and is denoted by the discrete probability function h(prevt|xt).1 If hogs are tested, the test results
become part of the producer’s production history, which is summarized by a production history
indicator level, Rt, a scalar defined as the number of consecutive months (up to a maximum of α1 ∈ {0,
1, 2, ..., 24}) the producer has delivered hogs prior to the current period without having a Salmonella
prevalence test level exceeding the Salmonella serological threshold level, α7 ∈ {10, 20, 30, 40}, set by
the slaughter plant.
The probability that the producer’s hogs will be tested on delivery, t(Rt) , declines as Rt
increases according to the following relationship:
(1) t(Rt) = max((a2e a3Rt ), a4),
where α2 is the maximum probability of being tested, α3 is a testing probability reduction parameter,
and α4 is the minimum probability of being tested. The evolution of the production history indicator is
described by the following expression:
(2) Rt+ι H
min((Rt +1), aɪ) if TesttFail(xt ) = 0
where Testt is a binary variable equal to one if the producer’s hogs are tested in period t and zero
if TesttFail(xt ) = ɪ,
otherwise, and Fail(xt) is a binary variable equal to one if the producer’s hogs are tested in period t and
1 We assume the prevalence of Salmonella at t=1 is independent of prevalence at t=0. Field tests reveal a low correlation
between consecutive monthly prevalence test results. However, there is some evidence that a low on-farm Salmonella
prevalence at t=0 is associated with a higher probability of a low on-farm Salmonella prevalence at t=1. We attribute this to
irreversible control measures, such as investments in farm buildings and equipment aimed at improving herd health
hygiene, which are not considered here. Seasonal effects could also be a factor, but these are also outside the scope of our
analysis.