Modelling the transmission dynamics of Theileria annulata: model structure and validation for the Turkish context

A mathematical model that describes the transmission dynamics of Theileria annulata is proposed that consists of 2 host components: the Hyalomma tick population and a compartmental model of T. annulata infection in the cattle population. The model was parameterized using data describing tick infestation and the infection status of cattle in Turkey from 2006 to 2008. The tick attachment rates are highly seasonal and because of the temporal separation of infectious and susceptible ticks virtually all ticks are infected by carrier cattle, so that annual peaks of disease in cattle do not impact on infection in the Hyalomma tick population. The impact of intervention measures that target the tick population both on the host and in the environment and their impact on the transmission of T. annulata were investigated. Interventions that have a limited ‘one-off’ impact and interventions that have a more permanent impact were both considered. The results from the model show the importance of targeting ticks during the period when they have left their first host as nymphs but have yet to feed on their second host.