Optimal isolation strategies of emerging infectious diseases with limited resources
A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and...
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1691 |
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| _version_ | 1832590101465530368 |
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| author | Yinggao Zhou Jianhong Wu Min Wu |
| author_facet | Yinggao Zhou Jianhong Wu Min Wu |
| author_sort | Yinggao Zhou |
| collection | DOAJ |
| description | A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and obtainanalytic solutions for the optimal control problem that minimize the outbreak size under the assumptionof limited resources for isolation. These solutions and their corresponding optimal control policies arederived explicitly in terms of initial conditions, model parameters and resources for isolation (such as the number of intensive care units).With sufficient resources, the optimal control strategy is the normal Bang-Bangcontrol. However, with limited resources the optimal control strategy requires to switch totime-variant isolation at an optimal rate proportional to the ratio of isolated cases over the entire infected population once the maximum capacityis reached. |
| format | Article |
| id | doaj-art-1eb94ecca36948c49cb5cc204adc1e20 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1eb94ecca36948c49cb5cc204adc1e202025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61691170110.3934/mbe.2013.10.1691Optimal isolation strategies of emerging infectious diseases with limited resourcesYinggao Zhou0Jianhong Wu1Min Wu2School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083Centre for Disease Modeling, York University, 4700 Keele Street, Toronto, ON M3J1P3School of Information Science and Engineering, Central South University, Changsha, Hunan 410083A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and obtainanalytic solutions for the optimal control problem that minimize the outbreak size under the assumptionof limited resources for isolation. These solutions and their corresponding optimal control policies arederived explicitly in terms of initial conditions, model parameters and resources for isolation (such as the number of intensive care units).With sufficient resources, the optimal control strategy is the normal Bang-Bangcontrol. However, with limited resources the optimal control strategy requires to switch totime-variant isolation at an optimal rate proportional to the ratio of isolated cases over the entire infected population once the maximum capacityis reached.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1691limited resource.optimal controlisolationsir model |
| spellingShingle | Yinggao Zhou Jianhong Wu Min Wu Optimal isolation strategies of emerging infectious diseases with limited resources Mathematical Biosciences and Engineering limited resource. optimal control isolation sir model |
| title | Optimal isolation strategies of emerging infectious diseases with limited resources |
| title_full | Optimal isolation strategies of emerging infectious diseases with limited resources |
| title_fullStr | Optimal isolation strategies of emerging infectious diseases with limited resources |
| title_full_unstemmed | Optimal isolation strategies of emerging infectious diseases with limited resources |
| title_short | Optimal isolation strategies of emerging infectious diseases with limited resources |
| title_sort | optimal isolation strategies of emerging infectious diseases with limited resources |
| topic | limited resource. optimal control isolation sir model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1691 |
| work_keys_str_mv | AT yinggaozhou optimalisolationstrategiesofemerginginfectiousdiseaseswithlimitedresources AT jianhongwu optimalisolationstrategiesofemerginginfectiousdiseaseswithlimitedresources AT minwu optimalisolationstrategiesofemerginginfectiousdiseaseswithlimitedresources |