Multiple models have been proposed to describe the epidemic spreading in the presence of interactions between two or more infectious diseases, but less is known about how dynamical aspects, such as time scales of diseases, affect the epidemic spreading. In this work, we evaluate the time shift produced in the number of people infected from one disease when interacting with another disease. Using a compartmental model, we produce different forms of relationship as competition, cooperation, and independence, assessing the effect of each one in the final result. We focus on the case of the unidirectional coupling between diseases, which enables us to study the impact of a perturbation to a driving disease on the driven one. We found that the prevalence of the driven disease is strongly affected if its time scale, defined by the time where the infection reaches the peak, is comparable to that of the driving disease. The secondary peak of the infection was observed under cooperative coupling if the time scale of the driving disease is much longer than that of the driven one.