A novel approach to mapping and calculating the rate of spread of endemic bovine tuberculosis in England and Wales

Abstract


Introduction
A disease can be defined as endemic when it is constantly present in a population (Thrusfield 2007) and persists without being reintroduced from outside (Segen 2006).Although the numbers of herds and cattle affected by bovine tuberculosis (bTB) in England and Wales have increased epidemically since the 1980s, closer study reveals substantial areas that are affected by persistent bTB, which should more accurately be considered endemic.
It is evident from time-series maps of the spread of bTB produced using annual surveillance data that the major mode of spread of endemic bTB in England and Wales is by expansion along the edges of existing endemic areas; only rarely do isolated outbreaks become new foci of endemic disease (for example see Figure 2 in Defra 2011).In order to characterise the spread of endemic bTB, we first need to develop a definition of endemicity in this context, and then identify the areas which are defined as endemic and map their expansion.This is the first time that such an approach has been taken to investigate the spatial epidemiology of bTB.Historically, the progression of bTB has been illustrated by mapping statistical parameters such as incidence and prevalence or the density of animals that react to bTB testing (AHVLA 2013).Although these maps provide valuable information about the spatial distribution of bTB, they do not discriminate between endemic disease and localised outbreaks which are unlikely to persist.Identification of the areas where bTB is endemic will allow better targeting of interventions to control the spread of the disease.
Developmental work explored various approaches to defining endemicity for bTB.We considered approaches using classical measures of incidence such as number of incidents per number of herds or herds tested within a grid cell; and attempts to specify for endemic disease were made by incorporating criteria such as confirmation of disease and recurrence of bTB.It was found that an approach based on proximity to confirmed disease helped eliminate sporadic incidents likely to be the result of long distance cattle movements and was therefore likely to produce the best estimates of the location of truly endemic disease.
We report a new and generally applicable mathematical method for predicting the endemic status of bTB in cattle for localities and times, and demonstrate how this method can be used to map endemic bTB and calculate the rate at which the endemic areas are expanding in England and Wales.

Data handling and map production
Data describing bTB testing and incidence were obtained from surveillance data recorded in the Animal and Plant Health Agency's VetNet database for nine 24 month intervals from 1 st September to 31 st August (to begin and end at a time when tests were least frequent) and

Spatial resolution
A custom script was used to generate hexagonal grids with cell sizes of 6.25km 2 and 25km 2 .
Advantages and disadvantages of hexagonal grids relative to square grids have been reviewed by Birch et al. (2007).Square grids are far more widely used than hexagonal grids, possibly because raster data and smaller grid cells can easily be aggregated into lower resolution grids.Whilst hexagonal grids are less practical in the context of data processing, they minimise the distance between points within the same cell, and all pairs of neighbouring cells share an equal length of edge, meaning that neighbouring hexagons are readily adaptable to smoothing.

Defining endemicity
Endemicity was defined in three steps.Firstly, measures related to the two key criteria of endemicity, disease presence and disease recurrence were assessed.Secondly, a range of candidate definitions of endemicity were identified to provide a new measure.Thirdly, it was necessary to identify a clear and communicable mapping solution to allow the proposed definitions to be understood, assessed and calibrated through expert and non-specialist stakeholder knowledge.The geo-processing workflow is included in the supplementary information.
Within each of the 24 month time periods, the distances from each farm holding to the nearest ten 'Officially Tuberculosis Free status -Withdrawn' (OTF-W) incidents were calculated.Data were aggregated by 6.25km 2 and 25km 2 hexagon cell and then mapped for rapid comparison of each measured distance.The more inclusive measure of the distance to the nearest holding with a bTB incident of any type was also measured and considered but was dropped in preference of distance to confirmed OTF-W incidents.From these maps it was possible to visually define a number of candidate definitions of endemicity using a combination of different distance thresholds (3, 5, 7 or 10km) to ranked nearest incidents (1 st to 10 th ).Examples include 10km from the 2 nd nearest OTF-W incident, or 3km from the 3 rd nearest OTF-W incident.
After investigating the outlying areas of endemicity as defined by our candidate definitions and comparing them with data from VetNet, distance to the 3 rd nearest OTF-W incident was shown to be the most reliable measure of endemicity.This definition suitably omitted areas where the disease was likely to have been seeded by long distance cattle movements.
Discussions with social science collaborators revealed that maps using contour lines were more likely to be understood than hexagon values which tended to obscure patterns at farm or parish level.A series of interpolated contours showing the expansion over time of the endemic area for selected distance thresholds to the third nearest OTF-W holding were produced to communicate the results.These were generated from the hexagonal cell values using an inverse distance weighting (IDW) interpolation.
Significant efforts we made to ensure the maps were clear to all non-specialist stakeholders: only expansion (rather than contraction) was shown, towns and major roads were added to help identify locations, and colours were optimised to avoid implying risk.These maps were then used in consultation with expert Veterinary Officers (VOs) as part of the validation process outlined in the next section.

