Effects of Punitive Measures on Free Riding and Collective Immunity Under Q-Learning–Driven Epidemic Dynamics

Free-riding behavior poses a critical challenge to achieving collective immunity in vaccination campaigns, particularly when individuals make decisions based on short-term self-interest. This study investigates how punitive interventions can mitigate free-riding and enhance vaccination uptake under adaptive decision-making. We develop an integrated evolutionary epidemic framework that combines evolutionary game theory with Q-learning, where individuals update their vaccination strategies by weighing vaccination cost, infection risk, vaccine effectiveness, and penalties for noncompliance. The model incorporates spatial interactions on structured populations, allowing local learning feedback and epidemic spreading to coevolve dynamically. Analytical results and numerical simulations reveal that punitive measures reshape the reinforcement learning reward structure, progressively discouraging free-riding and promoting cooperative vaccination behavior over repeated seasons. Vaccination effectiveness is a critical determinant: punishment alone is insufficient under low efficacy, whereas moderate-to-high efficacy regimes enable punitive incentives to align individual learning with collective welfare. Spatial clustering emerges as vaccinated individuals form stable blocks that impede transmission, reducing epidemic size and preventing resurgence. Extending the analysis across multiple network topologies demonstrates that while punitive intervention is broadly effective, its system-level impact is strongly modulated by network structure through local reinforcement, hub-driven dynamics, and information propagation. These findings highlight the importance of integrating adaptive learning dynamics, network heterogeneity, and behaviorally informed incentives into epidemic modeling, offering practical guidance for designing robust and resilient vaccination policies that mitigate free-riding and strengthen population-level immunity.