Quarantine and Vaccination in Hierarchical Epidemic Model
The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1450 |
| _version_ | 1827748838077628416 |
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| author | Elena Gubar Vladislav Taynitskiy Denis Fedyanin Ilya Petrov |
| author_facet | Elena Gubar Vladislav Taynitskiy Denis Fedyanin Ilya Petrov |
| author_sort | Elena Gubar |
| collection | DOAJ |
| description | The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained. |
| first_indexed | 2024-03-11T06:13:33Z |
| format | Article |
| id | doaj.art-9c8175df94c64a7881ac75f31a4ab847 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:33Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9c8175df94c64a7881ac75f31a4ab8472023-11-17T12:28:48ZengMDPI AGMathematics2227-73902023-03-01116145010.3390/math11061450Quarantine and Vaccination in Hierarchical Epidemic ModelElena Gubar0Vladislav Taynitskiy1Denis Fedyanin2Ilya Petrov3Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg 198504, RussiaFaculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg 198504, RussiaV. A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, RussiaV. A. Trapeznikov Institute of Control Sciences of RAS, Moscow 117997, RussiaThe analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained.https://www.mdpi.com/2227-7390/11/6/1450epidemic processcompartment epidemic modelsSEIRD modeloptimal controlvaccination |
| spellingShingle | Elena Gubar Vladislav Taynitskiy Denis Fedyanin Ilya Petrov Quarantine and Vaccination in Hierarchical Epidemic Model Mathematics epidemic process compartment epidemic models SEIRD model optimal control vaccination |
| title | Quarantine and Vaccination in Hierarchical Epidemic Model |
| title_full | Quarantine and Vaccination in Hierarchical Epidemic Model |
| title_fullStr | Quarantine and Vaccination in Hierarchical Epidemic Model |
| title_full_unstemmed | Quarantine and Vaccination in Hierarchical Epidemic Model |
| title_short | Quarantine and Vaccination in Hierarchical Epidemic Model |
| title_sort | quarantine and vaccination in hierarchical epidemic model |
| topic | epidemic process compartment epidemic models SEIRD model optimal control vaccination |
| url | https://www.mdpi.com/2227-7390/11/6/1450 |
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