B. Singh, S. Jain, R. Khandelwal, Sneha Porwal and G. Ujjainkar
Soewono and Supriatna [9] studied a simple SIR dengue disease transmission model with vaccination. In the present paper we have modified the model with assumption that a random fraction of the recovered host population can loses the immunity and becomes susceptible again. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations. Restricting the dynamics for the constant host and vector populations, the model is reduced to a three-dimensional planar equation. Two states of equilibrium are studied, one disease-free and other endemic. The basic reproduction number 0 Â is obtained. In this model the disease-free equilibrium state is stable if Â0 £ 1 and if 0 Â > 1, the stable endemic equilibrium appears. Numerical simulation and graphical presentation are also provided to justify the stability
