Process & Systems Modelling

Complex responses to movement-based disease control

Endemic livestock diseases cause significant loss to UK agriculture, and some endemic pathogens, such as Escherichia coli O157, also pose significant risks to human health. Hence, controlling such diseases benefits the livestock, farmers and human populations. Livestock disease controls are often linked to herd movements between farms, for example, via quarantine and pre- or postmovement testing. Designing effective controls, therefore, benefits from accurate assessment of the impacts of farm-to-farm spread of infection.

picture of a cow in a fieldWorking with colleagues at the University of Glasgow, SRUC and MRI, this work focused on characterising system level vulnerability to disease in terms of the expected number of additional farms directly infected by a single infected farm, a quantity known to the epidemiological modelling community as R*, which can also be correlated to the long-term proportion of infected farms (see figure). R* is a threshold quantity analogous to the more widely used basic reproduction number R0, for which any value greater than unity implies that the disease is expected to spread and persist. However, for metapopulations, calculation of R* is both more tractable and more meaningful than R0. For example, high R0 may only imply high within farm disease transmission. To date R* calculations have focused on so called household models of diseases in stable human populations and have not taken explicit account of movements of individuals between locations, which are a key driver of the between farm spread of endemic livestock disease. Applying algebraic methods, we have been able to calculate R* in the presence of both livestock movement and associated movement based controls, enabling us to demonstrate the use of R* as an indicator which aids the understanding of persistence and control of endemic disease.

Results show that under movementbased controls, an infection could be successfully controlled at high movement rates but persist at intermediate rates (see figure), due to the potential for undetected build-up of infections within herds. Ongoing application of this approach to a range of important livestock diseases, including E. coli O157, shows that disease control at the system level is complex, with changes in livestock movement aiding control of one disease, but exacerbating others.

(A) R* has a characteristic curve, starting at 0 for no movement (K=0), increasing to an intermediate peak, and then decreasing to 1 for high movement rates. Disease intervention with probability p reduces R*.
movement curves (A) and (B)spacer (B) The equilibrium proportion of farms infected depends on R*. When R*>1, the disease spreads sufficiently between farms to persist, otherwise it will ultimately fade out. When disease intervention probability p>0, then R*>1 only for intermediate movement rates K, and so the disease can only persist for a limited range of movement rates. Note that the lines for p=0.8 and p=1 are indistinguishable, because, for all values of K, R*<1, and so the equilibrium proportion of infected herds is zero.

Further details from: Jamie Prentice and Glenn Marion

Article date 2015

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