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Regular biennial cycles in epidemics caused by parametric resonance
Shiyang Chen1, Bogdan Epureanu1
1Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109, USA.
Biennial cycles in childhood infectious diseases like measles are driven by parametric resonance, a phenomenon arising from nonlinearity and seasonal forcing. Understanding these conditions helps predict disease outbreaks.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Childhood infectious diseases often exhibit multiyear cycles due to nonlinearity and seasonal forcing.
- Biennial (two-year) cycles are frequently observed in global measles incidence data.
Purpose of the Study:
- To elucidate the underlying mechanism of biennial cycles in infectious diseases.
- To identify conditions promoting large-amplitude biennial oscillations.
Main Methods:
- Utilized the SIR (Susceptible-Infectious-Recovered) model for disease dynamics.
- Employed the semi-analytical method of multiple scales (MMS) to analyze the system.
- Investigated the role of parametric resonance in generating biennial cycles.
Main Results:
- Demonstrated how parametric resonance emerges from the interplay of nonlinearity and periodic forcing.
- Derived the boundary defining resonance and non-resonance regions in parameter space.
- Assessed the influence of transmission, recovery, birth rates, seasonality amplitude, and stochasticity on resonance onset.
Conclusions:
- Parametric resonance is a key mechanism driving biennial oscillations in childhood infectious diseases.
- The study provides a framework for understanding and predicting disease periodicity based on system parameters.
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