Global Stability of an SIR Model Characterized by Vaccination and Treatment (Journal of Nonlinear Modeling and Analysis, 2024)
The global dynamics of a SIR model characterized by both vaccination and treatment are considered in the present paper. Global stabilityensures convergence to an equilibrium solution irrespective of the initial stateof infection. Various independent sets of sufficient conditions on parametersand functional relations are obtained through Lyapunov functionals for stability. It is also established how a disease-free environment can be provided bya proper combination of treatment and vaccination, which is a unique featureas far as SIR models are concerned, as many of the studies have ignored theinfluence of treatment. Results are illustrated with numerical examples andsimulations are provided to visualize the illustrations.
Keywords: Infectious disease model; vaccination and treatment; Lyapunov function; equilibrium; global stability.