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Mycobacterium bovis (Karlson & Lessel 1970), the cause of bovine tuberculosis (TB), remains a serious disease of cattle in the UK. There is strong circumstantial evidence that infectious badgers Meles meles (Lin. 1758) cause a significant proportion of the total number of cattle herd breakdowns, particularly in the south-west of England (Krebs et al. 1997). From 1975 to 1996 the Ministry of Agriculture, Fisheries and Food (MAFF) has attempted to control TB in the badger population through culling.
There have now been a number of attempts to model bovine TB in the badger (Anderson & Trewhella 1985; Bentil & Murray 1993; Smith et al. 1995; White & Harris 1995a,b; Ruxton 1996a,b; Smith, Cheeseman & Clifton-Hadley 1997; Swinton et al. 1997; White, Lewis & Harris 1997). The early approaches have, in general, been limited by a lack of accurate data on the epidemiology of bovine TB in the badger, and none of them has made any attempt to simulate the transmission of TB from badgers to cattle. The aim of this study was to construct a model capable of correctly simulating the prevalence and spatial distribution of TB in badgers and use it to examine the effect of different badger control strategies where the live test is utilised. In order to be able to simulate any reactive badger control policy that is invoked in response to detection of M. bovis in cattle, it is also necessary to simulate the transmission of TB from badgers to cattle.
In Britain the badger generally lives in territorial social groups, where each territory contains one main sett, which is the focus of activity, and usually a number of other setts. Some of these may be quite large and can be used for breeding when more than one sow reproduces in a territory (Neal & Cheeseman 1996). The status of a sett is not fixed so that different setts may be the main sett in different years (Neal & Cheeseman 1996). In an undisturbed population, the badger social group size averaged 8·8 adults in 1993, and may reach over 20 (Rogers et al. 1997b). Permanent movement between territories was rare, but temporary movement and short-term forays were much more common (Rogers et al. 1998). The distribution of animals between setts within a territory, and the frequency of changes between setts, is not well documented. Males and females are less active in winter and spring and tend not to travel to alternative setts within their territory, although young males may travel to setts in other territories in search of mating opportunities (Brown 1993). During summer and autumn males are more active than females and are more likely to traverse their territory and visit alternative setts (Brown 1993).
Between 1994 and 1996 the live test was used to identify setts with infected badgers within 24 areas. Each area was defined around herd incidents believed, after investigation, to have had a badger origin. Each area, of average size 12·25 km2, was surveyed for badgers and the location, size and activity of each sett was recorded. Baited cage traps were used at each active sett for a period of 1 week and the infection status of all badgers caught was determined. If one or more badgers gave a positive ELISA result, badgers continued to be trapped at that sett and all badgers destroyed, until there were no further signs of activity. For setts where no badgers that were trapped during the first week gave a positive blood test, all animals were released and trapping discontinued. No attempt was made in the field to group badger setts into territories. This can be done by standard bait marking techniques (Kruuk 1978) but is most reliable during spring and autumn.
The prevalence of infection in badgers caught under the live test trial was similar to that under the interim strategy, where badgers were trapped only on the farm in which the cattle breakdown occurred (Krebs et al. 1997). The live test trial was suspended in September 1996 before sufficient data had been collected to determine whether there was a significant effect on herd breakdown rate. An analysis of the available data concluded that the live test, as implemented, would be unlikely to reduce the overall prevalence of TB in badgers and thus the risk to cattle (Woodroffe, Frost & Clifton-Hadley 1999).
The low sensitivity of the ELISA test was seen as very disadvantageous. As a result, the current badger control strategy involves a large-scale experimental trial, with a scientific control, to determine the total level of effect of TB in the badger population on the number of cattle herd breakdowns (as recommended by Krebs et al. 1997). Only after determining the level of this effect can optimal control strategies be designed. Such strategies may, or may not, involve the use of a live test, but it is important to ascertain the optimal use of a live test so that it can be considered against other strategies.
