Estimating vulnerability to foot-and-mouth disease using stochastic disease simulation in farms and records of movements of animals

Abstract

Brazil is one of the major producers of beef and one of the main suppliers to the European Union and other countries. Due to major efforts of the Ministry of Agriculture and Livestock, Brazil currently has a zone free of foot-andmouth disease in approximately 60% of the national territory. The zone free of foot-and-mouth borders some neighboring countries which do not share an efficient disease surveillance system and, although major efforts are done to mitigate disease entry, it is of interest to investigate more vulnerable routes for diseases. The movement of live animals throughout the Brazilian territory is currently documented in electronic form through the issue of transit animal guides (GTAs). Geographical information about the location of farms, number of transported animals, date of issue of the GTAs, are available in the dataset. From these records, we simulate the spread of foot- and-mouth disease. An infected animal is randomly placed into one of the farms and stochastic models are used to spread the disease among the herd. New farms become contaminated following the entry of infected animals. Movement is represented using a directed network where the farms are represented by vertices (or nodes) and the movements of animals between farms are the edges. To simulate the transmission of disease, three epidemiological stochastic models of SIR (Susceptible-Infected-Recovered) type are used. The simplest model, named farm level, uses the farm as the basic epidemiological unit. The other two models, named Greenwood and Reed-Frost models, simulate the transmission of the disease using the animals within the farms as the basic epidemiological units. The animal level simulation generates the distribution of the daily number of infected farms and the daily number of infected animals during an epidemic cycle. The time period of the simulation is 28 days and the probability of a susceptible animal being infected by an infected animal was set as 0.4. From simulated results, and using network theory, it is possible to estimate the vulnerability of each farm and to identify those trajectories within the network most likely to spread the disease. In the network representation, the vulnerability of a vertex is the proportion of the simulations in which the vertex finishes the simulation period in the infected state. The vulnerability of an edge is the proportion of simulations in which both vertices, connected by the edge, appear simultaneously infected.