Summary The spatial and temporal risk of tick-borne disease depends fundamentally on the distribution, abundance and seasonal dynamics of the vector ticks. The latter factor exerts a major quantitative influence on the transmission dynamics of tick-borne parasites. The population model for Rhipicephalus appendiculatus applies throughout the range of this tick in eastern Africa, and predicts all three fundamental risk factors on the basis of the local temperature and rainfall conditions. Satellite imagery can provide more detailed, real-time measures of environmental conditions over extensive areas than climatic data. There is preliminary evidence to suggest that the population model could be driven by satellite-derived surrogates of its climatic predictors, thus providing wide-scale predictive risk maps of theileriosis.