Climate change influences more and more of our activities. These changes led to environmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number R-0 depends on the duration of transmission period and the date of the first contamination case that was declared ((t(0)) in the specific case of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium ((EE) and disease-free equilibrium ((DFE). We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.