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Complex behaviour in a dengue model with a seasonally varying vector population
Timothy A McLennan-Smith1, Geoffry N Mercer1
1National Centre for Epidemiology and Population Health, Australian National University, Canberra, Australia.
Mathematical Biosciences
|December 3, 2013
Summary
This study developed a seasonal dengue fever model to understand disease transmission dynamics. Identifying chaotic behavior in the model improves predictions for future dengue outbreaks.
Area of Science:
- Mathematical modeling of infectious diseases
- Epidemiology
- Nonlinear dynamics
Background:
- Dengue fever and dengue hemorrhagic fever are significant global public health issues.
- Seasonal variations in rainfall and temperature influence dengue transmission via mosquito vectors.
Purpose of the Study:
- To develop and analyze a seasonally forced, multi-subclass dengue mathematical model.
- To investigate the presence of deterministic chaos within the model's parameter space.
- To assess how chaotic dynamics impact the model's predictive capabilities for dengue outbreaks.
Main Methods:
- Development of a compartment-based model using ordinary differential equations.
- Incorporation of seasonal forcing in the vector population and host demographics.
- Application of the 0-1 test for deterministic chaos to analyze long-term model behavior.
Main Results:
- The model exhibits various solution types, including isola n-cycle solutions preceding chaos.
- Deterministic chaos was identified in three distinct regions of the parameter space for the single subclass model.
- Understanding these chaotic regions enhances confidence in the seasonal model's predictive power.
Conclusions:
- The developed seasonal dengue model, incorporating deterministic chaos analysis, offers improved insights into disease dynamics.
- Knowledge of parameter regions associated with chaos is crucial for refining dengue outbreak prediction.
- This research contributes to a more robust understanding of factors influencing dengue transmission patterns.
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