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 R0 is less than one, while the Endemic Equilibrium (EE) point is asymptotically stable if the basic reproduction number R0 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.