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中文摘要：
研究了一个具有脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的动力学行为，其中，脉冲生育和脉冲接种发生在不同时刻，得到了决定疾病流行与否的阈值．通过利用Poincare映射和中心流形定理，讨论了地方病周期解的flip分岔．进一步，数值模拟较好地验证了理论分析．
英文摘要：
The dynamical behaviors of an SIRS epidemic model with the effects of birth pulse, pulse vaccination and vertical transmission at different moments were studied. The threshold for a disease to be extinct or endemic was established. The Poincare map and center manifold theorem were used to discuss flip bifurcation of the endemic periodic solution. Numerical results for periodic solutions and bifurcation diagrams, which were illustrated with an example, were in good agreement with the theoretical analysis.
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