BIFURCATION AND STABILITY ANALYSIS OF A DISCRETE TIME SIR EPIDEMIC MODEL WITH VACCINATION

Abstract

In this paper, we study the qualitative behavior of a discrete-time epidemic model with vaccination. Analysis of the model shows forth that the Disease Free Equilibrium (DFE) point is asymptotically stable if the basic reproduction number R-0 is less than one, while the Endemic Equilibrium (EE) point is asymptotically stable if the basic reproduction number R-0 is greater than one. The results are reinforced with numerical simulations and enhanced with graphical representations like time trajectories, phase portraits and bifurcation diagrams for different sets of parameter values.