The epidemic threshold of vector-borne diseases with seasonality

Cutaneous leishmaniasis is a vector-borne disease transmitted to humans by sandflies. In this paper, we develop a mathematical model which takes into account the seasonality of the vector population and the distribution of the latent period from infection to symptoms in humans. Parameters are fitted to real data from the province of Chichaoua, Morocco. We also introduce a generalization of the definition of the basic reproduction number R0 which is adapted to periodic environments. This R0 is estimated numerically for the epidemic in Chichaoua; $$R_0\simeq$$ 1.94. The model suggests that the epidemic could be stopped if the vector population were reduced by a factor $$(R_0)^2\simeq$$ 3.76.