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Uncertainty quantification in simulations of epidemics using polynomial chaos
F Santonja1, B Chen-Charpentier
1Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain. francisco.santonja@uv.es
Computational and Mathematical Methods in Medicine
|August 29, 2012
Summary
This study introduces a novel polynomial chaos approach for epidemiological models with random parameters. This method quantifies variability in transmission dynamics and identifies key influential factors in disease spread.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Mathematical models are crucial for studying epidemiological processes.
- Traditional models often assume deterministic parameters, which is unrealistic due to inherent variability.
- Randomness in transmission parameters significantly impacts disease dynamics.
Purpose of the Study:
- To apply the polynomial chaos approach to epidemiological models with ordinary differential equations and random coefficients.
- To incorporate the variability of transmission parameters into mathematical models.
- To analyze the impact of parameter uncertainty on epidemic outcomes.
Main Methods:
- Utilizing the polynomial chaos approach to handle random coefficients in ordinary differential equations.
- Deriving an auxiliary system of differential equations from the stochastic model.
- Numerically integrating the auxiliary system to compute first- and second-order moments of stochastic processes.
- Performing sensitivity analysis using the polynomial chaos approach.
Main Results:
- The polynomial chaos approach provides a method to analyze epidemiological models with random parameters.
- The approach yields an auxiliary system for numerical integration, enabling moment calculations.
- Sensitivity analysis identifies critical parameters influencing model outputs.
- Demonstrated application to an obesity epidemic model.
Conclusions:
- The polynomial chaos approach is a viable tool for modeling epidemiological systems with parameter uncertainty.
- This method enhances the understanding of disease transmission dynamics by accounting for randomness.
- The sensitivity analysis aids in identifying key drivers of epidemics, informing public health strategies.
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