Critical behavior in interdependent spatial spreading processes with distinct characteristic time scales

The spread of an infectious disease is well approximated by metapopulation networks connected by human mobility flow and upon which an epidemiological model is defined. In order to account for travel restrictions or cancellation we introduce a model with a parameter that explicitly indicates the ratio between the time scales of the intervening processes. We study the critical properties of the epidemic process and its dependence on such a parameter. We find that the critical threshold separating the absorbing state from the active state depends on the scale parameter and exhibits a critical behavior itself: a metacritical point – a critical value in the curve of critical points – reflected in the behavior of the attack rate measured for a wide range of empirical metapopulation systems. Our results have potential policy implications, since they establish a non-trivial critical behavior between temporal scales of reaction (epidemic spread) and diffusion (human mobility) processes.