Vaccination equilibria interplayed with epidemics and interval reference points

Given the limitations of fixed payoffs and reference points, we introduce interval payoffs and reference points to capture fluctuations and diversity in objective costs and payoffs. We develop a prospect theory based evolutionary vaccination game model that incorporates fixed (interval) reference points to evaluate the role of psychological factors in updating vaccination strategies. The results suggest that, under a higher reference point, when vaccination costs are small, changes in the objective payoff of infected individuals have no significant effect on the vaccination equilibrium, especially when the interval objective payoff is relatively small. However, increasing vaccination costs decreases vaccination equilibrium. By analyzing the relationship between interval reference points and objective payoffs, we observe that when the objective payoff approaches the reference point, the vaccination equilibrium gradually decreases as the rationality coefficient decreases. In contrast, the vaccination equilibrium increases when the objective payoff deviates further from the reference point. In addition, we examine how different sensitivity coefficients affect individual behavior. When the gain sensitivity coefficient is small (or the loss sensitivity coefficient is high), the vaccination equilibrium is more responsive to changes in the loss (or gain) sensitivity coefficient. These findings suggest that vaccination decisions are affected by cost-effectiveness and individual sensitivity perception patterns, whether under a fixed or interval reference point.