title: SIR DYNAMICS WITH ECONOMICALLY DRIVEN CONTACT RATES.
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.
authors.affiliation: School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85282, USA; Mathematical and Computational Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287.
authors.forename: Benjamin R
authors.initials: BR
authors.lastname: Morin
authors.affiliation: School of Life Sciences, Arizona State University, Tempe, AZ.
authors.forename: Eli P
authors.initials: EP
authors.lastname: Fenichel
authors.affiliation: School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85282; Mathematical and Computational Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287; Santa Fe Institute, SFI, 1399 Hyde Park Road, Santa Fe, NM 87501; Adjunct Professor, Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853.
authors.forename: Carlos
authors.initials: C
authors.lastname: Castillo-Chavez
keywords: Economic-epidemiology; adaptive behavior; nonlinear incidence