Our results are consistent with those from other computer models that support the existence of a threshold group size for the persistence of bTB in badger populations at around 6–8 adults per group [14–16]. The general increases in prevalence with group size, albeit it in a non-linear pattern, also support the broader literature on the dynamics of disease in a range social host species . However, recent empirical work has found a negative relationship between bTB prevalence and badger abundance, with prevalence highest in smaller social groups and at lower population densities . The most plausible hypothesis to explain this finding is that badger contact behaviour changes according to group size, and greater mobility of badgers between groups at lower population densities may result in a higher proportion of contacts leading to disease transmission . However, there are no behavioural data available from free-living badger populations at low densities to test this hypothesis or to re-parameterise the model. In the absence of such data, the model assumed that individual badgers at all densities exhibited the behaviour patterns recorded in a moderate-density population , and this assumption probably explains the predicted increases in prevalence with group size in the model. A relatively higher frequency of contacts between badgers at lower densities would have the effect of lowering the threshold for disease persistence in much the same way as increased external transmission does, and thus the predictions of the model for lower social group sizes should be treated with caution, and considered as lower bounds in terms of disease persistence and prevalence.
The addition of external trickle-type infection in the model decreased the threshold group size for bTB persistence , allowing for persistence in smaller group sizes, and raised the prevalence in larger group sizes. It enabled an increase in prevalence to occur in already infected populations that consisted of larger group sizes. The driver for this was an increase in intra-group transmission rates. However, this effect was not consistent across all group sizes, and relatively greater impacts were achieved at lower group sizes, particularly just below the threshold level. At these lower group sizes, there is a more heterogeneous distribution of infection across groups, and hence it is more likely that external infection will result in disease being introduced into fully susceptible groups that do not have contiguous borders with infected groups. Following introduction of disease into susceptible groups, the relatively higher rates of intra-group transmission lead to higher levels of disease. These results suggest that only relatively minor changes in intra-group contact behaviour at lower densities may be sufficient to have a significant impact on the persistence of bTB in lower-density populations. With high levels of external infection, bTB is thus able to persist in smaller badger social groups commonly found within Europe , as well as in Ireland . In these situations, badger populations are likely to be fragmented, and external infections may provide a means for infection to reach those groups which would otherwise have been relatively isolated from dispersing individuals from other sub-populations.
External infections of badger populations may arise from livestock, other wildlife or environmental sources. For example, deer can shed M. bovis in faecal matter and nasal mucous  which can contaminate the environment, and cattle can shed M. bovis through nasal mucous  that can contaminate water sources . In larger badger group sizes, for example above 10–12, as are found in parts of south-west England where bTB is believed to be endemic in the badger population , external infection is not required for disease persistence. Nevertheless, even in these situations, significant external infection can cause increases in prevalence when there is endemic disease. Where these external sources of infection include maintenance hosts, disease control strategies should include management of these other potential sources of disease. However, effective control of bTB in the badger population may also help to reduce the significance of these external sources, especially if the other species are acting solely as spillover hosts . With larger group sizes, even occasional infectious disease contact can cause low levels of disease to persist, thereby complicating control measures.
Studies on bTB in other wildlife in south-west England have found several other wildlife species to be infected with bTB, for example various rodent species, foxes, red deer, roe deer, fallow deer and muntjac (Muntiacus reevesi) . However, only some of the affected species excrete bTB and are therefore capable of contributing to a pool of external infection. Of the affected species, only fallow deer and muntjac, at densities of over 56 per km2 and 47 per km2 respectively, are likely to act as maintenance hosts . Spillover host status may be provided by roe deer, red deer, muntjac and fallow deer at lower densities [32, 34]. However, the capacity of these species to maintain the disease as part of a multi-species host community has yet to be explored, and it may provide further opportunities for external infection to the badger population, as well being able to act as a spillover for bTB from badgers. Moreover, the presence of multispecies hosts of disease increases the possibility of contact across a wider variety of habitats due to a range of differences between species including foraging and dispersal distances. For example, the foraging distance of a badger may only reach 250 m whereas the foraging distance of a roe deer doe may be more than 1800 m [35, 36].
It is likely that a low level of seeding from external sources, for example external seeding from infected livestock and/or from infected environmental sources such as water, food and soil  occurs in many areas where bTB persists in wildlife populations around the world. In Northern Michigan, a survey of wildlife for M.bovis infection discovered infected opossums (Didelphis virginianus) and a grey fox (Urocyon cinereoargenteus) which had been located on bTB-depopulated cattle farms . M. bovis has been recovered from soil samples , badger setts and badger latrines  in areas with infected badgers, and has shown to be able to survive for long periods of time within soil  and on the forest floor in areas of high possum (Trichosurus vulpecula) density . Our analysis of external infection of bTB in badgers has shown that low levels of external infection alone are relatively unimportant compared with disease processes internal to the host population in determining the persistence of bTB in badgers above the threshold group size. However, at lower group sizes, as occur throughout many areas where bTB persists in cattle, external sources of infection are likely to assume a much greater significance. This may account for bTB infection in badgers in Switzerland, France and Spain [27, 43]. For example, bTB persists in badger populations in Ireland despite an average group size of 3.9 badgers . All else being equal, a greater level of external infection would be required to maintain bTB in badgers in Ireland, because of the smaller badger group sizes, than is the case in Britain, where group sizes are frequently well above the threshold level predicted by the model. However, our results suggest that the Irish situation is also more sensitive to the effects of external infection than that in Britain, since the group size in Ireland is within a critical range just below the threshold for disease persistence, where the potential role of any external sources is magnified. In Ireland, bTB persistence is therefore likely to be a consequence of a combination of badger-derived infection, infection from livestock and from other environmental sources [44, 45], as well as possible differences in badger behaviour at lower densities . In many parts of Britain, especially where badger densities are higher, bTB is likely to be maintained simply through badger-derived infection.
The control of bTB has been based historically on the testing and slaughter of infected cattle, or taken a dual approach, combining a test-and-slaughter policy with wildlife culling [46, 47]. Culling of badgers may result in more dispersal of individuals, with the potential to lead to a perturbation effect (higher bTB as a consequence of disruption to the badger social system due to badger culling [48, 49]). However, the extent of the any perturbation effect is likely to depend on both the extent of behavioural change in the badger population relative to the previous situation, as well as on the relative dependence of the disease system on badger-derived infection compared with cattle-derived infection. Perturbation is more likely to occur where bTB persistence is predominantly badger-derived, and where the effects of culling are to cause significant changes in behavioural patterns.
Our work suggests that the effectiveness of bTB control through badger culling is therefore dependent on the interplay between badger population density and group size (which determine social behaviour and the likely extent of any perturbation effect), and the presence and significance of external sources of infection. As badger populations are decreased by culling, especially where initially high-density populations are reduced significantly, disease may transiently increase due to a perturbation effect. Where a disease problem is still present in the cattle, disease may continue to persist, or even resurge, due to the role of cattle-derived infection in the system [50, 51], and this may be exacerbated by longer-term changes in the behaviour of the badger population. Any culling-based strategy to reduce bTB in badgers therefore needs to aim to reduce badger populations to not only below the level at which perturbation effects on disease are most pronounced, but also below the critical range where the disease in badgers can be maintained by trickle-type infection from other sources in the ecosystem.