Homophily and infections: static and dynamic effects

We analyze the effect of homophily in the diffusion of a harmful state between two groups of agents that differ in immunization rates. Homophily has a very different impact on the steady state infection level (that is increasing in homophily when homophily is small, and decreasing when high), and on the cumulative number of infections generated by a deviation from the steady state (that, instead, is decreasing in homophily when homophily is small, and increasing when high). If immunization rates are endogenous, homophily has the opposite impact on the two groups. However, the sign of the group-level impact is the opposite if immunization is motivated by infection risk or by peer pressure. If motivations are group-specific, homophily can be harmful to both groups.