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Influence of Transfer Epidemiological Processes on the Formation of Endemic Equilibria in the Extended SEIS Model

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  • Alexander R. Karimov

    (Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13 Bd.2, Moscow 125412, Russia
    Department of Electrophysical Installations, Institute of Nuclear Physics, National Research Nuclear University MEPhI, Kashirskoye Shosse 31, Moscow 115409, Russia)

  • Michael A. Solomatin

    (Department of Electrophysical Installations, Institute of Nuclear Physics, National Research Nuclear University MEPhI, Kashirskoye Shosse 31, Moscow 115409, Russia)

  • Alexey N. Bocharov

    (Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya St. 13 Bd.2, Moscow 125412, Russia)

Abstract

In the present paper, a modification of the standard mean-field model is considered, allowing for the description of the formation of a dynamic equilibrium between infected and recovered persons in a population of constant size. The key point of this model is that it highlights two-infection transfer mechanisms depending on the physical nature of the contact between people. We separate the transfer mechanism related directly to the movement of people (the so-called transport processes) from the one occurring at zero relative speed of persons (the so-called social contacts). Under the framework of a physical chemical analogy, the dependencies for the infection transfer rate constants are proposed for both purely transport and social mechanisms of spread. These dependencies are used in discussing the formation of quasi-stationary states in the model, which can be interpreted as endemic equilibrium states. The stability of such endemic equilibria is studied by the method of Lyapunov function.

Suggested Citation

  • Alexander R. Karimov & Michael A. Solomatin & Alexey N. Bocharov, 2024. "Influence of Transfer Epidemiological Processes on the Formation of Endemic Equilibria in the Extended SEIS Model," Mathematics, MDPI, vol. 12(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3585-:d:1522127
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    References listed on IDEAS

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    1. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
    2. Stephen Eubank & Hasan Guclu & V. S. Anil Kumar & Madhav V. Marathe & Aravind Srinivasan & Zoltán Toroczkai & Nan Wang, 2004. "Modelling disease outbreaks in realistic urban social networks," Nature, Nature, vol. 429(6988), pages 180-184, May.
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