Epidemic Threshold & Herd Immunity

SIR model on a network. R₀ = β/γ; herd immunity threshold p_c = 1 − 1/R₀. The epidemic percolates through the susceptible population, halting when the infected cluster fragments. Vaccinated nodes (blue) are removed from the network.

Transmission β8
Recovery γ4
Vaccination %20
Population400
R₀ = 2.0  |  Herd immunity threshold: 50%  |  S: 0 I: 0 R: 0
Susceptible Infected Recovered Vaccinated