Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization
This study establishes a compartment model for the categorized COVID-19 risk area. In this model, the compartments represent administrative regions at different transmission risk levels instead of individuals in traditional epidemic models. The county-level regions are partitioned into High-risk (H)...
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MDPI AG
2022-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/8/410 |
| _version_ | 1827627972011491328 |
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| author | Jiaji Pan Siqiang Sun Yixuan He Shen Ren Qing Li Zhongxiang Chen Hao Feng |
| author_facet | Jiaji Pan Siqiang Sun Yixuan He Shen Ren Qing Li Zhongxiang Chen Hao Feng |
| author_sort | Jiaji Pan |
| collection | DOAJ |
| description | This study establishes a compartment model for the categorized COVID-19 risk area. In this model, the compartments represent administrative regions at different transmission risk levels instead of individuals in traditional epidemic models. The county-level regions are partitioned into High-risk (H), Medium-risk (M), and Low-risk (L) areas dynamically according to the current number of confirmed cases. These risk areas are communicable by the movement of individuals. An LMH model is established with ordinary differential equations (ODEs). The basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> is derived for the transmission of risk areas to determine whether the pandemic is controlled. The stability of this LHM model is investigated by a Lyapunov function and Poincare–Bendixson theorem. We prove that the disease-free equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> < 1) is globally asymptotically stable and the disease will die out. The endemic equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> > 1) is locally and globally asymptotically stable, and the disease will become endemic. The numerical simulation and data analysis support the previous theoretical proofs. For the first time, the compartment model is applied to investigate the dynamics of the transmission of the COVID-19 risk area. This work should be of great value in the development of precision region-specific containment strategies. |
| first_indexed | 2024-03-09T13:24:17Z |
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| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T13:24:17Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-5e4413c007354f85a3566180319c27d12023-11-30T21:25:42ZengMDPI AGFractal and Fractional2504-31102022-07-016841010.3390/fractalfract6080410Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area CategorizationJiaji Pan0Siqiang Sun1Yixuan He2Shen Ren3Qing Li4Zhongxiang Chen5Hao Feng6College of Engineering and Design, Hunan Normal University, Changsha 410081, ChinaCollege of Engineering and Design, Hunan Normal University, Changsha 410081, ChinaState Key Laboratory of Developmental Biology of Freshwater Fish, College of Life Sciences, Hunan Normal University, Changsha 410081, ChinaCenter for Cryo-Biomedical Engineering and Artificial Organs, Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USACollege of Engineering and Design, Hunan Normal University, Changsha 410081, ChinaCollege of Engineering and Design, Hunan Normal University, Changsha 410081, ChinaState Key Laboratory of Developmental Biology of Freshwater Fish, College of Life Sciences, Hunan Normal University, Changsha 410081, ChinaThis study establishes a compartment model for the categorized COVID-19 risk area. In this model, the compartments represent administrative regions at different transmission risk levels instead of individuals in traditional epidemic models. The county-level regions are partitioned into High-risk (H), Medium-risk (M), and Low-risk (L) areas dynamically according to the current number of confirmed cases. These risk areas are communicable by the movement of individuals. An LMH model is established with ordinary differential equations (ODEs). The basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> is derived for the transmission of risk areas to determine whether the pandemic is controlled. The stability of this LHM model is investigated by a Lyapunov function and Poincare–Bendixson theorem. We prove that the disease-free equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> < 1) is globally asymptotically stable and the disease will die out. The endemic equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> > 1) is locally and globally asymptotically stable, and the disease will become endemic. The numerical simulation and data analysis support the previous theoretical proofs. For the first time, the compartment model is applied to investigate the dynamics of the transmission of the COVID-19 risk area. This work should be of great value in the development of precision region-specific containment strategies.https://www.mdpi.com/2504-3110/6/8/410COVID-19LMH epidemic modelLyapunov functionDulac criterionPoincare–Bendixson theoremdata analysis |
| spellingShingle | Jiaji Pan Siqiang Sun Yixuan He Shen Ren Qing Li Zhongxiang Chen Hao Feng Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization Fractal and Fractional COVID-19 LMH epidemic model Lyapunov function Dulac criterion Poincare–Bendixson theorem data analysis |
| title | Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization |
| title_full | Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization |
| title_fullStr | Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization |
| title_full_unstemmed | Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization |
| title_short | Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization |
| title_sort | dynamic behavior investigation of a novel epidemic model based on covid 19 risk area categorization |
| topic | COVID-19 LMH epidemic model Lyapunov function Dulac criterion Poincare–Bendixson theorem data analysis |
| url | https://www.mdpi.com/2504-3110/6/8/410 |
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