Parameter estimation and uncertainty quantification for an epidemic model
We examine estimation of the parameters of Susceptible-Infective-Recovered(SIR) models in the context of least squares. We review the use ofasymptotic statistical theory and sensitivity analysis to obtain measuresof uncertainty for estimates of the model parameters and the basicreproductive number...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.553 |
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| author | Alex Capaldi Samuel Behrend Benjamin Berman Jason Smith Justin Wright Alun L. Lloyd |
| author_facet | Alex Capaldi Samuel Behrend Benjamin Berman Jason Smith Justin Wright Alun L. Lloyd |
| author_sort | Alex Capaldi |
| collection | DOAJ |
| description | We examine estimation of the parameters of Susceptible-Infective-Recovered(SIR) models in the context of least squares. We review the use ofasymptotic statistical theory and sensitivity analysis to obtain measuresof uncertainty for estimates of the model parameters and the basicreproductive number ($R_0$)---an epidemiologically significant parametergrouping. We find that estimates of different parameters, such as thetransmission parameter and recovery rate, are correlated, with themagnitude and sign of this correlation depending on the value of $R_0$.Situations are highlighted in which this correlation allows $R_0$ to be estimated with greater ease than its constituentparameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used toinvestigate how the frequency at which data is sampled affects theestimation process and how the accuracy and uncertainty of estimatesimproves as data is collected over the course of an outbreak. We assessthe informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. Thistechnique can be used to design data sampling schemes in more generalcontexts. |
| format | Article |
| id | doaj-art-9faf36e91c024b9cae66021cad19dd67 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9faf36e91c024b9cae66021cad19dd672025-01-24T02:07:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-06-019355357610.3934/mbe.2012.9.553Parameter estimation and uncertainty quantification for an epidemic modelAlex Capaldi0Samuel Behrend1Benjamin Berman2Jason Smith3Justin Wright4Alun L. Lloyd5Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383Center for Quantitative Sciences in Biomedicine and Department of Mathematics, North Carolina State University, Raleigh, NC 27695, and Department of Mathematics & Computer Science, Valparaiso University, 1900 Chapel Drive, Valparaiso, IN 46383We examine estimation of the parameters of Susceptible-Infective-Recovered(SIR) models in the context of least squares. We review the use ofasymptotic statistical theory and sensitivity analysis to obtain measuresof uncertainty for estimates of the model parameters and the basicreproductive number ($R_0$)---an epidemiologically significant parametergrouping. We find that estimates of different parameters, such as thetransmission parameter and recovery rate, are correlated, with themagnitude and sign of this correlation depending on the value of $R_0$.Situations are highlighted in which this correlation allows $R_0$ to be estimated with greater ease than its constituentparameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used toinvestigate how the frequency at which data is sampled affects theestimation process and how the accuracy and uncertainty of estimatesimproves as data is collected over the course of an outbreak. We assessthe informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. Thistechnique can be used to design data sampling schemes in more generalcontexts.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.553parameter identifiability.inverse problemsensitivity analysissampling methodsasymptotic statistical theory |
| spellingShingle | Alex Capaldi Samuel Behrend Benjamin Berman Jason Smith Justin Wright Alun L. Lloyd Parameter estimation and uncertainty quantification for an epidemic model Mathematical Biosciences and Engineering parameter identifiability. inverse problem sensitivity analysis sampling methods asymptotic statistical theory |
| title | Parameter estimation and uncertainty quantification for an epidemic model |
| title_full | Parameter estimation and uncertainty quantification for an epidemic model |
| title_fullStr | Parameter estimation and uncertainty quantification for an epidemic model |
| title_full_unstemmed | Parameter estimation and uncertainty quantification for an epidemic model |
| title_short | Parameter estimation and uncertainty quantification for an epidemic model |
| title_sort | parameter estimation and uncertainty quantification for an epidemic model |
| topic | parameter identifiability. inverse problem sensitivity analysis sampling methods asymptotic statistical theory |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.553 |
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