GLOBAL STABILITY AND BIFURCATIONS ANALYSIS OF AN EPIDEMIC MODEL WITH CONSTANT REMOVAL RATE OF THE INFECTIVE

Abstract

In this thesis we consider an epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infective on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation.

Keyword: Epidemic model, nonlinear incidence rate, basic reproduction number, local and global stability