For some diseases, it is recognized that immunity acquired by natural infection and vaccination subsequently wanes. As such, immunity provides temporal protection to recovered individuals from an infection. An immune period is extended owing to boosting of immunity by asymptomatic re-exposure to an infection. An individual’s immune status plays an important role in the spread of infectious diseases at the population level. We study an age-dependent epidemic model formulated as a nonlinear version of the Aron epidemic model, which incorporates boosting of immunity by a system of delay equations and study the existence of an endemic equilibrium to observe whether boosting of immunity changes the qualitative property of the existence of the equilibrium. We establish a sufficient condition related to the strength of disease transmission from subclinical and clinical infective populations, for the unique existence of an endemic equilibrium.

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关于具有增强免疫力的流行病模型的地方病平衡的独特性的说明

对于某些疾病，人们认识到通过自然感染和疫苗接种获得的免疫力随后会减弱。因此，免疫为从感染中康复的个体提供了暂时的保护。由于无症状再次暴露于感染而增强了免疫力，因此延长了免疫期。个体的免疫状态在传染病在人群层面的传播中起着重要作用。我们研究了一个与年龄相关的流行病模型，该模型被表述为 Aron 流行病模型的非线性版本，该模型结合了通过延迟方程系统提高免疫力，并研究了地方病平衡的存在，以观察提高免疫力是​​否会改变病毒的定性特性。平衡的存在。