. Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects. Nonlinear Dyn 59, 503–513 (2010). https://doi.org/10.1007/s11071-009-9557-1

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  • DOI: https://doi.org/10.1007/s11071-009-9557-1

Keywords

  • Double epidemic hypothesis
  • Permanence
  • Nonlinear incidence
  • Time delay
  • SIR epidemic model