An epidemiological model of the dynamics of East Coast Fever (ECF) in East Africa caused by the protozoan parasite Theileria parva and transmitted by the brown-ear tick Rhipicephalus appendiculatus was developed. In the model, ticks are assigned to either on-host or off-host categories both of which differ in their capacity to receive and transmit the disease. Cattle are assigned to categories of susceptible, infected and infectious as well as recovered animals having immunity to the disease. The parameters of the model were estimated from data reported in the literature. A mathematical analysis of the ECF/tick/cattle model with and without disease was conducted. Depending on the ratio between fecundity and mortality rates in cattle and in the absence of disease, different scenarios emerge including extinction of ticks, coexistence of ticks and cattle and total extinction of ticks and cattle. Furthermore, the analysis of the model with the disease yielded threshold conditions for the existence and the persistence of stable coexistence equilibria for the epidemiological system that may lead to enzootic stability. The model was used to identify critical aspects of the dynamics required to develop management strategies: (i) tick control in areas where the disease is absent, (ii) threshold-based tick and disease control, and (iii) conditions permitting the establishment of enzootic stability of the ECF/tick/cattle system. The analysis also identifies critical areas requiring further field investigation, sets the basis for developing a realistic model for field implementation, and provides a tool for project development and evaluation in the context of international research.