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A stochastic simulation model of bovine TB was produced to examine badger population dynamics, disease epidemiology, transmission to cattle and the effect of different control strategies using a live test. Simulations without TB, using a carrying capacity dependent upon the maximum number of breeding females per social group, gave an average group size of 8·6 adults and yearlings. This is in close agreement with the average social group size at Woodchester Park, which was 8·8 adults in 1993 (Rogers et al. 1997b). Infection rates were adjusted to give a mean disease prevalence of about 16% for a carrying capacity similar to that seen at Woodchester Park. This resulted in a decrease in mean social group size to 6·6 adult and yearling badgers: equivalent to a population depression of 24%. Although this is higher than an earlier approach with a similar model in a microsimulation (Smith, Cheeseman & Clifton-Hadley 1997), it is still much lower than predicted by other models (Anderson & Trewhella 1985; White & Harris 1995a). If sex-biased transmission rates are included in the model, then the various infection parameters need to be increased in order to maintain a similar disease prevalence and spatial distribution. This results in a population depression of 20%, with 6·8 adults and yearlings per group.
The maximum social group size in the simulation, using a similar carrying capacity to Woodchester Park, was 33 animals. The largest recorded social group at Woodchester Park contained 27 known animals (Rogers et al. 1997b). The percentage of adult females breeding at Woodchester Park has usually stayed between 20% and 40%. In the simulation it varied between 24% and 52%. The simulated figures would be slightly higher than expected when the badger population size is depressed.
The above results give a very close representation to those seen in the field data, and support the accuracy of this simulation modelling approach. They cannot be taken as a formal validation of the model, because the data are being compared with the population used to generate the model input, albeit through indirect measurements. For a comparison of population recovery rates with field data following badger removal see Smith et al. (2001).
The level of population depression in the present model was slightly greater than in earlier models (Smith, Cheeseman & Clifton-Hadley 1997). This was due to the wider categorisation of the super-excretor class, as more animals would reach this class and die prematurely than in the earlier more restrictive super-infectious class. However, it is interesting to note that reducing the additional mortality rate of animals in this class does not affect the level of population depression until this additional mortality is almost totally removed, although any reduction in the mortality does slowly increase the disease prevalence. Because the transmission probabilities are adjusted to produce realistic prevalence levels, any inaccuracy in the calculation of the disease-induced mortality will be compensated for (Wallach & Genard 1998). The insensitivity of population depression to the level of disease-induced mortality therefore means that the model is very robust to the inaccuracy of this calculation. No evidence has been found in the field to support a significant level of population depression, but without knowing the true carrying capacity at Woodchester Park (i.e. removing TB from the population) it is probably not possible to measure a depression of some 20%.
Although this model was closely based on an earlier version (Smith et al. 1995; Smith, Cheeseman & Clifton-Hadley 1997), there are some important differences. In the current model the time step was decreased from 1 year to 6 months to more closely simulate the occasional rapid progression of TB. Also, the highly infectious state super-excretor was a slightly broader category than the previous super-infectious state. Despite this broader categorisation the ELISA test is 85% sensitive to animals in this category (R.S. Clifton-Hadley, unpublished data). Other minor changes in the present model include the removal of a low level of disease-induced mortality applied to infectious animals.
White & Harris (1995a) proposed a disease-free threshold group size of about six adults and yearlings in order to sustain an enzootic infection, and Smith et al. (1995) calculated a figure of eight animals per group in a diseased population simulation model. The results of the present study agree with these estimates, as when social group size drops below about 6·3 adults and yearlings (k ≈ 2) disease extinction may occur within 50 years. White & Harris (1995a) used a homogeneous group size to evaluate disease persistence. In this model it is interesting to note that if the carrying capacity is heterogeneous, then disease prevalence is reduced. However, these models have not considered density-dependent changes in contact rates between animals either within or between social groups, and this could also affect disease persistence and prevalence.
