Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

Parasite-mediated apparent competition occurs when one species affects another through the action of a shared parasite. One way of controlling the parasite in the more susceptible host is to manage the reservoir host. Culling can cause issues in terms of ethics and biodiversity impacts, therefore we ask: can treating, as compared to culling, a wildlife host protect a target species from the shared parasite? We used Susceptible Infected Recovered (SIR) models parameterized for the tick-borne louping ill virus (LIV) system. Deer are the key hosts of the vector (Ixodes ricinus) that transmits LIV to red grouse Lagopus lagopus scoticus, causing high mortality. The model was run under scenarios of varying acaricide efficacy and deer densities. The model predicted that treating deer can increase grouse density through controlling ticks and LIV, if acaricide efficacies are high and deer densities low. Comparing deer treated with 70% acaricide efficacy with a 70% cull rate suggested that treatment may be more effective than culling if initial deer densities are high. Our results will help inform tick control policies, optimize the targeting of control methods and identify conditions where host management is most likely to succeed. Our approach is applicable to other host-vector-pathogen systems.