Several models have been proposed for West Nile virus, they consider migration of birds population, the intermediates stages of mosquito life cycle, the feeding preferences and also the heterogeneity of the hosts. They do not take into account the seasonality of the disease. In this talk I will present a semi-discrete model for the transmission dynamics of vector-borne diseases. Here the transmission in a host population with a vector population is modelled in a SIS/SIR epidemiological framework, where contact between host and vector is assumed to occur only during the summer of each year. I will discuss two different types of threshold for the
spread of the disease are obtained: a ”shor-term threshold” and a ”long-term threshold”. The last one is compared to the definition of the basic reproduction number R0 for periodic continuous-time models, proposed by Bacaër and co-workers showing that they yield the same threshold. Finally I will show some simulations. The resulting behaviour may be reminiscent of the outbreaks of West Nile virus in Southern Europe.