Fragmentation-Dependent Epidemic Thresholds for Foot-and-Mouth Disease in Wildebeest Metapopulations: Basic Reproduction Numbers, Stability Conditions, and Critical Connectivity Levels

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.