The role of spatial mixing in the spread of foot-and-mouth disease.

A model of epidemic dispersal (based on the assumption that susceptible cattle were homogeneously mixed over space, or non-spatial model) was compared to a partially spatially explicit and discrete model (the spatial model), which was composed of differential equations and used geo-coded data (Euclidean distances between county centroids). While the spatial model accounted for intra- and inter-county epidemic spread, the non-spatial model did not assess regional differences. A geo-coded dataset that resembled conditions favouring homogeneous mixing assumptions (based on the 2001 Uruguayan foot-and-mouth disease epidemic), was used for testing. Significant differences between models were observed in the average transmission rate between farms, both before and after a control policy (animal movement ban) was imposed. They also differed in terms of daily number of infected farms: the non-spatial model revealed a single epidemic peak (at, approximately, 25 epidemic days); while the spatial model revealed two epidemic peaks (at, approximately, 12 and 28 days, respectively). While the spatial model fitted well with the observed cumulative number of infected farms, the non-spatial model did not (P<0.01). In addition, the spatial model: (a) indicated an early intra-county reproductive number R of approximately 87 (falling to <1 within 25 days), and an inter-county R<1; (b) predicted that, if animal movement restrictions had begun 3 days before/after the estimated initiation of such policy, cases would have decreased/increased by 23 or 26%, respectively. Spatial factors (such as inter-farm distance and coverage of vaccination campaigns, absent in non-spatial models) may explain why partially explicit spatial models describe epidemic spread more accurately than non-spatial models even at early epidemic phases. Integration of geo-coded data into mathematical models is recommended.