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Dynamic noise, chaos and parameter estimation in population biology
N Stollenwerk1, M Aguiar, S Ballesteros
1Centro de Matemática e Aplicações Fundamentais , Universidade de Lisboa, Avenida Prof. Gama Pinto 2, 1649-003 Lisbon , Portugal.
Interface Focus
|April 9, 2013
Summary
Parameter estimation for population dynamics models in epidemiology, including influenza and dengue fever, faces computational limits with complex models. Complex dengue models reveal interplay between randomness and deterministic chaos.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Biology
Background:
- Population biological dynamical systems are crucial for understanding disease spread.
- Parameter estimation calibrates these models using empirical time series data.
- Complex epidemiological models, like those for dengue fever, present significant computational challenges.
Purpose of the Study:
- To revisit and apply parameter estimation frameworks to population biological dynamical systems.
- To calibrate epidemiological models for influenza and dengue fever using time series data.
- To investigate the computational limits of advanced parameter estimation techniques for complex disease models.
Main Methods:
- Application of parameter estimation frameworks to population biological dynamical systems.
- Calibration of epidemiological models using empirical time series data (influenza, dengue fever).
- Utilizing maximum likelihood iterated filtering for parameter estimation in complex multi-strain models.
Main Results:
- Parameter estimation techniques reach computational limits with complex multi-strain dengue models.
- Initial parameter estimation for dengue fever in Thailand shows a nuanced interaction between stochasticity and the deterministic system.
- The underlying deterministic dengue model exhibits complex dynamics, including deterministic chaos and multiple attractor coexistence.
Conclusions:
- Advanced parameter estimation methods face computational hurdles for intricate epidemiological models.
- Stochasticity and deterministic dynamics play a subtle, interconnected role in dengue fever transmission.
- Deterministic models of dengue fever alone can display highly complex behaviors, suggesting inherent system complexity.
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