Nonsynchronous bifurcation of SIRS epidemic model with birth pulse and pulse vaccination

Abstract

In this paper, we construct an SIRS epidemic model with birth pulse and pulse vaccination at the different fixed moment. The stability of the infection-free periodic solution is obtained by using the Poincare map. The existence of nontrivial periodic solution bifurcated from the infection-free periodic solution is discussed by means of the bifurcation theory. It is shown that once a threshold is reached, a nontrivial periodic solution emerges via a supercritical bifurcation. Furthermore, some numerical simulations are given, which are in good accordance with the theoretical results.