一类具有疫苗接种和环境传播的新型冠状病毒肺炎模型的动力学分析  

Dynamic Analysis of the COVID-19 Epidemic Model with Vaccination and Environmental Transmission

作　　者：王晓静 李佳慧 闫慧林 郭松柏 梁宇 陈靖宜 WANG Xiaojing;LI Jiahui;YAN Huilin;GUO Songbai;LIANG Yu;CHEN Jingyi(School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616)

机构地区：[1]北京建筑大学理学院,北京102616

出　　处：《工程数学学报》2024年第3期458-468,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11901027);北京市教育委员会科研计划项目(SZ202110016008);北京建筑大学2023年度研究生创新项目(PG2023145).

摘　　要：依据传染病动力学的数学建模方法和新型冠状病毒肺炎(COVID-19)的传播机理,综合考虑疫苗接种及环境中的病毒载量对COVID-19传播的影响,建立了一类SEIARW传染病模型。首先,计算了模型的控制再生数,并证明了在控制再生数大于1时,模型存在唯一的地方病平衡点。然后,通过构造Lyapunov函数证明了无病平衡点和地方病平衡点的全局稳定性。最后,绘制出了控制再生数随其参数的变化曲线图,并拟合了2022年11月20日至12月5日期间北京显性感染者的疫情数据。数值模拟结果表明:提高疫苗接种率及疫苗效力能够降低疫情暴发的最终规模,并且加强环境中病毒的消杀能够有效减少潜伏期感染者、显性感染者和隐性感染者的人数。同时,应因地制宜地制定科学的防控策略,避免过度消毒损害人体健康和污染环境。Based on the method of mathematical modeling of infectious disease dynamics and the transmission mechanism of COVID-19,an SEIARW epidemic model is established,which incorporating vaccination and environmental transmission.Firstly,the control reproduction number of the model is calculated,and then the existence and uniqueness of the endemic equilibrium are given.Furthermore,two Lyapunov functions are constructed to prove the global stability of both the disease-free equilibrium and the endemic equilibrium.Finally,numerical simulations have been carried out to draw variation lines of the control reproduction number corresponding to its parameters and to fit the epidemic data of symptomatic in Beijing from November 20 to December 5,2022.The results show that increasing vaccination coverage and vaccine effectiveness can reduce the final size and strengthening the elimination of virus in the environment can effectively reduce the number of the exposed,asymptomatic and symptomatic.Meanwhile,scientific prevention and control strategies should be formulated according to local conditions to avoid excessive disinfection damaging human health and polluting the environment.

关 键 词：COVID-19 疫苗接种 环境传播 控制再生数 稳定性 

分 类 号：O175.1[理学—数学]