Spreading Dynamics of an SIQRS Epidemic Model and Quarantine Strategy Analysis

During the COVID-19 pandemic, large-scale nucleic acid testing and quarantine were widely adopted as measures to contain the disease. However, it also aroused some controversy whether massive testing lead to increased interpersonal contacts and thus exacerbate the epidemic spreading. In this paper, we study a scalar SIQRS (Susceptible-Infected-Quarantines-Recovered-Susceptible) model incorporating infection, curing, quarantine and vaccination processes. To characterize the effects of massive testings, we assume that the interpersonal contact frequency between individuals increases linearly with the quar-antine rate, which is in turn determined by the frequency of massive testings. Via equilibrium and stability analysis, we study the effects of the quarantine rate and find that there exists a threshold, above which massive testings are helpful in containing the disease and below which massive testings facilitate the epidemic spreading. Numerical simulations are conducted to demonstrate the correctness of the theoretical analysis and the effectiveness of the proposed quarantine strategy.