To vaccinate or not to vaccinate: A comprehensive study of vaccination-subsidizing policies with multi-agent simulations and mean-field modeling.

We combined the elements of evolutionary game theory and mathematical epidemiology to comprehensively evaluate the performance of vaccination-subsidizing policies in the face of a seasonal epidemic. We conducted multi-agent simulations to, among others, find out how the topology of the underlying social networks affects the results. We also devised a mean-field approximation to confirm the simulation results and to better understand the influences of an imperfect vaccine. The main measure of a subsidy' performance was the total social payoff as a sum of vaccination costs, infection costs, and tax burdens due to the subsidy. We find two types of situations in which vaccination-subsidizing policies act counterproductively. The first type arises when the subsidy attempts to increase vaccination among past non-vaccinators, which inadvertently creates a negative incentive for voluntary vaccinators to abstain from vaccination in hope of getting subsidized. The second type is a consequence of overspending at which point the marginal cost of further increasing vaccination coverage is higher than the corresponding marginal cost of infections avoided by this increased coverage. The topology of the underlying social networks considerably worsens the subsidy's performance if connections become random and heterogeneous, as is often the case in human social networks. An imperfect vaccine also worsens the subsidy's performance, thus narrowing or completely closing the window for vaccination-subsidizing policies to beat the no-subsidy policy. These results imply that subsidies should be aimed at voluntary vaccinators while avoiding overspending. Once this is achieved, it makes little difference whether the subsidy fully or partly offsets the vaccination cost.