Impact of Seasonality and Vertical Transmission on Mosquito Population in the Dynamics of Dengue Disease

Many epidemic diseases are season-related. Dengue is one of them. Since it is associated with a mosquito’s life cycle, it is genuinely affected by weather changes. In this paper, we model the dynamics of dengue disease transmission in the human population using two systems of delay differential equations. First, we carry out the modeling 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 that are affected by weather changes to be periodically time-dependent and re-deriving these parameters. We illustrate the conditions when the disease-free periodic solution is locally asymptotically stable and when it is unstable. Simulations in this case were compatible with the theoretical results.