This paper studies a dynamic vaccination game model embedded with vaccine cost-effectiveness and dyadic game during an epidemic, assuming the appearance of cooperation among individuals from an evolutionary perspective. The infection dynamics of the individuals' states follow a modified S/VIS (susceptible/vaccinated-infected-susceptible) dynamics. Initially, we assume that the individuals are unsure about their infection status. Thus, they make decisions regarding their options based on their neighbors' perceptions, the prevalence of the disease, and the characteristics of the available vaccines. We then consider the strategy updating process IBRA (individuals-based risk assessment) concerning an individual's committing vaccination based on a neighbor's decision. In the perspective of social dilemma, it presents the idea of social efficiency deficit to find the gap between social optimum and Nash equilibrium point based on dilemma strength by considering vaccine decision. The cost and cooperative behavior depend on disease severity, neighbor's attitude, and vaccine properties to obtain a reduced-order optimal solution to control infectious diseases. Vaccine factors (efficiency, cost, and benefit) are crucial in changing human vaccine decisions and cooperative behavior. It turns out that, even in the prisoner's dilemma case, where all defection attitude occurs, vaccine uptake (cooperation) increases. Finally, extensive numerical studies were presented that illustrate interesting phenomena and investigate the ultimate extent of the epidemic, vaccination coverage, average social benefits, and the social efficiency deficit concerning optimal strategies and the dynamic vaccine attitudes of individuals.PACS numbers.Theory and modeling; computer simulation, 87.15. Aa; Dynamics of evolution, 87.23. Kg.