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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 742086, 8 pages
http://dx.doi.org/10.1155/2012/742086
Research Article

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

1Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
2Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA

Received 8 May 2012; Revised 25 June 2012; Accepted 3 July 2012

Academic Editor: Thierry Busso

Copyright © 2012 F. Santonja and B. Chen-Charpentier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model.