Validation of the definition of endemicity used for the maps
To assist with validation of the geospatial definition of endemicity and to determine the appropriate distance threshold to use to create the contour polygons, two methods of validation were used.The first approach consisted of a focus group in collaboration with social scientists in which VOs with local knowledge of bTB spread were consulted to obtain their view of how endemic bTB is spreading in their areas.They were shown four versions of the temporal contour maps created with a distance threshold of 3km, 5km, 7km or 10km.
The second, mathematical, approach was also intended to discriminate between areas with endemic bTB and other areas which may be subject to sporadic bTB.The method calculated the effect of distance threshold and N-number (i.e. the N th nearest OTF-W incident) on the sensitivity and specificity of apparent endemicity.
The reference standards for endemicity and sporadicity were two subsets of the 141 "Stevenson districts" into which England and Wales can be divided.These districts had been designed by Stevenson et al. (2005) to analyse BSE incidence, each of them containing around 20,000 cows.The districts were ranked according to the incidence of bTB in herds between September 2002 and August 2011, divided into six groups of 23 and merged.In the 23 districts that had the highest bTB incidence, the range of incidence (by district) was 7.4 to 13.3 OTF-W incidents per 100 herds per year.These districts, containing 453 25km 2 hexagons, were considered to have unambiguous endemic bTB.The 23 districts with the lowest incidence contained 323 hexagons and were assumed to be affected by bTB sporadically, if at all: the incidence was no more than 0.34 OTF-W incidents per 100 herds per year.The method was also applied to 6.25km 2 hexagons with similar results.At least

Definition of endemicity
Figures 2a and 2b illustrate the distance from farms to the N th nearest OTF-W incident in [2005][2006][2007] for values of N between 1 and 6.Increasing the number of breakdowns required within given distances was effective at filtering out the influence of isolated incidents, which are likely to be the result of long-distance cattle movements from bTB-endemic areas (Gopal et al. 2006).However, requiring larger numbers of incidents to be within the threshold distance resulted in less consistency and spatial continuity in areas considered likely to correspond to recent and current spread based on the results of developmental work using incidence.Distance to N th nearest OTF-W incident had the advantage of producing consistent patterns across different cell sizes, and was readily adaptable to farm level, cell level or raster analysis.It had the disadvantage of being a continuous variable, making it difficult to define a clear cut off between endemic and non-endemic.Distances from holding to N th nearest holding were very much smaller than distances from holding to incident: excluding two isolated holdings, one located in central London and one located in the Welsh Mountains, the maximal distances to N th nearest holding for N1, N2, N3, N4, N6 and N10 were 5.3, 6.1, 6.4, 7.1, 7.7 and 9.3km respectively.Distance from holding to N th nearest incident (with a constant herd incidence) may nevertheless be biased towards areas with higher herd density.The 3 rd nearest incident was selected as the optimal threshold of N based on the consistency of the core area produced compared with that produced using smaller values of N, and the reduction in the influence of sporadic cases.

Validation of thresholds
Figure 4 illustrates the specificity and sensitivity of combinations of N-number and distance threshold in describing the endemic or non-endemic status of a 25km 2 hexagon correctly.For N1, N2, N3, N4, N6 and N10, the distances where the sensitivity and specificity intersect are similar would be 3.2, 5.6, 7.6, 9.0, 11.0 and 14.0km respectively.The values of sensitivity and specificity at the intersection point increase from 92.0 to 97.6% between N1 and N3, then more slowly to 99.0% at N10.Because a large N-number failed to detect some local endemic areas when the density of bTB incidents was low, N3 was considered most appropriate.The threshold distance for N3 was between 7 and 8km; using 7 km gave near-maximum specificity (98.4%) and slightly reduced sensitivity (96.8%), and was considered to be acceptable, given the poorer suitability of high N-numbers.
The results of the mathematical validation were supported by the outcome of the workshop with VOs.Based upon what they considered to be endemic bTB and their experience of where bTB had spread in their local areas, a combination of a 7km threshold with the thirdnearest OTF-W incident was found to best represent visually the current edge of the area affected by endemic bTB (Figure 3c).
Figure 5 illustrates the two year time period in which a hexagon first became endemic based on our definition.Retraction of endemicity (i.e.reversion to non-endemic status) may have occurred but was not calculated.Figure 5 -A map illustrating the two year time period in which a hexagon became endemic for the first time (defined by the presence of three OTF-W incidents within 7 km).Once a hexagon became endemic, it stayed endemic in this map.Reversion to non-endemic status may have occurred but was not calculated.

Rate of spread
The rate of spread for each hexagon where spread occurred between September 2001 and August 2012 is presented in Figure 6.Rate of spread was obtained for ~2,300 cells and varied between 0.04km / year and 15.9km / year, with a mean of 3.7km / year (SD = 2.2km / year), and a median of 3.3km / year.The upper 95 th percentile was 7.9km per year.

