SIR Epidemics on Network Trees

SIR spreading on a random tree network. The epidemic threshold is R0 = β/γ · (⟨k²⟩−⟨k⟩)/⟨k⟩ > 1. Visualize cascading infection fronts and final outbreak size.

Parameters

R₀ = 0
S: 0 I: 0 R: 0
SIR on trees — exact:
Final size satisfies:
R∞/N = 1 − e^(−R₀·R∞/N)

Color: S=blue I=red R=gray
Edge brightness = transmission