Network Epidemic Spread (SIR)

SIR Model on Networks: The SIR (Susceptible-Infected-Recovered) model partitions each node into one of three states. At each step, infected nodes transmit to susceptible neighbors with probability β, and recover with probability γ. The basic reproduction number R₀ = β/γ × ⟨k⟩ determines whether an epidemic spreads (R₀>1) or dies out. Scale-free networks (power-law degree distribution, as in the internet and social networks) have p_c → 0 — any infection spreads. Small-world networks (Watts-Strogatz 1998) have short average path lengths, accelerating spread. Network structure profoundly changes epidemic dynamics compared to the well-mixed assumption.