Qualitative analysis of the epidemic disease models with treatment

In this thesis, we analyze the complex dynamic nature of discrete-time SIR epidemic models obtained by discretizing a continuous SIR epidemic model exposed to treatment and immigration effects. Here we use the forward Euler method for discretization. First of all, we show the existence of equilibrium points of the model by reducing the three-dimensional system to the two-dimensional system. Next, we investigate the stability conditions of the obtained positive equilibrium point, the visibility of Flip and Neimark-Sacker bifurcation. We present this situation by making a topological classification of the equilibrium points of the model. We use the chaos control strategy. We perform numerical simulations to support analytical results. We apply all these analyzes for models with and without immigration to show the effect of immigration on dynamics.