Final and peak epidemic sizes for SEIR models with quarantine and isolation
Two $SEIR$ models with quarantine and isolation are considered, inwhich the latent and infectious periods are assumed to have anexponential and gamma distribution, respectively. Previous studieshave suggested (based on numerical observations) that a gammadistribution model (GDM) tends to predict a l...
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AIMS Press
2007-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.675 |
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| author | Z. Feng |
| author_facet | Z. Feng |
| author_sort | Z. Feng |
| collection | DOAJ |
| description | Two $SEIR$ models with quarantine and isolation are considered, inwhich the latent and infectious periods are assumed to have anexponential and gamma distribution, respectively. Previous studieshave suggested (based on numerical observations) that a gammadistribution model (GDM) tends to predict a larger epidemic peakvalue and shorter duration than an exponential distribution model(EDM). By deriving analytic formulas for the maximum and finalepidemic sizes of the two models, we demonstrate that either GDM orEDM may predict a larger epidemic peak or final epidemic size,depending on control measures. These formulas are helpful not onlyfor understanding how model assumptions may affect the predictions,but also for confirming that it is important to assume realisticdistributions of latent and infectious periods when the model isused for public health policy making. |
| format | Article |
| id | doaj-art-fd1ad5aa8e984ee5af433e2ef3c2dc77 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-fd1ad5aa8e984ee5af433e2ef3c2dc772025-01-24T01:54:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-07-014467568610.3934/mbe.2007.4.675Final and peak epidemic sizes for SEIR models with quarantine and isolationZ. Feng0Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395Two $SEIR$ models with quarantine and isolation are considered, inwhich the latent and infectious periods are assumed to have anexponential and gamma distribution, respectively. Previous studieshave suggested (based on numerical observations) that a gammadistribution model (GDM) tends to predict a larger epidemic peakvalue and shorter duration than an exponential distribution model(EDM). By deriving analytic formulas for the maximum and finalepidemic sizes of the two models, we demonstrate that either GDM orEDM may predict a larger epidemic peak or final epidemic size,depending on control measures. These formulas are helpful not onlyfor understanding how model assumptions may affect the predictions,but also for confirming that it is important to assume realisticdistributions of latent and infectious periods when the model isused for public health policy making.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.675disease control.final epidemic sizepeakepidemic sizeinfectious diseasesmathematical model |
| spellingShingle | Z. Feng Final and peak epidemic sizes for SEIR models with quarantine and isolation Mathematical Biosciences and Engineering disease control. final epidemic size peakepidemic size infectious diseases mathematical model |
| title | Final and peak epidemic sizes for SEIR models with quarantine and isolation |
| title_full | Final and peak epidemic sizes for SEIR models with quarantine and isolation |
| title_fullStr | Final and peak epidemic sizes for SEIR models with quarantine and isolation |
| title_full_unstemmed | Final and peak epidemic sizes for SEIR models with quarantine and isolation |
| title_short | Final and peak epidemic sizes for SEIR models with quarantine and isolation |
| title_sort | final and peak epidemic sizes for seir models with quarantine and isolation |
| topic | disease control. final epidemic size peakepidemic size infectious diseases mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.675 |
| work_keys_str_mv | AT zfeng finalandpeakepidemicsizesforseirmodelswithquarantineandisolation |