Sir Dynamics With Economically Driven Contact Rates

Benjamin R. Morin, Eli P. Fenichel, Carlos Castillo-Chavez

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)505-525
Number of pages21
JournalNatural Resource Modeling
Issue number4
StatePublished - Nov 2013


  • Adaptive behavior
  • Economic-epidemiology
  • Nonlinear incidence

ASJC Scopus subject areas

  • Modeling and Simulation
  • Environmental Science (miscellaneous)


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