Non-spatial models are often criticised for a lack of realism due to the assumption of homogeneous mixing throughout the population. Spatial models go some way towards addressing this issue by generally only allowing homogeneous mixing within small units of the model: badger social groups in this case. Homogenous mixing within badger social groups would be likely if all animals shared one sett, but would be less likely where more than one sett was occupied within a territory. Also, if there is behavioural segregation of infected or infectious badgers this assumption would no longer hold. Analysis of badger removal operations throughout the south-west has shown that disease prevalence may be greater in outlying setts (Woodroffe, Frost & Clifton-Hadley 1999), and analysis of trapping data at Woodchester has shown that social groups with more outlying setts tend to have a higher disease prevalence (Delahay et al. 2000). This heterogeneous mixing would affect disease transmission within social groups, and may exacerbate the effect of sex-biased transmission, particularly by emphasising the importance of pseudovertical transmission to cubs.
A second aspect not modelled previously is the interspecies transfer of infection to cattle. Previous attempts to simulate spatial control of TB in badgers have used an arbitrary approach by initiating local infection at particular prevalence levels and attempting immediate disease control (White & Harris 1995b). The current model is capable of initiating badger control dependent on the detection of infection in cattle, and because the initial population is stored in arrays various control strategies can be performed on identical disease patterns.
In the present model cattle herd breakdowns are highly correlated with disease prevalence and badger population density (measured as carrying capacity in the model). However, using this model disease prevalence in badgers is not always positively correlated with badger population density. This lack of a strong positive relationship may explain why, in the present model, disease prevalence in badgers is a much better predictor of herd breakdown than carrying capacity. In reality the interspecies transmission probability may vary from farm to farm because of factors relating to cattle management practice, and exposure to badgers and their excretory products. This variation between farms is likely to be much greater than the variation used in the present model, but herd breakdown rates at parish or county level may show less variation, due to averaging, and may therefore be a good predictor of disease prevalence in the badger.
Only seven of 20 simulations gave a significant positive correlation between disease prevalence and badger carrying capacity. A strong relationship is normally expected in conventional disease models, and the weak relationship found in this model is backed up by the difficulty of finding such a relationship in the field data collected at Woodchester Park (Smith et al. 1995). Thus, both empirical data and modelling demonstrate that this population is spatially heterogeneous with respect to disease, and this can impact on disease control strategies (May & Anderson 1984).
The inclusion of cattle into the model, albeit in a simple form, represents an important first step in realising the utility of models, and expanding them to include the species of economic interest. Despite the inclusion of cattle we have continued to examine the prevalence of disease in the badger as the primary goal, due to the noise associated with the low frequency of cattle herd breakdown (Fig. 3). This facilitates comparisons of control strategies.
During the live test trial an average of two badgers was caught and tested at each sett (Woodroffe, Frost & Clifton-Hadley 1999). If these setts were allocated to social groups by using the Dirichlet tessellation method, then an average of just over three badgers would have been sampled per social group, giving an average of 1·8 setts per social group (Woodroffe, Frost & Clifton-Hadley 1999). This partial trapping of social groups must have reduced the overall trapping efficacy, and this could have had a small negative effect. However, the pooling of setts into groups, even if errors occur, increases the number of badgers sampled, and this had a dramatic effect on the ability of the control strategy to reduce the prevalence of disease.
In order to have an effect similar to testing four individuals per social group, either the trapping efficacy must be increased above 95%, or the overall sensitivity of the live test must be increased to 70% or more. While both of these are possible, it is much easier and less time consuming to pool badger setts into social groups. We suggest that Dirichlet tessellations are used to investigate the proportion of badger setts that would be correctly allocated to a social group. To date, Dirichlet tessellations have been used to try and identify territorial boundaries (Doncaster & Woodroffe 1993).
Both reactive strategies were capable of reducing the prevalence of TB in the badger, and thus the number of cattle herd breakdowns. The strategy that tested and culled more infected social groups (ring culling) was more effective in reducing prevalence, although even this strategy took 10–20 simulated years to reduce disease prevalence in the badger by half. Woodroffe, Frost & Clifton-Hadley (1999) concluded that it is unlikely that the live test trial, as implemented, would be effective in reducing the prevalence of TB. The results of these simulations contradict their conclusion, but because many social groups were only partially trapped, trapping efficacy in the field will have been below 80%, and the time taken to noticeably reduce disease prevalence will have been too long to be useful.
