Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity
In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2021715?viewType=HTML |
| _version_ | 1819019591839383552 |
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| author | Yuhuai Zhang Xinsheng Ma Anwarud Din |
| author_facet | Yuhuai Zhang Xinsheng Ma Anwarud Din |
| author_sort | Yuhuai Zhang |
| collection | DOAJ |
| description | In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading. |
| first_indexed | 2024-12-21T03:37:45Z |
| format | Article |
| id | doaj.art-529c0fe70ea54731b8b5c8dc1d0ce76f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-21T03:37:45Z |
| publishDate | 2021-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-529c0fe70ea54731b8b5c8dc1d0ce76f2022-12-21T19:17:17ZengAIMS PressAIMS Mathematics2473-69882021-08-01611123591237810.3934/math.2021715Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunityYuhuai Zhang0Xinsheng Ma1Anwarud Din21. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China2. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310012, China3. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaIn this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.https://aimspress.com/article/doi/10.3934/math.2021715?viewType=HTMLstochastic seiq modeltemporary immunityextinctionstationary distributiongeneral incidence function |
| spellingShingle | Yuhuai Zhang Xinsheng Ma Anwarud Din Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity AIMS Mathematics stochastic seiq model temporary immunity extinction stationary distribution general incidence function |
| title | Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity |
| title_full | Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity |
| title_fullStr | Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity |
| title_full_unstemmed | Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity |
| title_short | Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity |
| title_sort | stationary distribution and extinction of a stochastic seiq epidemic model with a general incidence function and temporary immunity |
| topic | stochastic seiq model temporary immunity extinction stationary distribution general incidence function |
| url | https://aimspress.com/article/doi/10.3934/math.2021715?viewType=HTML |
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