This paper presents statistical methodology to analyze longitudinal binary responses for which a sudden change in the response occurs in time. Probability plots, transition matrices, and change-point models and more advanced techniques such as generalized auto-regression models and hidden Markov chains are presented and applied on a study on the activity of Rhipicephalus appendiculatus, the major vector of Theileria parva, a fatal disease in cattle. This study presents individual measurements on female R. appendiculatus, which are terminating their diapause (resting status) and become active. Comprehending activity patterns is very important to better understand the ecology of R. appendiculatus. The model indicates that activity and non-activity act in an absorbing way meaning that once a tick becomes active it shows a tendency to remain active. The change-point model estimates that the sudden change in activity happens on December 10. The reaction of ticks on acceleration and changes in rainfall and temperature indicates that ticks can sense climatic changes. The study revealed the underlying not visually observable states during diapause development of the adult tick of R. appendiculatus. These states could be related to phases during the dynamic event of diapause development and post-diapause activity in R. appendiculatus.