The effect of neighbourhood definitions on spatio-temporal models of disease outbreaks: Separation distance versus range overlap.

The definition of the spatial relatedness between infectious and susceptible animal groups is a fundamental component of spatio-temporal modelling of disease outbreaks. A common neighbourhood definition for disease spread in wild and feral animal populations is the distance between the centroids of neighbouring group home ranges. This distance can be used to define neighbourhood interactions, and also to describe the probability of successful disease transmission. Key limitations of this approach are (1) that a susceptible neighbour of an infectious group with an overlapping home range - but whose centroid lies outside the home range of an infectious group - will not be considered for disease transmission, and (2) the degree of overlap between the home ranges is not taken into account for those groups with centroids inside the infectious home range. We assessed the impact of both distance-based and range overlap methods of disease transmission on model-predicted disease spread. Range overlap was calculated using home ranges modelled as circles. We used the Sirca geographic automata model, with the population data from a nine-county study area in Texas that we have previously described. For each method we applied 100 model repetitions, each of 100 time steps, to 30 index locations. The results show that the rate of disease spread for the range-overlap method is clearly less than the distance-based method, with median outbreaks modelled using the latter being 1.4-1.45 times larger. However, the two methods show similar overall trends in the area infected, and the range-overlap median (48 and 120 for cattle and pigs, respectively) falls within the 5th-95th percentile range of the distance-based method (0-96 and 0-252 for cattle and pigs, respectively). These differences can be attributed to the calculation of the interaction probabilities in the two methods, with overlap weights generally resulting in lower interaction probabilities. The definition of spatial neighbourhood has important implications for models used in decision-support systems for disease preparedness and response. This research presents a first step towards more realistic representations that could be used in spatio-temporal models of disease outbreaks.