An application of queuing theory to SIS and SEIS epidemic models
In this work we consider every individual of a population to be a server whose state can be either busy (infected) or idle (susceptible). This server approach allows to consider a general distribution for the duration of the infectious state, instead of being restricted to exponential distributions....
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| Format: | Article |
| Language: | English |
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AIMS Press
2010-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.809 |
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| author | Carlos M. Hernández-Suárez Carlos Castillo-Chavez Osval Montesinos López Karla Hernández-Cuevas |
| author_facet | Carlos M. Hernández-Suárez Carlos Castillo-Chavez Osval Montesinos López Karla Hernández-Cuevas |
| author_sort | Carlos M. Hernández-Suárez |
| collection | DOAJ |
| description | In this work we consider every individual of a population to be a server whose state can be either busy (infected) or idle (susceptible). This server approach allows to consider a general distribution for the duration of the infectious state, instead of being restricted to exponential distributions. In order to achieve this we first derive new approximations to quasistationary distribution (QSD) of SIS (Susceptible- Infected- Susceptible) and SEIS (Susceptible- Latent- Infected- Susceptible) stochastic epidemic models. We give an expression that relates the basic reproductive number, $R_0$ and the server utilization, $\rho$. |
| format | Article |
| id | doaj-art-6ec9a6ea348849e5a41d9d172b8e6635 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6ec9a6ea348849e5a41d9d172b8e66352025-01-24T02:00:58ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-09-017480982310.3934/mbe.2010.7.809An application of queuing theory to SIS and SEIS epidemic modelsCarlos M. Hernández-Suárez0Carlos Castillo-Chavez1Osval Montesinos López2Karla Hernández-Cuevas3Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaFacultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaFacultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaFacultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, ColimaIn this work we consider every individual of a population to be a server whose state can be either busy (infected) or idle (susceptible). This server approach allows to consider a general distribution for the duration of the infectious state, instead of being restricted to exponential distributions. In order to achieve this we first derive new approximations to quasistationary distribution (QSD) of SIS (Susceptible- Infected- Susceptible) and SEIS (Susceptible- Latent- Infected- Susceptible) stochastic epidemic models. We give an expression that relates the basic reproductive number, $R_0$ and the server utilization, $\rho$.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.809sis; seis; queuing theory; $r_{0}$; basic reproductive number; stochastic epidemic models. |
| spellingShingle | Carlos M. Hernández-Suárez Carlos Castillo-Chavez Osval Montesinos López Karla Hernández-Cuevas An application of queuing theory to SIS and SEIS epidemic models Mathematical Biosciences and Engineering sis; seis; queuing theory; $r_{0}$; basic reproductive number; stochastic epidemic models. |
| title | An application of queuing theory to SIS and SEIS epidemic models |
| title_full | An application of queuing theory to SIS and SEIS epidemic models |
| title_fullStr | An application of queuing theory to SIS and SEIS epidemic models |
| title_full_unstemmed | An application of queuing theory to SIS and SEIS epidemic models |
| title_short | An application of queuing theory to SIS and SEIS epidemic models |
| title_sort | application of queuing theory to sis and seis epidemic models |
| topic | sis; seis; queuing theory; $r_{0}$; basic reproductive number; stochastic epidemic models. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.809 |
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