Quarantine generated phase transition in epidemic spreading

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

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Año: 2010

1063-651X

We study the critical effect of quarantine on the propagation of epidemics on an adaptive networkof social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model inthe presence of quarantine, where susceptible individuals protect themselves by disconnecting theirlinks to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by a simple analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold wc separating a phase (w < wc) where the disease reaches a large fraction of the population, from a phase (w ¸ wc) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that wc increases with the mean degree and heterogeneity of the network. We also find that wc is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.