Reaction–diffusion processes1 have been widely used to study dynamical processes in epidemics2,3,4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. 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.
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We acknowledge S. Meloni for the very many discussions and useful suggestions. J.G.-G. and A.A. acknowledge financial support from MINECO (projects FIS2015-71582-C2 and FIS2014-55867-P) and from the Departamento de Industria e Innovación del Gobierno de Aragón y Fondo Social Europeo (FENOL group E-19). A.A. acknowledges also financial support from the ICREA Academia, the James S. McDonnell Foundation.
The authors declare no competing financial interests.
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Gómez-Gardeñes, J., Soriano-Paños, D. & Arenas, A. Critical regimes driven by recurrent mobility patterns of reaction–diffusion processes in networks. Nature Phys 14, 391–395 (2018). https://doi.org/10.1038/s41567-017-0022-7
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