Flip bifurcations of an SIR epidemic model with birth pulse and pulse vaccination

In this paper, we study an SIR epidemic model with birth pulse and pulse vaccination. We present a new constructor method of Poincaré maps. Using this method, we construct a Poincaré map. However, for this Poincaré map, we can't directly use the bifurcation theorem to discuss the existence of flip bifurcations. We use a new method to investigate the existence of flip bifurcations. We establish that the system undergoes flip bifurcation when the maximum birth rate passes some critical values. Furthermore, some numerical simulations are given to illustrate our results.