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SIR DYNAMICS WITH ECONOMICALLY DRIVEN CONTACT RATES
Benjamin R Morin1, Eli P Fenichel2, Carlos Castillo-Chavez3
1School 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.
Natural Resource Modeling
|August 26, 2014
Summary
This study analyzes the susceptible-infected-recovered (SIR) model with generalized nonlinear incidence. Including adaptive behavior reveals complex dynamics and multiple equilibria, shifting focus from standard incidence in epidemic modeling.
Area of Science:
- Epidemiology
- Mathematical Biology
- Complex Systems
Background:
- The Susceptible-Infected-Recovered (SIR) model is a cornerstone of epidemiological analysis.
- Standard SIR models often employ simplified nonlinear incidence functions.
- Analyzing complex dynamics requires advanced mathematical frameworks.
Purpose of the Study:
- To adapt theorems for analyzing SIR models with generalized nonlinear incidence.
- To investigate the impact of adaptive behavioral responses on epidemic dynamics.
- To provide insights into epidemics as complex adaptive systems.
Main Methods:
- Adaptation of mathematical theorems for SIR model stability analysis.
- Application of theorems to standard and adaptive incidence structures.
- Analysis of epidemiological-economic incidence for complex dynamics.
Main Results:
- Demonstrated stability analysis for generalized nonlinear incidence in SIR models.
- Revealed that adaptive behavior can lead to multiple equilibria and oscillations.
- Identified nonlinearities driving complex epidemiological behavior.
Conclusions:
- Epidemics can be viewed as complex adaptive systems with nonlinear dynamics.
- Adaptive behavior significantly alters epidemic trajectories compared to standard incidence.
- Highlights the need for advanced models and research into complex epidemic dynamics.
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