In the epidemiological literature, the eradication of a wildlife disease through culling is usually described in terms of a constant hunting rate to simulate the selective removal of animals from the population. By using simple SI (susceptible–infected) models, it is easy to prove that, if the hunting rate is high enough, the population eventually drops below a critical threshold level under which the pathogen is deemed to be extinct. However, hunting costs as well as the monetary benefits of disease control are almost systematically neglected. Moreover, the hunting rate is usually assumed to be constant over time, while in reality health authorities can implement more flexible culling policies. In this work we examine a class of more realistic time-variant culling strategies in a cost–benefit framework. Culling strategies differ in the way decisions are made about when and how much to cull; that is, whether hunting occurs when disease prevalence, host population density, or the number of carcasses exceeds (or is below) a given threshold. For each culling strategy, the optimal value of the control parameters and the hunting rate are those that minimize the sum of the culling costs and the sanitary costs associated with infection over a specific period of time. Classical swine fever (CSF) in wild boar populations has been taken as a reference example because of its potential economic impact on industrialized and developing countries.

We show that the optimal time-flexible culling strategy is invariably more efficient than the best traditional strategy in which the hunting rate is held constant through time. We also show that the type of hunting strategy that is selected as optimal depends on the shape of the cost functions.