Qualitative Analysis of Both Hyperbolic and Non-hyperbolic Equilibria of a SIRS Model with Logistic Growth Rate of Susceptibles and Inhibitory Effect in the Infection

This paper describes a SIRS model with the logistic growth rate of susceptible class. The effect of an inhibitory factor in the infection is also taken into consideration. We have analysed local as well as global stabilities of the equilibrium points (both hyperbolic and non-hyperbolic) of the system and investigated the Transcritical bifurcation at the disease free equilibrium point with respect to the inhibitory factor. The occurrence of Hopf bifurcation of the system is examined and it was observed that this Hopf bifurcation is either supercritical or subcritical depending on parameters. Some numerical simulations are carried out for the validity of theoretical results.