The estimation of the effective reproductive number from disease outbreak data
We consider a single outbreak susceptible-infected-recovered (SIR)model and corresponding estimation procedures for theeffective reproductive number $\mathcal{R}(t)$. We discuss theestimation of the underlying SIR parameters with ageneralized least squares (GLS) estimationtechnique. We do this in th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.261 |
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| author | Ariel Cintrón-Arias Carlos Castillo-Chávez Luís M. A. Bettencourt Alun L. Lloyd H. T. Banks |
| author_facet | Ariel Cintrón-Arias Carlos Castillo-Chávez Luís M. A. Bettencourt Alun L. Lloyd H. T. Banks |
| author_sort | Ariel Cintrón-Arias |
| collection | DOAJ |
| description | We consider a single outbreak susceptible-infected-recovered (SIR)model and corresponding estimation procedures for theeffective reproductive number $\mathcal{R}(t)$. We discuss theestimation of the underlying SIR parameters with ageneralized least squares (GLS) estimationtechnique. We do this in the context of appropriate statisticalmodels for the measurement process. We use asymptotic statisticaltheories to derive the mean and variance of the limiting(Gaussian) sampling distribution and to perform post statisticalanalysis of the inverse problems. We illustrate the ideas andpitfalls (e.g., large condition numbers on the correspondingFisher information matrix) with both synthetic and influenzaincidence data sets. |
| format | Article |
| id | doaj-art-2700f535b39f45eea1d7828e6cce3592 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2700f535b39f45eea1d7828e6cce35922025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016226128210.3934/mbe.2009.6.261The estimation of the effective reproductive number from disease outbreak dataAriel Cintrón-Arias0Carlos Castillo-Chávez1Luís M. A. Bettencourt2Alun L. Lloyd3H. T. Banks4Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695We consider a single outbreak susceptible-infected-recovered (SIR)model and corresponding estimation procedures for theeffective reproductive number $\mathcal{R}(t)$. We discuss theestimation of the underlying SIR parameters with ageneralized least squares (GLS) estimationtechnique. We do this in the context of appropriate statisticalmodels for the measurement process. We use asymptotic statisticaltheories to derive the mean and variance of the limiting(Gaussian) sampling distribution and to perform post statisticalanalysis of the inverse problems. We illustrate the ideas andpitfalls (e.g., large condition numbers on the correspondingFisher information matrix) with both synthetic and influenzaincidence data sets.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.261basic reproduction ratio$\mathcal{r}$reproduction numberparameter estimationgeneralized least squares$\mathcal{r}_0$residual plots.$\mathcal{r}(t)$effective reproductive number |
| spellingShingle | Ariel Cintrón-Arias Carlos Castillo-Chávez Luís M. A. Bettencourt Alun L. Lloyd H. T. Banks The estimation of the effective reproductive number from disease outbreak data Mathematical Biosciences and Engineering basic reproduction ratio $\mathcal{r}$ reproduction number parameter estimation generalized least squares $\mathcal{r}_0$ residual plots. $\mathcal{r}(t)$ effective reproductive number |
| title | The estimation of the effective reproductive number from disease outbreak data |
| title_full | The estimation of the effective reproductive number from disease outbreak data |
| title_fullStr | The estimation of the effective reproductive number from disease outbreak data |
| title_full_unstemmed | The estimation of the effective reproductive number from disease outbreak data |
| title_short | The estimation of the effective reproductive number from disease outbreak data |
| title_sort | estimation of the effective reproductive number from disease outbreak data |
| topic | basic reproduction ratio $\mathcal{r}$ reproduction number parameter estimation generalized least squares $\mathcal{r}_0$ residual plots. $\mathcal{r}(t)$ effective reproductive number |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.261 |
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