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Global stability of an age-structured sir epidemic model with pulse vaccination strategy

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Abstract

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age (duration since infection). The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infection-free situation if the impulsive period T and proportion p satisfy R 0(p, T) < 1. Optimal problem is discussed: Pulse vaccination strategy with minimal costs at given R 0(p, T) < 1.

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Authors and Affiliations

  1. College of Mathematics and Information, Xinyang Normal University, Xinyang, 464000, China

    Helong Liu

  2. Beijing Institute of Information and Control, Beijing, 100037, China

    Jingyuan Yu

  3. Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, China

    Guangtian Zhu

Authors
  1. Helong Liu
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  2. Jingyuan Yu
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  3. Guangtian Zhu
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Corresponding author

Correspondence to Helong Liu.

Additional information

The research was supported by Natural Science Foundation of Henan Province under Grant No. 092300410206, and Science and Technology Program of Educational Department of Henan Province under Grant No. 2009A110015.

This paper was recommended for publication by Editor Dexing FENG.

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Liu, H., Yu, J. & Zhu, G. Global stability of an age-structured sir epidemic model with pulse vaccination strategy. J Syst Sci Complex 25, 417–429 (2012). https://doi.org/10.1007/s11424-011-9177-y

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  • DOI: https://doi.org/10.1007/s11424-011-9177-y

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