Abstract
BackgroundWhen modelling infectious diseases, accurately capturing the pattern of dissemination through space is key to providing optimal recommendations for control. Mathematical models of disease spread in livestock, such as for foot-and-mouth disease (FMD), have done this by incorporating a transmission kernel which describes the decay in transmission rate with increasing Euclidean distance from an infected premises (IP). However, this assumes a homogenous landscape, and is based on the distance between point locations of farms. Indeed, underlying the spatial pattern of spread are the contact networks involved in transmission. Accordingly, area-weighted tessellation around farm point locations has been used to approximate field-contiguity and simulate the effect of contiguous premises (CP) culling for FMD. Here, geographic data were used to determine contiguity based on distance between premises’ fields and presence of landscape features for two sample areas in Scotland. Sensitivity, positive predictive value, and the True Skill Statistic (TSS) were calculated to determine how point distance measures and area-weighted tessellation compared to the ‘gold standard’ of the map-based measures in identifying CPs. In addition, the mean degree and density of the different contact networks were calculated.ResultsUtilising point distances <1 km and <5 km as a measure for contiguity resulted in poor discrimination between map-based CPs/non-CPs (TSS 0.279-0.344 and 0.385-0.400, respectively). Point distance <1 km missed a high proportion of map-based CPs; <5 km point distance picked up a high proportion of map-based non-CPs as CPs. Area-weighted tessellation performed best, with reasonable discrimination between map-based CPs/non-CPs (TSS 0.617-0.737) and comparable mean degree and density. Landscape features altered network properties considerably when taken into account.ConclusionThe farming landscape is not homogeneous. Basing contiguity on geographic locations of field boundaries and including landscape features known to affect transmission into FMD models are likely to improve individual farm-level accuracy of spatial predictions in the event of future outbreaks. If a substantial proportion of FMD transmission events are by contiguous spread, and CPs should be assigned an elevated relative transmission rate, the shape of the kernel could be significantly altered since ability to discriminate between map-based CPs and non-CPs is different over different Euclidean distances.
Highlights
When modelling infectious diseases, accurately capturing the pattern of dissemination through space is key to providing optimal recommendations for control
While this model captured the regional pattern of spread well, accuracy at the individual farm level was low for infected premises (IP), with about 12% of reported case premises over the duration of the epidemic being captured by simulations [4]
Four pairs of premises shared identical point locations; three of these were sourced from address matches, and one from a postcode match
Summary
Accurately capturing the pattern of dissemination through space is key to providing optimal recommendations for control. Mathematical models of disease spread in livestock, such as for foot-and-mouth disease (FMD), have done this by incorporating a transmission kernel which describes the decay in transmission rate with increasing Euclidean distance from an infected premises (IP). This assumes a homogenous landscape, and is based on the distance between point locations of farms. For the model of Keeling et al this was derived from infection tracing following the livestock movement ban [3] While this model captured the regional pattern of spread well, accuracy at the individual farm level was low for IPs, with about 12% of reported case premises over the duration of the epidemic being captured by simulations [4]. This low accuracy is in part due to stochastic variation, assumed homogeneity of the landscape by the kernel is likely to have contributed
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