Preventive culling of farms is an important control measure to halt epidemics of highly infectious diseases of livestock such as classical swine fever, foot-and-mouth disease, and avian influenza. This paper introduces a novel prioritization scheme for culling of farms that is based on the idea that farms with the highest expected number of secondary infections should be culled first. Our simulations show that risk based culling outperforms ring culling in terms of the number of infected farms culled, the total number of farms culled, and the duration of the epidemic. As risk based culling reduced the number of infected farms that are culled it is therefore also expected to reduce the number of human infections. We find substantial variation in the outcome between different maps but for a given map risk based culling consistently outperformed ring culling. This indicates that the spatial structure has a large influence on the outcome of an epidemic, which is supported by previous research [4, 17, 19–21].

Although the model presented here is parameterised for the avian influenza epidemic that occurred in The Netherlands in 2003, the methodology of risk based culling is more generally applicable to other infectious diseases controlled by culling. The only information needed are the locations of the farms, the moments at which infected farms were culled (both essential for any control and usually available from surveillance), and an estimate of the distance-dependent probability of transmission. An extension of our method that could potentially further improve risk based culling would be to not only focus on the expected number of infections within one infection generation, but try to estimate the expected number of infections in second and perhaps even third infection generations in the future.

We assumed that all farms are equally infectious which is reasonable for avian influenza [12] but for other diseases this may be different. Variability in susceptibility and infectivity can also be taken into account in risk based culling, proving estimates are available. One example where such variability existed is foot-and-mouth outbreak in the UK. For this epidemic a model was derived that is similar to the model used in this paper [3, 4, 17] and it can be used to calculate the probability of infection and reproduction number per farm as needed for risk based culling.

It is possible with an extensive misspecification in, for example, the infectivity of farms that risk based culling would be less effective. Note though that alternative strategies (such as ring culling) may suffer similarly. The challenge here is to have a good epidemiological understanding of how a disease spreads and incorporate this knowledge into the calculations. We believe that if misspecifications are minor, the reproductive number still identifies patches of farms that are close together weighted by their distance to infected farms. Quantitatively the outcomes may differ to some extent but qualitatively (risk based culling is about prioritizing) they may still be accurate. The effectiveness of risk based culling also depends on the culling capacity relative to the spread of disease. If the culling capacity is too low any control is impossible. If the culling capacity is very high then the order of culling becomes irrelevant. In between these extremes, culling resources need to be used efficiently and risk based culling can aid in this.

One advantage of risk based culling is that it does not require a certain arbitrary ring to be set. It can be argued however that the threshold needed in risk based culling to set the minimum risk level for culling is also arbitrary, and there is indeed not one clear risk based threshold (*thr*) that achieves the best results across all three criteria. If the threshold is decreased, the number of farms culled is increased and the pool of susceptible farms depletes quicker, which means an epidemic is stopped earlier. An epidemic that stops more rapidly is likely going to have less infected farms culled, and thus less human infections. Vice versa, if the threshold is increased, the total number of farms culled decreases but the length of the epidemic and the number of infected farms culled increase. Which strategy is best thus depends what goals decision makers want to achieve. Economically the cost of the total number of farms culled and the cost of a longer epidemic can be weighted. The impact on public health (human casualties) is however difficult to weigh and are dependent on the disease. With a disease like avian influenza which has a clear zoonotic potential reducing the public health impact is arguably the most important.

For policy makers our risk based culling policy may be more difficult to justify to stake holders and the public than the simple traditional ring culling strategy. In addition, to be acceptable any culling strategy would have to satisfy the requirements of regulatory bodies. An intuitively appealing strategy may be to apply a risk based prioritization scheme within a culling ring. In our results this proved to be quite efficient (as shown in Table 2), primarily because most farms that are selected in a risk based prioritization scheme are located within a ring of 3 km from an infected farm (Table 2).

In the past mainly ring culling strategies have been considered in practice and literature [3, 4, 20, 22]. In [20, 22] a strategy was modelled that prioritised farms with high probability of infection. In this work the probability of infection per farm was based on the distance to the infected farms weighted by the number of sheep and cows. In risk based culling selection of farms is done by combining the probability of infection (dependent on distance to the infected farms) with the reproduction number (dependent on the local density of farms). Our results demonstrate that including the local density of farms to determine the order of preventive culling to control an epidemic is a promising strategy. This paper provides a guideline that could help improve the effectiveness of culling.