Many epidemic diseases are season-related. Dengue is one of them. Since it is associated with a mosquito`s life cycle that is genuinely affected by weather changes. In this paper, we model the dynamics of Dengue disease transmission in the human population by two systems of delay differential equations. First, we carry out the modelling with the vertical transmission in the mosquito population and demonstrate its basic properties. Then we implement the seasonality effect in a second model by choosing some of the parameters affected by weather changes to be periodically time-dependent and re-derive these parameters. We illustrate the conditions when the disease-free periodic solution is locally asymptotically stable and when it is unstable. Simulations of this case were compatible with the theoretical results.