SIR Epidemics on Networks

Watch a disease spread through different network topologies. SIR model: Susceptible → Infected → Recovered. The reproductive number R₀ = β·k/γ determines whether an epidemic occurs. Click any node to start an infection.

Network type Infection rate β 0.30 Recovery rate γ 0.10 Nodes N 80

R₀ = β·⟨k⟩/γ—

Susceptible—

Infected—

Recovered—

Final attack %—

Day0

Above threshold R₀>1, epidemic spreads; below it, it dies out. Scale-free networks (Barabási-Albert) have hubs with very high degree — making them far more vulnerable (R₀→∞ in the mean-field limit as N→∞). Watts-Strogatz small-world networks interpolate between regular lattices and random graphs, balancing high clustering with short path lengths.