Abstract:
Habitat fragmentation alters the spatial structure of wildlife populations, creating heterogeneous landscapes where disease persistence depends on connectivity patterns. We develop a multi-patch SEIR metapopulation model for Foot-and-Mouth Disease (FMD) in fragmented wildebeest populations of the Serengeti-Mara ecosystem. We derive the metapopulation basic reproduction number Rmeta = max(Rin,Rbetweenρ(C)), where ρ(C) is the spectral radius of the connectivity matrix. Critical connectivity thresholds are identified: spectral radius 1.85 (90% CI: 1.65-2.05) for poor patches, 1.45 (90% CI: 1.30-1.60) for average patches, and 0.95 (90% CI: 0.85-1.05) for excellent patches. Backward bifurcations occur under high patch heterogeneity, enabling disease persistence even when Rmeta < 1. Critical community size increases from 450,000 to 950,000 animals under fragmentation. Patch-specific vaccination thresholds range from 18% to 62%. Optimal corridor width is 1-1.5 km, and optimal buffer zones are 10-20 km. Combined interventions achieve 68% R0 reduction and 89% outbreak prevention. Model limitations include exponential distribution assumptions, constant migration rates, and omission of seasonal movements and livestock interactions; thresholds should be interpreted as theoretical guidance. Code is open-source at https://github.com/isaacmose/fmdmetapopulation-theory.
