Critical regimes driven by recurrent mobility patterns of reaction–diffusion processes in networks

Reaction–diffusion processes 1 have been widely used to study dynamical processes in epidemics 2–4 and ecology 5 in networked metapopulations. In the context of epidemics 6 , reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility 7 , such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states 8,9 . Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction–diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.