Epidemic phase transition of the SIS type in networks
Delft University of Technology - Mekelwey 4, NL-2628 CD Delft, The Netherlands, EU
Accepted: 11 January 2012
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 (τc−1−τ−1) for effective infection rates τ↓τc, 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 τc was the missing part in the general steady-state theory of a SIS-type epidemic on a network.
PACS: 89.20.-a – Interdisciplinary applications of physics / 89.75.Hc – Networks and genealogical trees
© EPLA, 2012