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Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

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  • Toshikazu Kuniya

    (Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan)

Abstract

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings.

Suggested Citation

  • Toshikazu Kuniya, 2018. "Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs," Mathematics, MDPI, vol. 6(9), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:147-:d:165434
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    References listed on IDEAS

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    1. Christina E. Mills & James M. Robins & Marc Lipsitch, 2004. "Transmissibility of 1918 pandemic influenza," Nature, Nature, vol. 432(7019), pages 904-906, December.
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