An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate

Authors

  • Jianzhong Gao School of Science, Chang’an University, Xi’an, 710064
  • Tailei Zhang School of Science, Chang’an University, Xi’an, 710064

DOI:

https://doi.org/10.13447/j.1674-5647.2019.03.06

Keywords:

Logistic death rate, birth pulse, threshold value, global stability, permanence

Abstract

In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results. 

Downloads

Published

2019-12-16

Abstract View

  • 37527

Pdf View

  • 2755

Issue

Vol. 35 No. 3 (2019)

Section

Articles

How to Cite

An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate. (2019). Communications in Mathematical Research, 35(3), 247-263. https://doi.org/10.13447/j.1674-5647.2019.03.06