Optimal rewiring in adaptive networks in multi-coupled vaccination, epidemic and opinion dynamics

We investigate the emerging scenarios from an epidemic model with vaccination coupled with opinion dynamics in a non-static network. In contrast to prior studies, our approach involves a multi-coupled process that takes into account the interaction among opinion dynamics, epidemic spreading, vaccination, and network restructuring. The network structure evolves as agents with differing opinions disconnect from one another and connect with agents that share similar opinions about vaccination. We consider a SIS-like model with an extra vaccinated state. Agents can have continuous opinions and every time an agent disconnects from a neighbor, they connect to a new neighbor. Our Monte Carlo simulations have revealed a series of notable results. First, we note a spontaneous emergence of network homophily, accompanied by scenarios with a complete fragmentation of the network. Second, we show the presence of a first-order phase transition with metastable states. Third, we observe the intriguing presence of scenarios with a dual effect: an increase in the probability of rewiring can decrease the infection rate in the long-term, but it can be accompanied by a side effect in the short-term namely the potential amplification the epidemic peak. This non-trivial side effect in the short-term is a transient byproduct of the fragmentation of the network into smaller, disconnected subnetworks. Overall, our non-monotonic results suggest that high values of rewiring that do not lead to the breakup of the network are optimal.