Global stability of a multi-group delayed epidemic model with logistic growth
In this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231173?viewType=HTML |
| _version_ | 1797751979573772288 |
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| author | B. M. Almuqati F. M. Allehiany |
| author_facet | B. M. Almuqati F. M. Allehiany |
| author_sort | B. M. Almuqati |
| collection | DOAJ |
| description | In this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has a crusher role in the global stability of a disease-free and endemic equilibria. That is, if $ \mathcal{R}_0 $ is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable, whereas, if $ \mathcal{R}_0 $ is greater than one, then a unique endemic equilibrium exists and is globally asymptotically stable. In addition, we construct suitable Lyapunov functions to investigate the global stability of disease-free and endemic equilibria. Finally, we introduce numerical simulations of the model. |
| first_indexed | 2024-03-12T16:57:31Z |
| format | Article |
| id | doaj.art-3b387fa9d06a4a829ad4c6e5a7dd8490 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T16:57:31Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3b387fa9d06a4a829ad4c6e5a7dd84902023-08-08T01:26:54ZengAIMS PressAIMS Mathematics2473-69882023-07-01810230462306110.3934/math.20231173Global stability of a multi-group delayed epidemic model with logistic growthB. M. Almuqati0F. M. Allehiany1Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaDepartment of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaIn this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has a crusher role in the global stability of a disease-free and endemic equilibria. That is, if $ \mathcal{R}_0 $ is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable, whereas, if $ \mathcal{R}_0 $ is greater than one, then a unique endemic equilibrium exists and is globally asymptotically stable. In addition, we construct suitable Lyapunov functions to investigate the global stability of disease-free and endemic equilibria. Finally, we introduce numerical simulations of the model.https://www.aimspress.com/article/doi/10.3934/math.20231173?viewType=HTMLmulti-group epidemic modeldelay distributionglobal stabilitylyapunov functionslogistic growth |
| spellingShingle | B. M. Almuqati F. M. Allehiany Global stability of a multi-group delayed epidemic model with logistic growth AIMS Mathematics multi-group epidemic model delay distribution global stability lyapunov functions logistic growth |
| title | Global stability of a multi-group delayed epidemic model with logistic growth |
| title_full | Global stability of a multi-group delayed epidemic model with logistic growth |
| title_fullStr | Global stability of a multi-group delayed epidemic model with logistic growth |
| title_full_unstemmed | Global stability of a multi-group delayed epidemic model with logistic growth |
| title_short | Global stability of a multi-group delayed epidemic model with logistic growth |
| title_sort | global stability of a multi group delayed epidemic model with logistic growth |
| topic | multi-group epidemic model delay distribution global stability lyapunov functions logistic growth |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231173?viewType=HTML |
| work_keys_str_mv | AT bmalmuqati globalstabilityofamultigroupdelayedepidemicmodelwithlogisticgrowth AT fmallehiany globalstabilityofamultigroupdelayedepidemicmodelwithlogisticgrowth |