Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos
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 deter...
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Online Access: | http://dx.doi.org/10.1155/2012/742086 |
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doaj-288e9ed56bf546119955d9e643fe67892020-11-25T00:14:07ZengHindawi LimitedComputational and Mathematical Methods in Medicine1748-670X1748-67182012-01-01201210.1155/2012/742086742086Uncertainty Quantification in Simulations of Epidemics Using Polynomial ChaosF. Santonja0B. Chen-Charpentier1Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, SpainDepartment of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USAMathematical 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.http://dx.doi.org/10.1155/2012/742086 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
F. Santonja B. Chen-Charpentier |
spellingShingle |
F. Santonja B. Chen-Charpentier Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos Computational and Mathematical Methods in Medicine |
author_facet |
F. Santonja B. Chen-Charpentier |
author_sort |
F. Santonja |
title |
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
title_short |
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
title_full |
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
title_fullStr |
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
title_full_unstemmed |
Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
title_sort |
uncertainty quantification in simulations of epidemics using polynomial chaos |
publisher |
Hindawi Limited |
series |
Computational and Mathematical Methods in Medicine |
issn |
1748-670X 1748-6718 |
publishDate |
2012-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2012/742086 |
work_keys_str_mv |
AT fsantonja uncertaintyquantificationinsimulationsofepidemicsusingpolynomialchaos AT bchencharpentier uncertaintyquantificationinsimulationsofepidemicsusingpolynomialchaos |
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