Modeling exploratory vaccination behavior and epidemic dynamics under partial compliance

Traditional epidemiological behavior models based solely on rational payoff maximization often fail to capture the full complexity of vaccination decision-making, where individuals may exhibit uncertainty, spontaneous strategy changes, or imperfect responses to epidemic risk. To provide a more realistic representation of behavioral adaptation, we develop a coupled epidemiological-behavioral susceptible-vaccinated-infectious-recovered-susceptible model incorporating conditional vaccination behavior, partial compliance, and a random exploration mechanism that allows spontaneous switching between vaccination strategies independent of direct payoff differences. The model combines disease transmission dynamics with evolutionary imitation processes in which individuals choose between unconditional and conditional vaccination strategies according to perceived infection risk and vaccination cost. This generates a nonlinear feedback loop in which epidemic prevalence influences vaccination uptake, while behavioral adaptation simultaneously modifies disease transmission. Analytical results establish the existence and stability conditions of disease-free and endemic equilibria and show that the effective reproduction number depends explicitly on adaptive vaccination behavior and compliance. Numerical simulations reveal threshold effects, bistability, and abrupt transitions between low- and high-vaccination coverage. The results demonstrate that incorporating exploratory and adaptive behavioral responses can substantially alter epidemic outcomes and this provides a more realistic framework for studying vaccination dynamics and epidemic control strategies.