TWO DIFFERENT VACCINATION STRATEGIES IN AN SIR EPIDEMIC MODEL WITH SATURATED INFECTIOUS FORCE

Abstract

Two different vaccination and treatment strategies in the SIR epidemic model with saturation infectious force are analyzed. With the continuous vaccination and treatment, it is obtained that the disease free equilibrium and endemic equilibrium are globally asymptotically stable by using Lassall theorem and Pioncare–Bendixon trichotomy. Moreover, with pulse vaccination and treatment at different time, the dynamics of the epidemic model is globally investigated by using Floquet theory and comparison theorem of impulsive differential equation and analytic method. We obtain the conditions of global asymptotical stability of the infection-free periodic solution and permanence of the model. Finally, we compare the two different vaccination and treatment strategies, and obtain that the elimination of disease is independent of treatment in the case of the pulse vaccination.