A model to test how ticks and louping ill virus can be controlled by treating red grouse with acaricide

Ticks are the most important vectors of disease‐causing pathogens in Europe. In the U.K., Ixodes ricinus L. (Ixodida: Ixodidae) transmits louping ill virus (LIV; Flaviviridae), which kills livestock and red grouse, Lagopus lagopus scoticus Lath. (Galliformes: Phasianidae), a valuable game bird. Tick burdens on grouse have been increasing. One novel method to reduce ticks and LIV in grouse may be acaricide treatment. Here, we use a mathematical model parameterized with empirical data to investigate how the acaricide treatment of grouse might theoretically control ticks and LIV in grouse. Assuming a situation in which ticks and LIV impact on the grouse population, the model predicts that grouse density will depend on deer density because deer maintain the tick population. In low deer densities, no acaricide treatment is predicted to be necessary because abundances of grouse will be high. However, at higher deer densities, the model predicts that grouse densities will increase only if high numbers of grouse are treated, and the efficacy of acaricide is high and lasts 20 weeks. The qualitative model predictions may help to guide decisions on whether to treat grouse or cull deer depending on deer densities and how many grouse can be treated. The model is discussed in terms of practical management implications.