A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

Pub Date : 2024-05-02 DOI:10.1007/s10255-023-1078-y

Song-bai Guo, Yu-ling Xue, Xi-liang Li, Zuo-huan Zheng

引用次数: 0

Abstract

Inspired by the transmission characteristics of the Coronavirus disease 2019 (COVID-19), an epidemic model with quarantine and standard incidence rate is first developed, then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals, which means that the epidemic is uniformly persistent if the control reproduction number \({{\cal R}_c} > 1\). This approach can be applied to the related biomathematical models, and some existing works can be improved by using that. In addition, the infection-free equilibrium V⁰ of the model is locally asymptotically stable (LAS) if \({{\cal R}_c} < 1\) and linearly stable if \({{\cal R}_c} = 1\); while V⁰ is unstable if \({{\cal R}_c} > 1\).

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具有检疫和标准发病率的流行病模型的均匀持续性新分析方法

受冠状病毒病2019（COVID-19）传播特性的启发，首先建立了一个具有检疫和标准发病率的流行病模型，然后提出了一种新的分析方法来寻找感染个体数量的最终下限，即如果控制繁殖数为（{{\cal R}_c} >1\），则流行病是均匀持续的。这种方法可以应用到相关的生物数学模型中，现有的一些著作也可以利用这种方法加以改进。此外，如果 \({{\cal R}_c} < 1\) ，模型的无感染均衡 V0 是局部渐近稳定的；如果 \({{\cal R}_c} = 1\) ，V0 是线性稳定的；而如果 \({{\cal R}_c} > 1\) ，V0 是不稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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