The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Lévy noise with a nonlinear incidence and vaccination. Mainly, we derive a stochastic threshold [Formula: see text] which depends on model parameters and stochastic coefficients for a better understanding of the dynamical spreading of the disease. First, we prove the well posedness of the model. Then, we study the extinction and the persistence of the disease according to the values of [Formula: see text]. Furthermore, using different scenarios of Tuberculosis disease in Morocco, we perform some numerical simulations to support the analytical results.

中文翻译：

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包含调和均值和疫苗接种的 Lévy 过程的延迟流行病模型的随机阈值

本文的目的是研究由具有非线性发病率和疫苗接种的 Lévy 噪声驱动的延迟流行病模型的随机阈值。主要是，我们推导出一个随机阈值 [公式：见文本]，它取决于模型参数和随机系数，以便更好地理解疾病的动态传播。首先，我们证明了模型的适定性。然后，我们根据[公式：见正文]的值来研究疾病的灭绝和持续存在。此外，使用摩洛哥结核病的不同情况，我们进行了一些数值模拟以支持分析结果。