An Improved Method to an Impulsive and Delayed Discretized Model

Abstract

In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R * and R * , and further prove that the disease-free periodic solution is globally attractive if R * is less than unit and the disease can invade if R * is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.