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

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 \({{\cal R}_c} > 1\).