Metapopulation Epidemic Dynamics

SIR waves across connected patches — synchronization, extinction, and persistence

0.35
0.15
0.010
4
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R₀ = β/γ
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Synchrony
-
Total infected %
0
Day
Metapopulation SIR model: Each patch has susceptible S, infected I, recovered R populations. Within-patch dynamics follow SIR equations; travel couples patches.
dSᵢ/dt = −βSᵢIᵢ/Nᵢ + m·Σⱼ(Sⱼ − Sᵢ)
dIᵢ/dt = βSᵢIᵢ/Nᵢ − γIᵢ + m·Σⱼ(Iⱼ − Iᵢ)
Key insight: Even patches with local R₀ < 1 can sustain an epidemic if connected to high-R₀ patches — the network effective R₀ exceeds any single-patch R₀. Travel synchronizes epidemic waves across patches, creating simultaneous peaks (high m) or asynchronous dynamics (low m). Asynchrony is the main buffer against metapopulation extinction.