摘要
讨论了一类具有垂直传染与饱和发生率的SEIR模型的稳定性,考虑了接种免疫对传染病传播的影响。通过计算得到模型的基本再生数R0,证明了当R0≤1时,无病平衡点是局部渐近稳定和全局渐近稳定的。利用Hurwitz判据和第二加性复合矩阵证明了当R0>1时,地方病平衡点是局部渐近稳定的,且在一定条件下是全局渐近稳定的。
The stability of susceptible-exposed-infectious-recovered( SEIR) model with vertical transmission and saturated incidence rate was discussed,and the effect of vaccination on transmission of infectious disease was considered. The basic reproductive number R0 of the model was calculated. The disease-free equilibrium was proved to be local asymptotically stable and global asymptotically stable when R0≤ 1. The endemic equilibrium was proved to be local asymptotically stable and global asymptotically stable under certain conditions when R0> 1 by using Hurwitz criterion and the second additive compound matrix.
出处
《河南科技大学学报（自然科学版）》
CAS
北大核心
2017年第1期78-83,8,共6页
Journal of Henan University of Science And Technology:Natural Science
基金
国家自然科学基金项目(61174209
11471034)
关键词
垂直传染
饱和发生率
SEIR
稳定性
vertical transmission
saturated incidence rate
SEIR
stability
