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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| Format: | Online |
| Language: | English |
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Hindawi Publishing Corporation
2012
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3426294/ |
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pubmed-3426294 |
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pubmed-34262942012-08-27 Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos Santonja, F. Chen-Charpentier, B. Research Article 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. Hindawi Publishing Corporation 2012 2012-08-15 /pmc/articles/PMC3426294/ /pubmed/22927889 http://dx.doi.org/10.1155/2012/742086 Text en Copyright © 2012 F. Santonja and B. Chen-Charpentier. https://creativecommons.org/licenses/by/3.0/ 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. |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Santonja, F. Chen-Charpentier, B. |
| spellingShingle |
Santonja, F. Chen-Charpentier, B. Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos |
| author_facet |
Santonja, F. Chen-Charpentier, B. |
| author_sort |
Santonja, F. |
| 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 |
| 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. |
| publisher |
Hindawi Publishing Corporation |
| publishDate |
2012 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3426294/ |
| _version_ |
1611551856198156288 |