一类具有时滞的COVID-19动力学模型及传播预测

A Dynamics Model of COVID-19 with Time-lag and Dissemination Prediction

建立可用于COVID-19疫情评估的一类具有时滞的新冠肺炎传播动力学模型(SI 2R模型)。研究利用时滞描述感染者在核酸检测阳性前的潜伏期,考虑防控隔离和医学追踪隔离等隔离措施的效果,将感染者分为两类:一类感染者具有传染能力,另一类感染者由于被隔离其感染能力可忽略不计,构建了SI 2R模型,并详细讨论系统解的存在性、有界性和平衡点的分类,再利用Lyapunov-LaSalle不变性原理证明了平衡点的全局稳定性。以2021年12月15日—2022年1月13日的西安市疫情数据为依据,拟合得到SI^(2)R模型的动力学参数,对西安市COVID-19疫情进行了预测和评估。结果表明,具有时滞的SI 2R传染病动力学模型对疫情的理论估计与西安市疫情的实际情况较为符合,可用于COVID-19传播行为分析,为疫情防控策略的制定提供了理论支持。

The purpose of this essay is to establish a class of new coronavirus disease transmission dynamic model(SI 2R)with time-lag that can be used to evaluate the outbreak of Corona Virus Disease 2019(COVID-19).A class of transmission dynamic model(SI 2R)with time-lag was constructed to describe the incubation period of infected patients before positive nucleic acid test.Considering the effect of isolation measures such as preventive and control isolation and medical follow-up isolation,the infected patients was divided into two categories(one with infectious ability and one with negligible infectious ability due to isolation).The classification of existence,boundedness and equilibrium points of understanding is discussed in detail.The global stability of equilibrium points is proved by the Lyapunov-LaSalle invariance principle.The dynamic parameters of the SI 2R model were fitted to obtain the prediction and evaluation of the COVID-19 epidemic in Xi'an based on the epidemic data from December 15,2021 to January 13,2022.The theoretical estimation of the epidemic by the SI^(2)R infectious disease dynamic model with time-lag was in good agreement with the actual situation of the epidemic in Xi'an.The SI 2R infectious disease dynamics model with time-lag can be used to analyze the transmission behavior of COVID-19,and can provide theoretical support for the development of epidemic prevention and control strategies.