  We study how the herd immunity threshold and the expected epidemic size
depend on homophily with respect to vaccine adoption. We find that the presence
of homophily considerably increases the critical vaccine coverage needed for
herd immunity and that strong homophily can push the threshold entirely out of
reach. The epidemic size monotonically increases as a function of homophily
strength for a perfect vaccine, while it is maximized at a nontrivial level of
homophily when the vaccine efficacy is limited. Our results highlight the
importance of vaccination homophily in epidemic modeling.
