In this paper, we are interested in finding the periodic oscillation of seasonally forced SEIR models with pulse vaccination. Many infectious diseases show seasonal patterns of incidence. Pulse vaccination strategy is an effective tool to control the spread of these infectious diseases. Assuming that the seasonally dependent transmission rate is a T-periodic forcing, we obtain the existence of positive T-periodic solutions of seasonally forced SEIR models with pulse vaccination by Mawhin’s coincidence degree method. Some relevant numerical simulations are presented to illustrate the effectiveness of such pulse vaccination strategy.

中文翻译：

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具有脉冲接种的季节强制SEIR模型的周期解的存在性

在本文中，我们有兴趣寻找带有脉冲疫苗接种的季节性强制SEIR模型的周期性振荡。许多传染病显示出季节性的发病模式。脉冲疫苗接种策略是控制这些传染病传播的有效工具。假设季节性相关的传输速率是T周期强迫，我们通过Mawhin符合度法获得了带有脉冲疫苗接种的季节性强制SEIR模型的正T周期解的存在。提出了一些相关的数值模拟，以说明这种脉冲疫苗接种策略的有效性。