Emergence of reputation-driven vaccination and degree-weight assortativity on heterogeneous networks

Understanding the evolution of vaccination behavior is fundamental for unraveling real-world epidemic dynamics and informing public health governance strategies. Traditional studies typically assume that individual fitness depends solely on vaccination decisions and health status within a single season. However, for multifaceted reasons, people may also value long-term health status accumulated over time (which we refer to as health reputation). In this paper, we construct an evolutionary game model to investigate how health reputation influences the evolution of vaccination behavior on heterogeneous social networks. Computer simulation results show that when vaccination costs are high, an increase in the uniform reputation weight may lead to a non-monotonic change in vaccination coverage. Nevertheless, after isolating the scaling effect of immediate payoffs, we find that health reputation almost consistently promotes the emergence of vaccination behavior. Introducing heterogeneity in reputation weights can further enhance vaccination levels in most cases. Especially when the weights are assortatively correlated with node degrees, vaccination coverage is significantly increased. More importantly, when individuals adaptively optimize their own weights based on Q-learning, an assortative relationship between weights and node degrees spontaneously emerges, meaning that high-degree nodes tend to evolve higher health reputation weights. This work suggests that health reputation may play a significant role in vaccination decision-making in the real world and interacts subtly with the heterogeneity of social network structures.