Incorporating Game Theory into Voluntary Vaccination

Aiming to achieve widespread immunity to infectious diseases, voluntary vaccination becomes a challenge for people because of the existence of the temptation of free-ride which brings the vaccination coverage below the social optimum. In this manuscript, we integrate a game-theoretic framework into the SIR epidemiological process, while we also try to investigate the effects of varying different factors on the voluntary vaccination coverage. In our model, individuals are assumed to possess adequate information about their circumstance and then they are able to estimate the costs and benefits of vaccination. To maximize the benefits, various factors are considered, such as the cost of the vaccine, the effectiveness of the vaccine, the likelihood of being infected and etc. In this wok, we mainly focus on studying the effects of varying four parameters. As indicated by the results, the Nash equilibrium can hardly achieve a high level if the vaccination cost is higher than the infectious risk; nevertheless, widespread immunity can be achieved by appropriately adjusting the vaccine price and the risk of infection. Our work sheds light on how benefits affect individuals' choices regarding to vaccination and finally influence the herd immunity coverage in a well-mixed population.