Abstract:
In this paper, global dynamics of an SIR model are investigated in which the incidence rate is
being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated).
Analytical study of the model shows that the model has two equilibrium points (diseasefree
equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is
locally asymptotically stable when reproduction number is less than one. Some conditions on the
model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some
sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are
obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf
bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies.