Rescue of endemic states in interconnected networks with adaptive coupling

MARIÁNGELES SERRANO; FEDERICO VAZQUEZ; MAXI SAN MIGUEL

Lyon

Conferencia; STATPHYS 26; 2016

We study the dynamics of the susceptible-infected-susceptible modelfor epidemic spreading on interconnected networks with adaptivecoupling, where healthy individuals in one layer avoid contact withinfected nodes in the other layer by rewiring at random theirinternetwork connections. Our goal is to assess the effects of suchrewiring on the prevalence of the epidemics. To understand thenon-trivial behaviors of the interconnected system, we put forward amodel and provide an analytical formalism based on the mean field andpair approximation assumptions and we also perform extensive numericalsimulations. We find that the rewiring reduces the effectiveconnectivity for disease transmission between layers, which bringsimportant consequences like a reduction of the disease prevalence ineach layer as compared to the values for static interconnections,which approach their single network values as the rewiringincreases. In the thermodynamic limit, the rewiring can even induce atransition to the healthy phase if it overcomes a finite and smallcritical value in a region of infectivities where the interconnectednetworks support weak endemic states. We find this thresholdanalytically as a function of the infectivity for some specific valuesof average intra- and inter-connections in identical layers. Forfinite systems, we find that a disease outbreak on one network doesnot always imply an outbreak in the other network, a genuine effectwhich is not observed in the case of static interconnections. Theeffective decrease in connectivity caused by the rewiring is able tokeep the disease confined in only one of the networks until finitesize effects cut out the disease and thus in finite systems there is afinite probability that an endemic state never spreads to the wholesystem.