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Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model

Journal of Mathematical Biology volume 54, Article number: 101 (2007) Cite this article

Abstract

In this paper, we develop a new approach to deal with asymptotic behavior of the age-structured homogeneous epidemic systems and discuss its application to the MSEIR epidemic model. For the homogeneous system, there is no attracting nontrivial equilibrium, instead we have to examine existence and stability of persistent solutions. Assuming that the host population dynamics can be described by the stable population model, we rewrite the basic system into the system of ratio age distribution, which is the age profile divided by the stable age profile. If the host population has the stable age profile, the ratio age distribution system is reduced to the normalized system. Then we prove the stability principle that the local stability or instability of steady states of the normalized system implies that of the corresponding persistent solutions of the original homogeneous system. In the latter half of this paper, we prove the threshold and stability results for the normalized system of the age-structured MSEIR epidemic model.

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  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan

    Hisashi Inaba

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  1. Hisashi Inaba
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Inaba, H. Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model. J. Math. Biol. 54, 101 (2007). https://doi.org/10.1007/s00285-006-0033-y

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  • DOI: https://doi.org/10.1007/s00285-006-0033-y

Keywords

  • Homogeneous epidemic system
  • Stable population
  • Stability principle
  • Basic reproduction ratio
  • Endemic steady state

Mathematical Subject Classification (2000)

  • 92D30
  • 92D25