We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion of vaccinated individuals and the time between doses. If the is less than 1 (), then we obtain precise conditions for the existence and global stability of a disease-free solution. Otherwise, if , then a globally stable solution emerges with positive coordinates.

中文翻译：

---

SIR 模型中的脉冲疫苗接种：全球动态、分歧和季节性


我们分析了受脉冲疫苗接种 SIR 模型启发的周期性强制动力系统。我们根据接种疫苗的个体的比例和剂量之间的时间来充分描述其动态。如果 小于 1 ()，那么我们就获得了无病解的存在和全局稳定性的精确条件。否则，如果 ，则出现具有正坐标的全局稳定解。