Epidemic phase transition of the SIS type in networks

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 -1 c -τ -1 ) for effective infection rates τ ↓ τc, the derivative of y∞ at the epidemic threshold τc = 1 λ 1 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 1 λ 1 ,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.