SIR model on cities connected by gravity-law mobility
Each node is a city with SIR dynamics: Ṡ=−βSI/N, İ=βSI/N−γI, Ṙ=γI, with R₀=β/γ. Between cities i,j, the gravity model gives flux F_{ij} ∝ N_i N_j / d_{ij}² — larger, closer cities exchange more people. The epidemic starts in the largest hub and spreads through the travel network. Node colour encodes infected fraction; edge width encodes flow.