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Mathematical analysis for an age-structured SIRS epidemic model

  • Received: 27 March 2019 Accepted: 19 June 2019 Published: 01 July 2019
  • In this paper, we investigate an SIRS epidemic model with chronological age structure in a demographic steady state. Although the age-structured SIRS model is a simple extension of the well-known age-structured SIR epidemic model, we have to develop new technique to deal with problems due to the reversion of susceptibility for recovered individuals. First we give a standard proof for the well-posedness of the normalized age-structured SIRS model. Next we examine existence of endemic steady states by fixed point arguments and bifurcation method, where we introduce the next generation operator and the basic reproduction number $R_0$ to formulate endemic threshold results. Thirdly we investigate stability of steady states by the bifurcation calculation and the comparison method, and we show existence of a compact attractor and discuss the global behavior based on the population persistence theory. Finally we give some numerical examples and discuss the effect of mass-vaccination on $R_0$ and the critical coverage of immunization based on the reinfection threshold.

    Citation: Kento Okuwa, Hisashi Inaba, Toshikazu Kuniya. Mathematical analysis for an age-structured SIRS epidemic model[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 6071-6102. doi: 10.3934/mbe.2019304

    Related Papers:

  • In this paper, we investigate an SIRS epidemic model with chronological age structure in a demographic steady state. Although the age-structured SIRS model is a simple extension of the well-known age-structured SIR epidemic model, we have to develop new technique to deal with problems due to the reversion of susceptibility for recovered individuals. First we give a standard proof for the well-posedness of the normalized age-structured SIRS model. Next we examine existence of endemic steady states by fixed point arguments and bifurcation method, where we introduce the next generation operator and the basic reproduction number $R_0$ to formulate endemic threshold results. Thirdly we investigate stability of steady states by the bifurcation calculation and the comparison method, and we show existence of a compact attractor and discuss the global behavior based on the population persistence theory. Finally we give some numerical examples and discuss the effect of mass-vaccination on $R_0$ and the critical coverage of immunization based on the reinfection threshold.


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