Applications of occupancy urn models to epidemiology
This paper shows how occupancy urn models can be used to derive usefulresults in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is,the total number of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2009-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.509 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590199891165184 |
|---|---|
| author | Carlos M. Hernández-Suárez Oliver Mendoza-Cano |
| author_facet | Carlos M. Hernández-Suárez Oliver Mendoza-Cano |
| author_sort | Carlos M. Hernández-Suárez |
| collection | DOAJ |
| description | This paper shows how occupancy urn models can be used to derive usefulresults in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is,the total number of infected at the end of an outbreak. We also use this approach to derive point and interval estimates of the Basic Reproduction Ratio, $R_{0}$. We show that this construction does not require that the underlying SIR model be a homogeneousPoisson process, leading to a geometric distribution for the number ofcontacts before removal, but instead it supports a generaldistribution. The urn model construction is easy to handle and represents a rich field for further exploitation. |
| format | Article |
| id | doaj-art-905f9b88acd54bc5b06fcf4db4a8b0ce |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-905f9b88acd54bc5b06fcf4db4a8b0ce2025-01-24T01:59:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016350952010.3934/mbe.2009.6.509Applications of occupancy urn models to epidemiologyCarlos M. Hernández-Suárez0Oliver Mendoza-Cano1Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaFacultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaThis paper shows how occupancy urn models can be used to derive usefulresults in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is,the total number of infected at the end of an outbreak. We also use this approach to derive point and interval estimates of the Basic Reproduction Ratio, $R_{0}$. We show that this construction does not require that the underlying SIR model be a homogeneousPoisson process, leading to a geometric distribution for the number ofcontacts before removal, but instead it supports a generaldistribution. The urn model construction is easy to handle and represents a rich field for further exploitation.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.509urn models; $r_{0}$; basic reproductive ratio; stochastic epidemic models. |
| spellingShingle | Carlos M. Hernández-Suárez Oliver Mendoza-Cano Applications of occupancy urn models to epidemiology Mathematical Biosciences and Engineering urn models; $r_{0}$; basic reproductive ratio; stochastic epidemic models. |
| title | Applications of occupancy urn models to epidemiology |
| title_full | Applications of occupancy urn models to epidemiology |
| title_fullStr | Applications of occupancy urn models to epidemiology |
| title_full_unstemmed | Applications of occupancy urn models to epidemiology |
| title_short | Applications of occupancy urn models to epidemiology |
| title_sort | applications of occupancy urn models to epidemiology |
| topic | urn models; $r_{0}$; basic reproductive ratio; stochastic epidemic models. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.509 |
| work_keys_str_mv | AT carlosmhernandezsuarez applicationsofoccupancyurnmodelstoepidemiology AT olivermendozacano applicationsofoccupancyurnmodelstoepidemiology |