Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic
In this study, a deterministic SEQIR model with standard incidence and the corresponding stochastic epidemic model are explored. In the deterministic model, the reproduction number is given, and the local asymptotic stability of the equilibria is proved. When the reproduction number is less than uni...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6125064 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558049953316864 |
|---|---|
| author | Shijie Liu Maoxing Liu |
| author_facet | Shijie Liu Maoxing Liu |
| author_sort | Shijie Liu |
| collection | DOAJ |
| description | In this study, a deterministic SEQIR model with standard incidence and the corresponding stochastic epidemic model are explored. In the deterministic model, the reproduction number is given, and the local asymptotic stability of the equilibria is proved. When the reproduction number is less than unity, the disease-free equilibrium is locally asymptotically stable, whereas the endemic equilibrium is locally asymptotically stable in the case of a reproduction number greater than unity. A stochastic expansion based on a deterministic model is studied to explore the uncertainty of the spread of infectious diseases. Using the Lyapunov function method, the existence and uniqueness of a global positive solution are considered. Then, the extinction conditions of the epidemic and its asymptotic property around the endemic equilibrium are obtained. To demonstrate the application of this model, a case study based on COVID-19 epidemic data from France, Italy, and the UK is presented, together with numerical simulations using given parameters. |
| format | Article |
| id | doaj-art-9b1407969db141b8a0f6b404d41b269a |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9b1407969db141b8a0f6b404d41b269a2025-02-03T01:33:21ZengWileyDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/6125064Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 PandemicShijie Liu0Maoxing Liu1Department of MathematicsDepartment of MathematicsIn this study, a deterministic SEQIR model with standard incidence and the corresponding stochastic epidemic model are explored. In the deterministic model, the reproduction number is given, and the local asymptotic stability of the equilibria is proved. When the reproduction number is less than unity, the disease-free equilibrium is locally asymptotically stable, whereas the endemic equilibrium is locally asymptotically stable in the case of a reproduction number greater than unity. A stochastic expansion based on a deterministic model is studied to explore the uncertainty of the spread of infectious diseases. Using the Lyapunov function method, the existence and uniqueness of a global positive solution are considered. Then, the extinction conditions of the epidemic and its asymptotic property around the endemic equilibrium are obtained. To demonstrate the application of this model, a case study based on COVID-19 epidemic data from France, Italy, and the UK is presented, together with numerical simulations using given parameters.http://dx.doi.org/10.1155/2021/6125064 |
| spellingShingle | Shijie Liu Maoxing Liu Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic Discrete Dynamics in Nature and Society |
| title | Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic |
| title_full | Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic |
| title_fullStr | Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic |
| title_full_unstemmed | Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic |
| title_short | Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic |
| title_sort | dynamic analysis of a stochastic seqir model and application in the covid 19 pandemic |
| url | http://dx.doi.org/10.1155/2021/6125064 |
| work_keys_str_mv | AT shijieliu dynamicanalysisofastochasticseqirmodelandapplicationinthecovid19pandemic AT maoxingliu dynamicanalysisofastochasticseqirmodelandapplicationinthecovid19pandemic |