Quarantine generated phase transition in epidemic spreading

M. DICKINSON; C. LAGORIO; F. VAZQUEZ; L. A. BRAUNSTEIN; P A MACRI; M. MIGUELES; S. HAVLIN; H. E. STANLEY

Boston

Conferencia; Horizons in Emergency & Scaling; 2011

We study the critical e®ect ofquarantine on the propagation of epidemics on an adaptive network ofsocial contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptibleindividuals protect themselves by disconnecting their links to infectedneighbors with probability w, and reconnecting them to other susceptibleindividuals chosen at random. Starting from a single infected individual,we show by an analytical approach and simulations that there is a phasetransition at a critical rewiring (quarantine) threshold wc separating aphase (w < wc) where the disease reaches a large fraction of the popu-lation, from a phase (w >= wc) where the disease does not spread out.We ¯nd that in our model the topology of the network strongly a®ectsthe size of the propagation, and that wc increases with the mean degreeand heterogeneity of the network. We also ¯nd that wc is reduced ifwe perform a preferential rewiring, in which the rewiring probability isproportional to the degree of infected nodes.