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

Piergiorgio Castioni,Manlio De Domenico,Riccardo Gallotti

doi:10.1038/s42005-021-00631-2

Piergiorgio Castioni, Manlio De Domenico + Show 1 more

Open Access

https://doi.org/10.1038/s42005-021-00631-2

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Abstract

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.

Highlights

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 this work, we introduced a model for epidemic spreading on metapopulation network with arbitrary topology
It is structured as a reaction-diffusion process where the reaction part is that of a standard SIR model with site-dependent transition rates, while the diffusive part corresponds to a random walk whose dynamics is scaled by a parameter which allows us to tune the speed of mobility with respect to the epidemic spread

Summary

Introduction

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. Models for human mobility can range from Markov chains encoding standard diffusion[35] to more sophisticated dynamics encoding higher-order memory[36,37]: they are often encoded into origin-destination (OD) matrices which are later encoded into the essential diffusive part in the dynamical equations that describe the spatio-temporal evolution of epidemics in terms of reaction-diffusion processes. Quite often those models assume that an epidemic unfolds slower than the average time people need to move around[38]. Changes in human mobility can be due to extraordinary travel restrictions, cancellations or to the effects of other restrictions such as school and workplace closure or delayed access to point of interests, from restaurants and gyms to shopping malls and museums, as happened during the COVID-19 pandemic[41,42,43,44]

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