Opinion-driven vaccination and epidemic dynamics on heterogeneous networks.

Vaccination campaigns play a pivotal role in controlling infectious diseases. Their success, however, depends not only on vaccine efficacy and availability but also significantly on public opinion and the willingness of individuals to vaccinate. This paper investigates a coupled opinion-epidemic model on heterogeneous networks, where individual opinions influence vaccination probability, and opinions themselves evolve through a combination of peer interaction and local risk perception derived from observed infection rates. Embedding the coupled dynamics in scale-free networks, particularly Barabási-Albert structures, allows us to examine the role of network heterogeneity beyond homogeneous-mixing assumptions. Using Monte Carlo simulations and a semi-analytical microscopic Markov-chain approach, we derive and numerically validate analytical expressions for the critical infection threshold and stable vaccinated population where risk perception dominated peer influence. Our results show that stronger local risk perception enhances pro-vaccination opinions and suppresses infection, while dominant peer influence can increase long-term infection levels. These findings underscore the importance of accounting for social behavior and network structure when designing effective vaccination and epidemic control strategies.