摘要
[目的]由于流行病会随着时间的变化而发生变化,因此,结合现实情况,研究一种受接种疫苗比率和免疫率影响的带时变性质的SVEIR疾病传播模型的平衡点的动力学性质.[方法]首先,通过构建动力学模型研究平衡点的存在性;其次,利用下一代矩阵法得出模型的基本再生数R0和有效再生数Re;最后,通过Lyapunov定理和Routh-Hurwitz判别方法对病毒的基本再生数和有效再生数进行稳定性分析.[结果]通过python数值仿真实验,得出当R0<1时,疾病会消失;当R0>1时,流行病会转化为地方流行病;当R0=1时,系统会出现临界分岔现象.[结论]接种疫苗是疾病防控的关键措施之一.R0的取值决定流行病的演化结果.
[Objective]Generally,because epidemic will change with time,the dynamics of the equilibrium point of a time-varying SVEIR disease transmission model affected by the vaccination rate and immunization rate is studied by combining with the reality.[Methods]First,the existence of equilibrium point was studied by constructing a dynamics model;Second,the basic regeneration numbers R 0 and effective regeneration numbers R e are obtained by using the next generation matrix method;Finally,the stability of the basic regeneration numbers and effective regeneration numbers were analyzed by using Lyapunov theorem and Routh-Hurwitz discrimination method.[Results]Through python numerical simulation experiment,it is obtained that when R 0<1,the disease will disappear;When R 0>1,the epidemic will transform into a local epidemic;When R 0=1,the system will have a critical bifurcation.[Conclusions]Vaccination is one of the key measures of disease prevention and control.The value of vaccine R 0 determines the evolution of epidemic.
作者
王海玲
翁智峰
WANG Hailing;WENG Zhifeng(Xiamen University Tan Kah Kee College,School of Information Science and Technology,Zhangzhou 363105,China;Huaqiao University,School of Mathematics and Science,Quanzhou 362021,China)
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2024年第2期329-334,共6页
Journal of Xiamen University：Natural Science
基金
福建省教育教学改革研究项目(FBJG20170154)
福建省高校产学合作项目(2018H6018)
教育部产学协同育人项目(JGH2019003,JGH2019023)
漳州市自然科学基金(ZZ2018J26)。
