SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis
In this paper, we developed a SIRV epidemic model based on a vaccination game, incorporating vaccination dynamics and data memory effects using the Caputo fractional derivative. This approach effectively captured the nonlocal and power-law characteristics of influenza transmission. We confirmed the...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024318 |
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| _version_ | 1832590751981109248 |
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| author | Qun Dai Zeheng Wang |
| author_facet | Qun Dai Zeheng Wang |
| author_sort | Qun Dai |
| collection | DOAJ |
| description | In this paper, we developed a SIRV epidemic model based on a vaccination game, incorporating vaccination dynamics and data memory effects using the Caputo fractional derivative. This approach effectively captured the nonlocal and power-law characteristics of influenza transmission. We confirmed the model's biological well-posedness, proved the uniqueness and existence of solutions, and analyzed stability. Furthermore, we established global Ulam-Hyers stability. The results showed that the epidemic incidence depended on the number of reproductions in the system. Through the Grünwald-Letnikov method, we developed the numerical simulations. We validated our theoretical findings and provided insights into the impact of vaccination on influenza progression. Our simulations revealed that strategic vaccination decisions were influenced by individual perceptions of the benefits and costs to achieving control of the influenza disease. |
| format | Article |
| id | doaj-art-76511d2efe704f01b55c97e03662f4f9 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-76511d2efe704f01b55c97e03662f4f92025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126792682110.3934/era.2024318SIRV fractional epidemic model of influenza with vaccine game theory and stability analysisQun Dai0Zeheng Wang1School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, ChinaSchool of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, ChinaIn this paper, we developed a SIRV epidemic model based on a vaccination game, incorporating vaccination dynamics and data memory effects using the Caputo fractional derivative. This approach effectively captured the nonlocal and power-law characteristics of influenza transmission. We confirmed the model's biological well-posedness, proved the uniqueness and existence of solutions, and analyzed stability. Furthermore, we established global Ulam-Hyers stability. The results showed that the epidemic incidence depended on the number of reproductions in the system. Through the Grünwald-Letnikov method, we developed the numerical simulations. We validated our theoretical findings and provided insights into the impact of vaccination on influenza progression. Our simulations revealed that strategic vaccination decisions were influenced by individual perceptions of the benefits and costs to achieving control of the influenza disease.https://www.aimspress.com/article/doi/10.3934/era.2024318influenzavaccination gamecaputo fractional derivativeulam-hyers stabilitylyapunov stability |
| spellingShingle | Qun Dai Zeheng Wang SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis Electronic Research Archive influenza vaccination game caputo fractional derivative ulam-hyers stability lyapunov stability |
| title | SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis |
| title_full | SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis |
| title_fullStr | SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis |
| title_full_unstemmed | SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis |
| title_short | SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis |
| title_sort | sirv fractional epidemic model of influenza with vaccine game theory and stability analysis |
| topic | influenza vaccination game caputo fractional derivative ulam-hyers stability lyapunov stability |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024318 |
| work_keys_str_mv | AT qundai sirvfractionalepidemicmodelofinfluenzawithvaccinegametheoryandstabilityanalysis AT zehengwang sirvfractionalepidemicmodelofinfluenzawithvaccinegametheoryandstabilityanalysis |