Abstract:

An SIRS epidemic model with generalized Logistic death rate and standard incidence was formulated. By use of the discrete dynamical system determined by the stroboscopic map, an “infectionfree” periodic solution of the model under impulsive vaccination was obtained. Based on Floquet theory and the comparison theorem of impulsive differential equation, the analysis of global asymptotic stability of the “infectionfree” periodic solution was given. And the sufficient condition for the permanence of the system was obtained. The results show that in order to prevent the epidemic disease from generating an endemic, an appropriate vaccination rate and an appropriate vaccination period can be chosen.

Key words:  Logistic death rate, impulsive vaccination, global asymptotic stability, permanence, periodic solution