However, of greater interest is the effect of changing from a reactive strategy to a proactive strategy using the live test. Issues of human resources have not been considered here as it has been assumed that all social groups within the control area can be tested and trapped in each year. Given the large difference in the effect of the reactive and proactive strategies, it seems very likely that this effect would be seen in reality. Each reactive culling area is a distinct patch within a diseased badger population, whereas the proactive culling occurs over the entire simulated area, resulting in no possibility of immigration of infected animals. Simulations with proactive trapping occurring for 5 years out of every 10 still gave a very strong reduction in disease prevalence. During non-culling years the badger population began to recover, but the disease prevalence did not immediately increase.
If a proactive control strategy were to be used, it would be necessary to determine which areas should be subjected to culling, and how much culling is cost-effective. The current UK badger control field trial involves proactive culling, but without any live test. The areas for this experiment were determined by analysis of the cattle herd breakdown rates. It would probably be more effective to demarcate these areas based upon systematic collection of data on the prevalence on TB in the badger population, but to date no easy method of determining this has been found and validated. A live test offers at least a partial solution, and could be combined with a cost–benefit analysis, with proactive badger culling, using the live test, performed at different intensities (e.g. every year, every second year, etc.).
The reactive culling strategies, in particular, depend upon a number of assumptions. First, TB must be detected very early in cattle and the subsequent control must be performed within an average of 6–12 months after the infection occurred. Changing the super-excretor badger to cattle transmission rate (0·025 per 6 months) has a significant effect on the success of the reactive control strategies. When this transmission rate exceeds about 0·1 6 months−1 then the ring culling strategy becomes almost as effective as the proactive strategy.
We have made no attempt to simulate the behaviour of individual badgers. There is evidence that TB infection is more prevalent in individuals residing in outlier setts (Woodroffe, Frost & Clifton-Hadley 1999) or at least in social groups with more outlying setts (Delahay et al. 2000). This may have some effect on their probability of being trapped, and also any outlier setts that are wrongly assigned to a social group may negatively impact on the success of the control. Similarly, the mapping of one herd of cattle to each badger social group is simplistic and a more accurate mapping system is required in order to investigate fully the spatial consequences of control. Such an approach is now under investigation using a Graphical Information System (GIS) version of the model. In addition, the majority of the data used in the model is derived from a single population.
Mycobacterium bovis is capable of surviving in the environment (King, Lovell & Harris 1999) and this aspect has not been considered here. Environmental survival of M.bovis would lead to a reduced correlation between prevalence of TB in badgers and the number of cattle herd breakdowns and an increased ability for the disease to survive in a post-culled population. This would make the disease more difficult to control, and increase the negative effect of releasing lactating sows.
Because of the simplistic representation of cattle herds in the model so far, cattle-to-cattle and cattle-to-badger transmission of TB has not been considered, nor has the movement of infected cattle. Cattle-to-cattle transmission of the disease seems to be low even under conditions of isolation (Costello et al. 1998) and would only be relevant to a model of badger control if the cattle were moved between herds. Cattle-to-badger transmission is therefore likely to be even lower, but may be important where infectious cattle are placed in herds with access to relatively high-density, disease-free, badgers. Cattle movement, the importation of infected cows and immigration of infected badgers should all be considered once optimum control strategies have been identified. These may not involve the use of a live test, and so these aspects are not considered here.
The consequences of culling on the badger population size, growth rate and recovery have not been investigated here as we have been concerned with use of a live test. This area is reported elsewhere (Smith et al. 2001), where control strategies not using a live test are also examined.
In conclusion, the model suggests that proactive culling is much more efficient than reactive culling. It is therefore more effective to increase the number of animals tested than to increase the trapping efficacy. Also, a live test with increased sensitivity could significantly reduce the time taken to decrease disease prevalence in the badger. Analysis of results obtained for the current culling trial (Krebs et al. 1997; Bourne et al. 1999) should also help to provide further data to evaluate the suggested options.