When imitation meets exploration: quantifying social efficiency deficits (SED) in vaccination behaviour.

Vaccination behaviour plays a critical role in shaping epidemic dynamics, yet the societal consequences of decentralized vaccination decisions remain difficult to quantify. We develop a behavioural-epidemiological framework that combines adaptive vaccination dynamics, behavioural exploration and socially desirable vaccination strategies. To evaluate the societal impact of vaccination behaviour, we introduce the social efficiency deficit (SED), a novel metric that quantifies the welfare loss arising from decentralized vaccination decisions and measures the gap between individual incentives and collective epidemic-control objectives. Numerical simulations and global sensitivity analysis reveal that transmission intensity, waning immunity, vaccination costs, compliance and behavioural exploration are key determinants of epidemic outcomes and social welfare. In particular, behavioural exploration promotes sustained vaccination uptake, suppresses infection prevalence and can reduce social inefficiency by bringing behavioural outcomes closer to socially desirable levels. The proposed framework provides a quantitative approach for assessing vaccination-related social dilemmas and offers new insights for designing effective and socially efficient public health interventions.