A behavioral game-theoretic model for vaccination with fractional-order imitation and aspiration dynamics

This research work introduces a new modeling technique that simulates the vaccination game, integrating imitation and aspiration social learning dynamics using the Caputo fractional-order derivative. We investigated a fractional-order epidemic model that incorporates imitation and aspiration dynamics in both pure and combined imitation and aspiration frameworks, considering symmetric and asymmetric aspiration levels. This approach is particularly relevant, as conventional game-theoretic models of vaccine behavior often fail to accurately represent the intricate and flexible characteristics of human decision-making processes. The Caputo fractional-order derivative enables a more precise representation of the memory and hereditary effects inherent in individuals' decision-making processes regarding vaccination. We also examine the interaction between social influence, characterized by imitation, and individual ambition levels, offering a complete framework for analyzing the impact of these variables on vaccination behavior within a community through the evolutionary game theory (EGT) framework, and investigate how public health policy, individual risk perception, and societal dynamics affect the vaccination rate. The findings demonstrate the advantages of employing the Caputo fractional-order derivative for policymaking in capturing the complex temporal dynamics of vaccination games, offering valuable insights for developing effective vaccination strategies and public health initiatives.