  In this work, we study an epidemic model with vaccination coupled with
opinion dynamics in a dynamic network. 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. We
have observed the emergence of network homophily and, in certain cases, the
complete fragmentation of the network. Our Monte Carlo simulations also show
first-order phase transitions with metastable states. An increase in the
probability of rewiring yields a dual effect, namely: (a) in the short term, it
has the potential to intensify the epidemic peak; (b) in the long term, it can
diminish the rate of infection. This transient increase in the epidemic peak is
attributed to the fragmentation of the network into smaller, disconnected
sub-networks. Therefore, our results suggest that rewiring is optimal when it
is as high as possible but before the network starts breaking apart.