Discussion
We have developed a novel, and generally applicable method for assessing the spread of endemic bTB in England and Wales.This information can be used to investigate the factors associated with spread, and to identify areas for targeted interventions to stop and reverse endemic spread.
The most frequently used numerator to measure bTB is the number of incidents, usually attributed to the time period in which the incident was detected.If only those bTB incidents that had OTF status withdrawn (OTF-W) are counted, there is more certainty that the incident represents true bTB infection, although the number of incidents decreases.There may, however, be advantages in taking into account the number of OTF status suspended (OTF-S) incidents and inconclusive reactors in assessing the development of endemicity, since these events may represent the early stages of infection (Clegg et al. 2011), thus allowing better estimates of the timing of recently-arrived endemic bTB.
The simplest individual animal numerator is the number of reactors to the SICCT skin test.An advantage of counting reactors rather than incidents is that in long incidents, repeated detection of reactors may contribute data in more than one time period.Another is that the number of reactors tends to increase with size of herd and OTF status (Conlan et al. 2012), information that is not contained in a simple count of incidents.During developmental work attempts were made to filter the number of reactors to select those that were probably infected locally, those which were "recurrent" reactors (those in herds in which a previous incident was closed in the previous 24 months) and those that had visible lesions or yielded M. bovis in culture.All three filters reduced the numerator considerably, but can be valuable in discriminating for animals that have proven endemic bTB infection.
All measures of detection of bTB using classical incidence measures were too variable; causing the annual pattern of bTB detected in 6.25km² hexagonal cells to be too haphazard for the creation of distinct annual fronts.Two smoothing methods, one using data from the six surrounding cells and the other using kernel smoothing, were used to improve the continuity of each year's boundary of the endemic area, but inevitably they allowed artefactual regularity to creep in.
Presence of bTB was indicated by detection via targeted surveillance testing in England and Wales.As such, it is dependent on the frequency and efficacy of both the testing strategy and the diagnostic test.Prior to 2013, the frequency of bTB testing of a herd was determined at a local level, based on the level of bTB within their parish in the previous six years.In 2011, 47% of herds in England had an annual parish testing interval (PTI), 11% had a PTI of two years, 0.8% had a PTI of three years, and 42% had a PTI of four years, while all herds in Wales have been tested annually since October 2008 (AHVLA 2012).In areas of three or four yearly testing, not all herds will be tested within the defined two-year period assessed in this study, which will have reduced the estimated number of herds or animals infected (the numerator).Long testing intervals can also lead to an underestimation of incidence due to loss of undetected infected animals through sale and routine slaughter.If unaccounted for, testing interval introduces an element of bias to any approach to assess temporal trends in incidence, whereby earlier years (where fewer herds were tested annually) will be more affected by underestimation of incidence.One way to address the influence of testing interval is to use the testing history of herds to estimate the probability of a herd being infected at different time points prior to the test which resulted in an incident.
The distance approach used here allowed for the calculation of the rate of spread of the endemic front using a boundary displacement approach.Boundary displacement is less widely used compared to trend surface analysis (TSA) and other models involving distance regression from a point of origin, which have been used to obtain rate of spread for infectious and non-endemic areas, and defined endemic areas which were in agreement with the experience of bTB field veterinarians.These thresholds have been found to be most appropriate when using data for England and Wales between 2001 and 2011.However, it would be prudent to bear in mind that changes in the epidemiology of bTB over time as well as changes to surveillance regimes, may affect the suitability of these thresholds.The definition developed here has allowed the expansion of the endemic fronts of bTB in England and Wales to be mapped, which in turn enables further analysis of the factors associated with this expansion.
spanning 2001/03 to 2009/11 using Microsoft Access 2003.Geographic data were processed and maps were produced in ArcGIS 10.0 (ESRI 2011).Custom scripts were written in Python 2.6 (Python Software Foundation 2012).

Figure 1 :
Figure 1: Step by step overview of the process by which rate of spread was calculated.(a) Areas of spread were identified as the difference between areas for two non-overlapping 24 month time periods.(b) If the centroid of a 6.25 km 2 hexagon was located within an area of spread, lines crossing the centroid were created at 5° intervals.(c) The lines were clipped in order to retain only the segments linking the boundaries of the endemic areas before and after the time period for which rate of spread was calculated.(d) The shortest segment was identified and its length was divided by the number of years between the two time periods to obtain a value for rate of spread.

Figure 4 -
Figure 4 -Calculated sensitivity and specificity (vertical axes) with which the 23 Stevenson districts with the greatest OTF-W incidence per 100 herds can be distinguished from the 40 lowest-incidence Stevenson districts using the distance to the N th nearest OTF-W incident each year and a distance threshold (horizontal axes).

Figure 6 -
Figure 6 -A map illustrating the hexagons where endemic bTB (defined by the presence of three OTF-W incidents within 7 km) spread between 2001 and 2012.Rate of spread in km per year is calculated for the two year time period during which endemic bTB first passed through the hexagon.Reversion to non-endemic status may have occurred but was not calculated.Hexagons which were classed as endemic prior to 2001 are coloured yellow and are considered to be the 'core' endemic area.