Bovine tuberculosis

50 A.J.K. Conlan and J.L.N. Wood

R 0 = βLH^1 - q

with q = 0 corresponding to density dependence
and q = 1 frequency dependence (Conlan et al.,
2012). Unfortunately, at least from herd level
models, the density-dependent parameter is
poorly identified, with a suggestion that trans-
mission is closer to density rather than fre-
quency dependence for a range of alternative
models (Conlan et al., 2012, 2015). However,
the additional flexibility of the non-linear
density- dependent term provides the opportu-
nity to fit the empirical increase phenomenologi-
cally while ensuring that transmission rates are
bounded as herd sizes increase.

4.2.2 Age-dependent patterns of

incidence and transmission

The first estimate of R 0 from the overall within-
herd prevalence, considered above, depends on
an implicit assumption that the risk of transmis-
sion within the herd is constant with respect to
age. We can test the validity of this assumption
by calculating the force of infection – or the rate

at which test-negative animals become test-

positive – with respect to age. Data from the 19th

and early 20th centuries, once again tabulated

by Francis, demonstrates the increasing risk of

becoming test-positive with respect to age that

we would expect given the progressive nature of

bovine TB infection (Fig 4.3a). However, at least

from these historical data, the rate at which ani-

mals became test-positive decreases with age

(Fig. 4.3b) with a peak in the very youngest age

group considered by Francis (0–0.5 years old).

This pattern is perhaps suggestive of pseudo-

vertical transmission, but it should also be noted

that tuberculin testing is no longer carried out in

calves under the age of 6 weeks. Interpreting

such historic data is fraught with difficulty with

many potential confounding factors. While this

general pattern remains true in contemporary

managed populations for infected animals

detected through meat inspection (Frankena

et al., 2007; Shittu et al., 2013), it is not the case

for the rates of culture confirmation of reactor

animals in managed herds (Brooks-Pollock et al.,

2013) and contemporary unmanaged herds in

Ethiopia (Firdessa et al., 2012) and India

(Thakur et al., 2010) where the proportion of

Fig. 4.3. (a) Percentage of animals reacting to skin test within coarse age groups (b) Estimated force of
infection within the same age groups. Adapted from Francis, J. (1947) Bovine Tuberculosis, Table I.

A

40

20

0

0–0.5 0.5–1.5 1.5–2.5 2.5–5.0

Age range (Years)

5.0–10.0 2.5–5.0 5.0–10.0

% Reactors

B

0.6

0.4

0.2

0–0.5 0.5–1.5 1.5–2.5

Age range (Years)

Force of infection

Study Bang, 1885 Bang, 1886–1898 Bang, 1899–1904

Burrow, 1937 Burrow, 1933