Note on “Optimal control of vaccination and treatment for an SIR

Abstract. In the article “Optimal control of vaccination and treatment for an SIR epidemiological model-World Journal of Modelling and Simulation, Vol. 8(2012) No. 3, pp. 194-204 ” authors have shown global stability for the SIR model considered. For this they constructed a Lyapunav function. We note that although this function is positive definite in the feasible region but its derivative along the solution trajectories of the model system is not negative definite everywhere in the feasible region. Thus this is not the right choice. We construct another Lyapunav function and establish that the endemic equilibrium is globally asymptotically stable in the entire feasible region whenever it exists