一类具有疫苗接种和垂直传播的SEIV传染病模型的动力学分析
Dynamic Analysis of a Class of SEIV Infectious Disease Models with Vaccination and Vertical Transmission
王春霞 1王晓东 1热木孜亚·热布哈提 1王凯1
作者信息
- 1. 新疆医科大学医学工程技术学院,新疆 乌鲁木齐 830017
- 折叠
摘要
利用动力学方法建立了一类具有疫苗接种,并同时考虑垂直传播的SEIV传染病模型,利用下一代矩阵算法给出了决定疾病是否流行的阈值R0.当R0<1 时,模型存在唯一的无病平衡点,并通过建立合适的Lyapunov函数证明了无病平衡点是全局渐近稳定的;当R0>1 时,模型存在唯一的地方病平衡点,并证明了它是一致持久的.最后,通过数值模拟,验证了以上结论.此外,为了更好地控制和预防疾病,模拟研究了几个关键参数对疾病传播的影响.
Abstract
A SEIV infectious disease model with both vaccination and vertical transmission is established by using the dynamic method.The threshold R0 is given by the next generation matrix method to determine the prevalence of the disease.When R0<1,the model has a unique disease-free equilibrium,and it is proved that the disease-free equilibrium is globally asymptotically stable by establishing a suitable Lyapunov function.When R0>1,the model has a unique endemic equilibrium and is consistently persistent.The above conclusions were verified by numerical simulation.In addition,in order to better control and prevent the disease,the effect of several key parameters on the disease transmission is simulated.
关键词
疫苗接种/垂直传播/基本再生数/平衡点/稳定性Key words
vaccination/vertical transmission/basic reproduction number/equilibrium/stability引用本文复制引用
出版年
2025
国家科技期刊平台
NSTL
万方数据