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• We proposed a mathematical pathogen-host model with a time delay for the dynamics of the banana black leaf streak disease. • Model accounted for the two reproduction means of the pathogen spores, seasonality and time delay to describe the incubation. • The basic reproduction number R0 does not depend on the time delay and is related to both sexual and asexual spore production. • The stability of the system was shown to not depend on the time delay, i.e. on the duration of the incubation period. • Results proved that the control of sexual spore production is not sufficient. We provide numerical simulations. Black Sigatoka Disease, also called Black Leaf Streak Disease (BLSD), is caused by the fungus Mycosphaerella fijiensis and is arguably one of the most important pathogens affecting the banana and plantain industries. Theoretical results on its dynamics are rare, even though theoretical descriptions of epidemics of plant diseases are valuable steps toward their efficient management. In this paper, we propose a mathematical model describing the dynamics of BLSD on banana or plantain leaves within a whole field of plants. The model consists of a system of periodic non-autonomous differential equations with a time delay that accounts for the time of incubation of M. fijiensis ' spores. We compute the basic reproduction number of the disease and show that it does not depend on the time delay, meaning that the persistence of BLSD would not qualitatively change even if the incubation period of the pathogen is perturbed. We derive local and global long-term dynamics of the disease and provide numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]