Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence
We studied a class of a stochastic hybrid SIQRS model with nonlinear incidence and vertical transmission and obtained a threshold $ \Delta $ to distinguish behaviors of the model. Concretely, the disease was extinct exponentially when $ \Delta < 0 $. If $ \Delta > 0 $, the model we dis...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024613?viewType=HTML |
| _version_ | 1797206079892881408 |
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| author | Shan Wang Feng Wang |
| author_facet | Shan Wang Feng Wang |
| author_sort | Shan Wang |
| collection | DOAJ |
| description | We studied a class of a stochastic hybrid SIQRS model with nonlinear incidence and vertical transmission and obtained a threshold $ \Delta $ to distinguish behaviors of the model. Concretely, the disease was extinct exponentially when $ \Delta < 0 $. If $ \Delta > 0 $, the model we discussed admitted an invariant measure. A new class of the Lyapunov function was constructed in proving the latter conclusion. Some remarks were presented to shed light on the major results. Finally, several numerical simulations were provided to test the reached results. |
| first_indexed | 2024-04-24T09:01:19Z |
| format | Article |
| id | doaj.art-f7386a879ad04608a0036f598f565202 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T09:01:19Z |
| publishDate | 2024-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f7386a879ad04608a0036f598f5652022024-04-16T01:28:41ZengAIMS PressAIMS Mathematics2473-69882024-04-0195125291254910.3934/math.2024613Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidenceShan Wang0Feng Wang11. Department of Mathematics, Pingxiang University, Pingxiang 337000, China1. Department of Mathematics, Pingxiang University, Pingxiang 337000, China 2. School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaWe studied a class of a stochastic hybrid SIQRS model with nonlinear incidence and vertical transmission and obtained a threshold $ \Delta $ to distinguish behaviors of the model. Concretely, the disease was extinct exponentially when $ \Delta < 0 $. If $ \Delta > 0 $, the model we discussed admitted an invariant measure. A new class of the Lyapunov function was constructed in proving the latter conclusion. Some remarks were presented to shed light on the major results. Finally, several numerical simulations were provided to test the reached results.https://www.aimspress.com/article/doi/10.3934/math.2024613?viewType=HTMLstochastic siqrs modelvertical transmissionextinctioninvariant measure |
| spellingShingle | Shan Wang Feng Wang Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence AIMS Mathematics stochastic siqrs model vertical transmission extinction invariant measure |
| title | Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence |
| title_full | Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence |
| title_fullStr | Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence |
| title_full_unstemmed | Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence |
| title_short | Asymptotic behavior of a stochastic hybrid SIQRS model with vertical transmission and nonlinear incidence |
| title_sort | asymptotic behavior of a stochastic hybrid siqrs model with vertical transmission and nonlinear incidence |
| topic | stochastic siqrs model vertical transmission extinction invariant measure |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024613?viewType=HTML |
| work_keys_str_mv | AT shanwang asymptoticbehaviorofastochastichybridsiqrsmodelwithverticaltransmissionandnonlinearincidence AT fengwang asymptoticbehaviorofastochastichybridsiqrsmodelwithverticaltransmissionandnonlinearincidence |