Pulse vaccination on SEIR epidemic model with nonlinear incidence rate

Abstract

In this paper, we consider an SEIR epidemic model with two time delays and nonlinear incidence rate, and study the dynamical behavior of the model with pulse vaccination. By using the Floquet theorem and comparison theorem, we prove that the infection-free periodic solution is globally attractive when R ∗ < 1 , and using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination when R ∗ > 1 .