Epidemic Spatial Heterogeneity: Multi-Patch SIR

SIR dynamics on a network of spatial patches with heterogeneous connectivity and mobility. Patches exchange infected individuals via travel matrix m_ij. Spatial structure can prevent or amplify outbreaks depending on network topology.

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Spatial heterogeneity: Metapopulation models (Hanski 1991, Grenfell 2001) show that patchy environments can raise epidemic threshold. Effective R₀ depends on network structure. Hubs drive super-spreading; isolated patches act as refugia.