Contact Process

SIS Epidemic on Networks — Phase Transition at λc = 1/ρmax

Network (click node to infect)

Prevalence over time

Network

Nodes
30

Infection rate λ
0.50

Recovery rate μ
1.00

Infected: — | R₀ ≈ — | λc ≈ —

SIS contact process: infected nodes recover (S→I→S) at rate μ, spread at rate λ.
Critical threshold: λc = μ/ρmax where ρmax = largest adjacency eigenvalue.
Above threshold: endemic steady state. Below: extinction (absorbing state).