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Resistance mechanisms matter in SIR models
Timothy C Reluga1, Jan Medlock
1Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. timothy@reluga.org
Mathematical Biosciences and Engineering : MBE
|July 31, 2007
Summary
Four disease models considering temporary or partial resistance were compared. Behavioral resistance can cause complex dynamics like bistability, unlike immune resistance, highlighting the need for accurate modeling assumptions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Immunology
Background:
- SIR-style models are crucial for understanding infectious disease dynamics.
- Disease resistance can stem from behavioral changes or immunological responses, and may be partial or temporary.
- Understanding these resistance mechanisms is key to accurate pandemic preparedness.
Purpose of the Study:
- To compare four SIR-style models of disease resistance.
- To investigate the impact of behavioral versus immunological resistance on disease dynamics.
- To identify conditions leading to complex dynamics like backward bifurcations and bistability.
Main Methods:
- Comparative analysis of four compartmental epidemiological models.
- Exploration of parameter regions relevant to interpandemic influenza.
- Mathematical investigation of model behavior, focusing on bifurcations and stability.
Main Results:
- Backward bifurcations and bistability were observed in models where resistance is behavioral.
- These complex dynamics were not found when resistance was modeled as purely immunological.
- Model outcomes are sensitive to the specific assumptions made about the nature of resistance.
Conclusions:
- Modeling assumptions regarding disease resistance significantly impact epidemiological predictions.
- Behavioral resistance introduces complexities not present with immunological resistance alone.
- Future modeling efforts must align resistance mechanisms with biological realities for accurate forecasting.
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