In this paper, we establish an influenza A epidemic model with vaccination and asymptomatic patient. The most important is that the method of the stability proof at the endemic equilibrium. We convert the model to a nonlinear Volterra integral equation, and prove the stability at the origin of this integral equation to obtain the local stability of the endemic equilibrium. Furthermore, combining with the uniqueness and the global attractiveness, we give the global stability of the endemic equilibrium. The method can be seen as a supplement for proving the global stability of the epidemic model, especially for the high-dimensional system.

中文翻译：

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接种疫苗的甲型流感模型的全局稳定性

在本文中，我们建立了一个包含疫苗接种和无症状患者的甲型流感流行模型。最重要的是地方性平衡的稳定性证明方法。我们将模型转换为非线性沃尔泰拉积分方程，并证明该积分方程在原点的稳定性，从而得到地方性平衡的局部稳定性。此外，结合独特性和全局吸引力，我们给出了地方性均衡的全局稳定性。该方法可以看作是证明流行病模型的全局稳定性的补充，特别是对于高维系统。