SIR Epidemic on a network: each node is Susceptible (green), Infected (red), or Recovered (grey). At each time step, each infected node transmits to susceptible neighbors with probability β, and recovers with probability γ.
The basic reproduction number R₀ = β/γ determines outbreak size. R₀ > 1 → epidemic; R₀ < 1 → fizzles. Network structure matters: small-world shortcuts (rewiring p) allow rapid spread across the network, while highly clustered local structure can contain outbreaks. High-degree "superspreader" nodes disproportionately drive transmission.