SIR DYNAMICS WITH ECONOMICALLY DRIVEN CONTACT RATES

Authors

  • BENJAMIN R. MORIN,

    Corresponding author
    1. School of Human Evolution and Social Change, Arizona State University, Tempe, USA
    2. Mathematical and Computational Modeling Sciences Center, Arizona State University, Tempe, AZ
    • Corresponding author. Benjamin R. Morin, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85282, e-mail: brmorin@asu.edu

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  • ELI P. FENICHEL,

    1. School of Life Sciences, Arizona State University, Tempe, AZ
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  • CARLOS CASTILLO-CHAVEZ

    1. School of Human Evolution and Social Change, Arizona State University, Tempe
    2. Mathematical and Computational Modeling Sciences Center, Arizona State University, Santa Fe Institute, Tempe, AZ 85287, Santa Fe, NM 87501
    3. Adjunct Professor, Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853
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  • We dedicate this article to Kenneth Cooke who passed away on August 25, 2007 at the age of 82.

Abstract

The susceptible-infected-recovered (SIR) model has greatly evidenced epidemiology despite its apparent simplicity. Most applications of the SIR framework use a form of nonlinear incidence to describe the number of new cases per instant. We adapt theorems to analyze the stability of SIR models with a generalized nonlinear incidence structure. These theorems are then applied to the case of standard incidence and incidence resulting from adaptive behavioral response based on epidemiological-economic theory. When adaptive behavior is included in the SIR model multiple equilibria and oscillatory epidemiological dynamics can occur over a greater parameter space. Our analysis, based on the epidemiological-economic incidence, provides new insights into epidemics as complex adaptive systems, highlights important nonlinearities that lead to complex behavior, and provides mechanistic motivation for a shift away from standard incidence, and outlines important areas of research related to the complex-adaptive dynamics of epidemics.

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