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 language | English (US) |
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Pages (from-to) | 505-525 |
Number of pages | 21 |
Journal | Natural Resource Modeling |
Volume | 26 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2013 |
Keywords
- Adaptive behavior
- Economic-epidemiology
- Nonlinear incidence
ASJC Scopus subject areas
- Modeling and Simulation
- Environmental Science (miscellaneous)