Epidemic Threshold for the SusceptibleInfectiousSusceptible Model on Random Networks
Abstract
We derive an analytical expression for the critical infection rate r_{c} of the susceptibleinfectioussusceptible (SIS) disease spreading model on random networks. To obtain r_{c}, we first calculate the probability of reinfection π, defined as the probability of a node to reinfect the node that had earlier infected it. We then derive r_{c} from π using percolation theory. We show that π is governed by two effects: (i) the requirement from an infecting node to recover prior to its reinfection, which depends on the SIS disease spreading parameters, and (ii) the competition between nodes that simultaneously try to reinfect the same ancestor, which depends on the network topology.
 Publication:

Physical Review Letters
 Pub Date:
 June 2010
 DOI:
 10.1103/PhysRevLett.104.258701
 arXiv:
 arXiv:0909.3811
 Bibcode:
 2010PhRvL.104y8701P
 Keywords:

 89.75.Hc;
 05.70.Ln;
 89.75.Da;
 Networks and genealogical trees;
 Nonequilibrium and irreversible thermodynamics;
 Systems obeying scaling laws;
 Condensed Matter  Disordered Systems and Neural Networks;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 Phys. Rev. Lett. 104, 258701 (2010)