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Sustained oscillations via coherence resonance in SIR
Rachel Kuske1, Luis F Gordillo, Priscilla Greenwood
1Department of Mathematics, University of British Columbia, Canada. rachel@math.ubc.ca
Journal of Theoretical Biology
|December 19, 2006
Summary
This study uses multiple scale analysis to understand sustained oscillations in a stochastic SIR model. Coherence resonance drives nearly regular fluctuations in infected and susceptible populations.
Area of Science:
- Mathematical modeling
- Epidemiology
- Stochastic processes
Background:
- Stochastic SIR models exhibit complex dynamics.
- Understanding sustained oscillations is crucial for disease modeling.
- Deterministic and stochastic elements interact in epidemiological models.
Purpose of the Study:
- To analyze sustained oscillations in a stochastic SIR model.
- To develop a new multiple scale analysis method.
- To identify the phenomenon driving population dynamics.
Main Methods:
- Application of a novel multiple scale analysis.
- Explicit construction of a stochastic amplitude equation.
- Comparison of power spectral densities.
Main Results:
- The analysis captures the interplay between deterministic and stochastic factors.
- A stochastic amplitude equation describes population fluctuations.
- Power spectral density agreement confirms coherence resonance.
Conclusions:
- Coherence resonance is identified as the driving mechanism for oscillations.
- The study provides validity criteria for the approximation.
- Explicit parameter ranges for observing coherence resonance are given.
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