Epidemic phase transition of the SIS type in networks

Delft University of Technology - Mekelwey 4, NL-2628 CD Delft, The Netherlands, EU

^a P.F.A.VanMieghem@tudelft.nl.

Received: 9 August 2011
Accepted: 11 January 2012

Abstract

By making only one approximation of a mean-field type, we determine the nature of the SIS type of epidemic phase transition in any network: the steady-state fraction of infected nodes y_∞ is linear in (τ_c⁻¹−τ⁻¹) for effective infection rates τ↓τ_c, the derivative of y_∞ at the epidemic threshold is exactly computed and depends on the largest eigenvalue λ₁ of the adjacency matrix and on the first- and third-order moments of the corresponding eigenvector. Since coupled oscillators in a network synchonize at a coupling strength proportional to , a similar characterization of the phase transition is suggested. The behavior of y_∞ around τ_c was the missing part in the general steady-state theory of a SIS-type epidemic on a network.