Author(s)

Yujing Liu, Lijun Zhang, Shujing Gao

Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, China.

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.

Discrete Epidemic Model, Time Delay, Pulse Vaccination, Extinction

Liu, Y. , Zhang, L. and Gao, S. (2016) An Improved Method to an Impulsive and Delayed Discretized Model. Applied Mathematics, 7, 108-123. doi: 10.4236/am.2016.71010.