Global Stability of an SIR Model Characterized by Vaccination and Treatment

Abstract

The global dynamics of a SIR model characterized by both vaccination and treatment are considered in the present paper. Global stability ensures convergence to an equilibrium solution irrespective of the initial state of infection. Various independent sets of sufficient conditions on parameters and functional relations are obtained through Lyapunov functionals for stability. It is also established how a disease-free environment can be provided by a proper combination of treatment and vaccination, which is a unique feature as far as SIR models are concerned, as many of the studies have ignored the influence of treatment. Results are illustrated with numerical examples and simulations are provided to visualize the illustrations.