Homophily in the adoption of digital proximity tracing apps shapes the evolution of epidemics

We study how homophily of human physical interactions affects the impact of digital proximity tracing on the epidemic evolution. Analytical and numerical results show the existence of different dynamical regimes with respect to the mixing rate between adopters and nonadopters, revealing a rich phenomenology in terms of the reproduction number as well as the attack rate. We corroborate our findings with Monte Carlo simulations on different real contact networks. Our results indicate that depending on infectivity and adoption, mixing between adopters can be beneficial as well as detrimental for disease control.