SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis

Qun Dai; Zeheng Wang; Qun Dai; Zeheng Wang

doi:10.3934/era.2024318

Electronic Research Archive

2024, Volume 32, Issue 12: 6792-6821. doi: 10.3934/era.2024318

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Research article

SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis

Qun Dai ^†,
Zeheng Wang ^{†
,
,}

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China
† These authors contributed equally to the work

Received: 28 August 2024 Revised: 29 November 2024 Accepted: 13 December 2024 Published: 19 December 2024

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.
- influenza,
- vaccination game,
- Caputo fractional derivative,
- Ulam-Hyers stability,
- Lyapunov stability
Citation: Qun Dai, Zeheng Wang. SIRV fractional epidemic model of influenza with vaccine game theory and stability analysis[J]. Electronic Research Archive, 2024, 32(12): 6792-6821. doi: 10.3934/era.2024318

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Abstract

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.

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