We are working on a deterministic SEIR model for the transmission dynamics of two strains of dengue disease, which allows transmission by exposed humans and mosquitoes. The goal of this research is to analyse the two strains model rigorously. That analysis includes: finding the steady states and their local and global stability properties, discussing the basic reproduction number(R(0)) for two strains model, incorporate vaccine against the strains of dengue and discussing the difficulties in developing the vaccine, calculating the final size of the epidemic and predict the number of cases for the next epidemic outbreak by using the current data that is available. We will try to find the ways for eradicating the disease using mathematical modelling and dynamical system techniques. Once this model analysis is completed, we will focus on non-autonomous version of this model and we will see the effect of closing the schools during the outbreak.