SIR Metapopulation — Spatial Epidemic
Day:
0
S:
—
I:
—
R:
—
R₀:
—
Seed Outbreak
Reset
Pause
Vaccinate 30%
Transmission β
β=0.25
Recovery γ
γ=0.10
Mobility m
m=0.15
Cities N
12
Metapopulation SIR: each patch has local SIR dynamics + mobility between patches. dS/dt = −βSI/N + m·Σ(Sⱼ−S). Spatial heterogeneity creates travelling epidemic waves. R₀ = β/γ; epidemic occurs when R₀ > 1.