In this study, an epidemiological model with the provaccination and antivaccination susceptible groups is proposed, and the social dilemma of the model is analyzed. During a pandemic, such as the current COVID-19, many individuals get confused to choose the option of adopting a provaccination or antivaccination strategy based on the number of infected people and the payoff of being infected. In the proposed model, people can obtain immunity either through vaccination or by getting infected with the disease which is known as natural immunity. In addition, increasing the waning immunity influences the choice of adopting the provaccination or antivaccination strategy. We used the behavior model to analyze the choice of the two strategies, where any individual can choose a strategy based on the number of infected individuals from each group. Moreover, individuals who are already infected can choose their strategy based on the payoff of their disease cost or vaccination cost. Our results show that, at Nash equilibrium, individuals in both groups behave the same. Further, from our numerical results, increasing the number of vaccinations can reduce the social dilemma whereas an increase in the waning immunity rate increases the social dilemma.