Abstract
Individual's perception of the participant in a vaccine program reflects their intrinsic appreciation of the trade-off between vaccine behavior, risk of infection, and memory effect. Here we present a mean-field approximation and fractional-order model embedded with the evolutionary game theory (EGT) process for susceptible-vaccinated -infected-recovered (SVIR) epidemic dynamics, where the two types of immunity, artificial and natural immunity, are considered. Besides the well-known vaccination game models, we successfully establish a theoretical ap-proach of fractional-order dynamics for vaccination games in which epidemic spread and individual decisions are supposed to evaluate social behavior. The EGT governs the strategy adoption, while the fractional-order pro-cess directs the memory effect state. Our analytical forecasts are validated by numerical simulation of the finite difference method and Adams-Bashforth-Moulton algorithm for the mean-field and Caputo fractional-order de-rivative that assesses various graphs at varying parameters. Our results show that an effective vaccine may mean-ingfully minimize the risk of infection. However, despite vaccines' obvious impacts and advantages on a community, many individuals choose not to vaccinate for various reasons, leading to anti-vaccination groups and vaccine apprehension. In this aspect, people are interested in gaining natural immunity. Notably, the individ-ual's risk perception is fundamental for controlling the infection, while the fractional-order dynamics mainly dictate the degree of freedom with memory effect. Higher fractional order with EGT leads to an improved vacci-nation intake, while a cheaper and reliable vaccine ensures to lessening of contagious disease. The proposed model captures relevant disease behavior and the memory effect of a synchronized pandemic event, emphasizing the underlying role of social schemes.(c) 2022 Elsevier Ltd. All rights reserved.