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.

Original languageEnglish (US)
Pages (from-to)505-525
Number of pages21
JournalNatural Resource Modeling
Volume26
Issue number4
DOIs
StatePublished - Nov 2013

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Incidence
Nonlinear Incidence
Contact
Epidemiology
Economics
Control nonlinearities
economic theory
Adaptive systems
epidemiology
behavioral response
Multiple Equilibria
Adaptive Behavior
nonlinearity
Adaptive Dynamics
Adaptive Systems
Complex Dynamics
Theorem
Instant
Parameter Space
Complex Systems

Keywords

  • Adaptive behavior
  • Economic-epidemiology
  • Nonlinear incidence

ASJC Scopus subject areas

  • Modeling and Simulation
  • Environmental Science (miscellaneous)

Cite this

Sir Dynamics With Economically Driven Contact Rates. / Morin, Benjamin R.; Fenichel, Eli P.; Castillo-Chavez, Carlos.

In: Natural Resource Modeling, Vol. 26, No. 4, 11.2013, p. 505-525.

Research output: Contribution to journalArticle

Morin, Benjamin R. ; Fenichel, Eli P. ; Castillo-Chavez, Carlos. / Sir Dynamics With Economically Driven Contact Rates. In: Natural Resource Modeling. 2013 ; Vol. 26, No. 4. pp. 505-525.
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