SIR Epidemic Model

Kermack-McKendrick (1927): Susceptible → Infected → Recovered. The basic reproduction number R₀ = β/γ determines whether an epidemic takes off. The spatial grid shows local spread; the chart tracks global compartments over time.

β (transmission) 0.30 γ (recovery rate) 0.10 Spatial mixing 0.05 Initial infected % 1%

3.0

R₀ = β/γ

Epidemic will spread

Susceptible

Infected

Recovered

Step: 0

The SIR model: dS/dt = −βSI/N, dI/dt = βSI/N − γI, dR/dt = γI. R₀ > 1 → epidemic, R₀ < 1 → disease dies out. Herd immunity threshold: p_c = 1 − 1/R₀. The spatial version uses a grid where each cell mixes mainly with neighbors — creating visible wavefronts of infection sweeping through the population.