Multi-Patch Metapopulation Dynamics of Foot-and-Mouth Disease in Fragmented Wildebeest Populations: Effects of Patch Size, Isolation, Asymmetric Migration, and Demographic Heterogeneity
Isaac Mose *
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.
Vincent Major Bulinda
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.
Joash M. Kerongo
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.
Andrea Otwande Kiage
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.
Mogoi N. Evans
Department of Mathematics and Actuarial Science, Kisii University, Kisii, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Habitat fragmentation can alter wildlife movement, contact structure, and disease persistence, yet conventional epidemiological models often provide limited representation of these spatial effects. This study develops a multipatch susceptible-exposed-infectious-recovered metapopulation model to examine foot-and-mouth disease transmission in fragmented wildebeest (Connochaetes spp.) populations in the Serengeti-Mara ecosystem. The framework incorporates patch size, isolation, asymmetric migration, habitat quality, edge effects, seasonal forcing, demographic heterogeneity, competition among SAT1, SAT2, and SAT3 serotypes, and environmental persistence. The metapopulation basic reproduction number is evaluated through the spectral properties of the patch-connectivity matrix, and parameter uncertainty is represented using 90% uncertainty intervals. Model outputs indicate a local persistence threshold of approximately 5,000-8,000 animals (90% uncertainty interval: 4,200-8,800). Under strongly asymmetric migration, the source-patch reproduction number reaches 1.77 (1.60-1.94), whereas sink-patch values remain below one. Seasonal movement increases the reproduction number from 1.12 (1.02-1.22) during low-movement periods to 1.62 (1.48-1.76) during peak migration. Increasing fragmentation from two to 100 patches reduces the metapopulation reproduction number from 1.49 (1.35-1.63) to 0.87 (0.78-0.96). Elevated transmission is also associated with patch edges, poor habitat quality, adult age classes, breeding-season males, and wet-season water sources. These findings provide a model-based account of how landscape structure and heterogeneous movement may influence FMD persistence, while remaining conditional on the stated assumptions and parameter estimates.
Keywords: Foot-and-mouth disease, wildebeest, habitat fragmentation, metapopulation model, seir model, asymmetric migration, basic reproduction number, Serengeti-mara ecosystem