Impacts of reinforcement learning-driven subsidy policies on evolutionary vaccination dynamics

In voluntary vaccination, adaptive adjustments in government subsidy policies play a crucial role in influencing vaccination levels. The Bush-Mosteller model, a type of reinforcement learning, offers an excellent framework to study the decision-making process of the government. In this work, we study how the government adaptively adjusts to different subsidy policies that affect the vaccination level. Here, we incorporate the per capita treatment cost for infections and the per capita subsidy into a Bush-Mosteller model where the former serves as the payoff and the latter defines the aspiration level, and the gap between the payoff and the aspiration level determines whether the stimulus is positive, resulting in continuation of the current policy, or negative, prompting policy adjustment. Our results reveal that while increasing the total subsidy amount can enhance vaccination levels, reducing the relative vaccination costs fails to increase vaccination levels under a fixed subsidy budget. Provided the total subsidy exactly covers vaccination costs, vaccination levels depend on the dominant strategy: dominance of the partial-offset policy results in a decline, dominance of the free subsidy policy leads to an increase, and the coexistence of both policies maintains the initial level. This study sheds light on the role of adaptive subsidy policies driven by reinforcement learning in shaping vaccination dynamics.