Multi-factor vaccination game and optimal control of a SVIS epidemic model

Infectious diseases represent a major global health challenge, characterized by their abrupt onset and rapid transmission, leading to millions of deaths annually. Vaccination can not only protect individuals, but also establish a group immune barrier to effectively prevent the spread of diseases, which is crucial in the prevention and control of infectious diseases. However, individual vaccination decisions are affected by many factors, typically to maximize personal benefits. Therefore, a SVIS epidemic network model based on complete information is proposed, and the stability of the equilibrium points is analyzed by using Jacobian matrix and Lyapunov stability theory. This study explores vaccination behavior within the framework of game theory, in which individuals seek to maximize their own benefits through strategic decision-making. However, such self-interested behavior often results in high social costs. Subsequently, to address the gap between individual income and social cost, we propose an optimal control strategy that minimizes societal costs while ensuring sufficient coverage to suppress transmission. Finally, The simulation results not only validate the efficacy of game-theoretic approaches, but also demonstrate their capability to achieve optimal control with minimized social costs. In addition, the simulation results also show that network structure has a significant impact on the speed and scope of disease transmission, and the social benefits are different in different network environments.