一类具有疫苗效应的SVEAIRD模型研究——以COVID-19为例  

A Class of SVEAIRD Models with Vaccine Effect:A Case Study of COVID-19

作　　者：梁媛 张太雷[1] 曹欢 LIANG Yuan;ZHANG Tailei;CAO Huan(School of Science,Chang'an University,Xi'an 710064,Shaanxi,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《山西师范大学学报(自然科学版)》2025年第1期10-19,共10页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：陕西省自然科学基金研究计划(2022JM-023).

摘　　要：提出了一类SVEAIRD传染病动力学模型来揭示疫苗接种对传染病传播的影响.首先,给出了模型的基本再生数,研究了无病平衡点的局部渐近稳定性;其次,基于我国COVID-19疫情传播的病例数据,利用统计学方法、优化理论以及非线性最小二乘拟合对该模型的参数进行了估计;通过平均百分比误差显示了模型拟合的精准度;最后,为了确定关键参数对疫情暴发的影响,还进行了不确定性和敏感性分析.研究结果表明,接种疫苗不仅会降低感染者对易感者的有效传染率,而且会降低感染者对疫苗丧失效力的接种者的有效传染率,提高疫苗的覆盖率和有效性可以减小感染峰值的规模以及推迟峰值到达的时间.We propose an SVEAIRD infectious disease dynamic model to reveal the impact of vaccination on the spread of infectious diseases.Firstly,the basic reproduction number of the model was given,and the local as-ymptotic stability of the disease-free equilibrium point is studied.Secondly,based on the case data of COVID-19 transmission in China,statistical methods,optimization theory and nonlinear least squares fitting were used to esti-mate the parameters of the model.The accuracy of model fitting is shown by the average percentage error.Finally,uncertainty and sensitivity analyses are conducted to determine the impact of key parameters on the outbreak of the epidemic.The research results show that vaccination not only reduces the effective transmission rate of infec-ted individuals to susceptible individuals,but also reduces the effective transmission rate of infected individuals to vaccinated individuals who have lost their effectiveness.Improving vaccine coverage and effectiveness can reduce the scale of peak infection and delay the time of peak arrival.

关 键 词：疫苗接种 动力学模型 COVID-19 参数估计 敏感性分析 

分 类 号：O175[理学—数学]