Dynamical analysis of an SIR epidemic model with game-theoretic vaccination behavior

Fengjun Li; Tao Zhang; Qimin Zhang; Fengjun Li; Tao Zhang; Qimin Zhang

doi:10.3934/math.2026030

AIMS Mathematics

2026, Volume 11, Issue 1: 684-716. doi: 10.3934/math.2026030

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Research article

Dynamical analysis of an SIR epidemic model with game-theoretic vaccination behavior

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, China

Received: 03 October 2025 Revised: 12 December 2025 Accepted: 16 December 2025 Published: 09 January 2026
MSC : 37N25

In this paper, a susceptible–infectious–recovered infectious disease model with the game inoculation process is established. First, the basic regeneration number $ R_0 $ of the model is obtained, and the positive and bounded connections of the system are proved. second, the stability of each equilibrium point is discussed by analyzing the characteristic equations of the system. Next, by taking $ \omega $ as the parameter, the conditions for the occurrence of Hopf bifurcation are obtained. Furthermore, we use the method of parameter estimation to analyze the influence of each parameter on this system. Finally, through a numerical simulation, we verify all previous conclusions. Of course, symmetry provides a tractable framework for analyzing vaccination games but may overlook heterogeneity-driven phenomena.
- dynamic analysis,
- SIR epidemic model,
- game vaccination behavior
Citation: Fengjun Li, Tao Zhang, Qimin Zhang. Dynamical analysis of an SIR epidemic model with game-theoretic vaccination behavior[J]. AIMS Mathematics, 2026, 11(1): 684-716. doi: 10.3934/math.2026030

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Abstract

In this paper, a susceptible–infectious–recovered infectious disease model with the game inoculation process is established. First, the basic regeneration number $ R_0 $ of the model is obtained, and the positive and bounded connections of the system are proved. second, the stability of each equilibrium point is discussed by analyzing the characteristic equations of the system. Next, by taking $ \omega $ as the parameter, the conditions for the occurrence of Hopf bifurcation are obtained. Furthermore, we use the method of parameter estimation to analyze the influence of each parameter on this system. Finally, through a numerical simulation, we verify all previous conclusions. Of course, symmetry provides a tractable framework for analyzing vaccination games but may overlook heterogeneity-driven phenomena.

References

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