In this paper, we study the dynamics for dengue disease transmission in population containing mother and infant with maternal antibody. The aim is to find a control measure to reduce the dengue transmission in infant population. Mathematical model is the important tool in analyzing the spread and control of dengue diseases. The analysis of the model for the transmission of this disease is done in this paper. From the analysis of our model, we obtain two equilibrium states. One is the disease free state  and the another one is the endemic equilibrium state  Conditions are established for the stability analysis of each equilibrium state and the relations with the basic reproductive numbers. We use Lyapunov function to show that if the basic reproductive number  is not more than 1, then the disease free equilibrium state is globally asymptotically stable. If  is greater than 1, then there exists a unique endemic equilibrium state which is asymptotically stable on the positive octant.