An Incentive System for Salmonella Control in the Pork Supply Chain

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, R_t, 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(R_t) , declines as R_t
increases according to the following relationship:

(1)    t(Rt) = max((a2e ^a3R^t ), 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:

min((Rt +1), aɪ)  if Test_tFail(x_t ) = 0
where Testt is a binary variable equal to one if the producer’s hogs are tested in period t and zero

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.

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