The impact of heterogeneity on the co-evolution of cooperation and epidemic spreading in complex networks

The dynamics of herd immunity depend crucially on the interaction between collective social behavior and disease transmission, but the role of heterogeneity in this context frequently remains unclear. Here, we dissect this co-evolutionary feedback by coupling a public goods game with an epidemic model on complex networks, including multiplex and real-world networks. Our results reveals a dichotomy in how heterogeneity shapes outcomes. We demonstrate that structural heterogeneity in social networks acts as a powerful catalyst for cooperation and disease suppression. This emergent effect is driven by highly connected hubs who, facing amplified personal risk, adopt protective strategies out of self-interest. In contrast, heterogeneity in individual infection costs proves detrimental, undermining cooperation and amplifying the epidemic. This creates a ``weakest link'' problem, where individuals with low perceived risk act as persistent free-riders and disease reservoirs, degrading the collective response. Our findings establish that heterogeneity is a double-edged sword: its impact is determined by whether it creates an asymmetry of influence (leverage points) or an asymmetry of motivation (weakest links), recommending disease intervention policies that facilitate cooperative transition in hubs (strengthening the leverage point) and homogenize incentives to weakest links.