Eliminating bovine tuberculosis in cattle and badgers: insight from a dynamic model

Bovine tuberculosis (BTB) is a multi-species infection that commonly affects cattle and badgers in Great Britain. Despite years of study, the impact of badgers on BTB incidence in cattle is poorly understood. Using a two-host transmission model of BTB in cattle and badgers, we find that published data and parameter estimates are most consistent with a system at the threshold of control. The most consistent explanation for data obtained from cattle and badger populations includes within-host reproduction numbers close to 1 and between-host reproduction numbers of approximately 0.05. In terms of controlling infection in cattle, reducing cattle-to-cattle transmission is essential. In some regions, even large reductions in badger prevalence can have a modest impact on cattle infection and a multi-stranded approach is necessary that also targets badger-to-cattle transmission directly. The new perspective highlighted by this two-host approach provides insight into the control of BTB in Great Britain.


Table of Contents
The FMD outbreak began on 19 February 2001, after which testing for bovine TB in cattle was reduced or delayed (supplementary figure 1). However, because tests are generally scheduled during the winter months, the reduction in testing was not as severe as it might have been if the FMD outbreak had been earlier in the year. By the 19 February in the previous year, 20% of tests for that year had already taken place. Furthermore, not all tests were cancelled during the outbreak, in particular short interval tests (SIT) of herds identified as infected continued.
By comparing the number of tests that took place during weeks 1 to 7 of 2001 with the number of tests for the same period in the previous year, we estimated number of tests that would have taken place in the absence of FMD, assuming that testing patterns would have remained constant between the two years (sup table 1). Counting all test types, we estimate that 39% of usual tests took place during 2001.
Reactor detection rates vary considerably by test type, so we also used the average reactor rate by test type between 2000 and 2002 to estimate the number of reactors that would have been found if testing had not been reduced in 2001. As the majority of reactors are disclosed during short interval tests (SIT) and nearly 60% of SIT took place during 2001, we estimate that the removal rate of reactors was approximately 43% less due to the reduction in testing during FMD. This estimate provides a rough guide only, as the number of tests in a given year depends on the number of reactors found. Nevertheless, it provides a starting place for the sensitivity analysis in the main paper.

Equilibrium prevalence of infection
Following on from model equations (1) in the main text, to obtain the equilibria, we set each equation to zero. Taking the equation for I C we have: where γ ' = γ C + µ C is the total removal rate of infected cattle due to testing and background slaughter rates. Setting I C = 1− S C and rearranging leads to a quadratic equation for S C * : Therefore, The equivalent equation can be derived for S B * : . For a high transmission setting, the cattle removal rate has the biggest impact of cattle prevalence. It is notable that there are no threshold values for the prevalence of infection in badgers or the badger-to-cattle transmission rate; as spillover from badgers increases the fraction of infected cattle increases monotonically.

Supplementary Figure 2: The equilibrium prevalence of infected cattle as a function of four variables a) the cattle-to-cattle transmission rate; b) the badger-to-cattle transmission rate; c) the prevalence of infected badgers; and d) the removal rate of infected cattle.
In the main paper we describe the impact of R CC on infection prevalence in cattle and badgers ( Woodroffe et al. [9] observed an increase in badger infection prevalence when cattle testing was reduced. Figure 3 in the main paper illustrates the effect of reducing cattle testing on badger prevalence as a function of the badger-to-badger reproduction number. We additionally explored the impact of reducing cattle testing as a function of badger-to-badger reproduction number R BB and cattle-to-badger reproduction number R CB . Supplementary figure 6 shows the relative change in badger prevalence when cattle removal is reduced as a function of badger-to-badger reproduction number and the cattle-to-badger reproduction number. We assumed a 40% drop in cattle testing, inline with the estimates above and other parameters as in the main text ( R CC = 1.05 and R BC = 0.05 ). As shown in figure 3 of the main text, we find that if R BB > 1.5 cattle testing has almost no impact on infection prevalence in badgers. Supplementary figure 6 shows that for increasing values of R CB the impact of reducing cattle testing is reduced, further supporting the argument that R CB ≪ 0.2 .