一类具有饱和发生率的SEIR模型的稳定性
发布时间：2019-03-19 14:12
【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R01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。
[Abstract]:The stability of a class of SEIR models with the incidence of vertical infection and saturation was discussed, and the effects of the vaccination on the spread of infectious diseases were considered. By calculating the basic regeneration number R0 of the model, it is proved that the non-disease equilibrium point is local asymptotic stability and global asymptotic stability when R0 = 1. The Hurwitz criterion and the second additive compound matrix are used to prove that when R01, the local disease equilibrium point is locally asymptotically stable and is globally asymptotically stable under certain conditions.
【作者单位】： 北京科技大学数理学院;
【基金】：国家自然科学基金项目(61174209,11471034)
【分类号】：O175
本文编号：2443600
[Abstract]:The stability of a class of SEIR models with the incidence of vertical infection and saturation was discussed, and the effects of the vaccination on the spread of infectious diseases were considered. By calculating the basic regeneration number R0 of the model, it is proved that the non-disease equilibrium point is local asymptotic stability and global asymptotic stability when R0 = 1. The Hurwitz criterion and the second additive compound matrix are used to prove that when R01, the local disease equilibrium point is locally asymptotically stable and is globally asymptotically stable under certain conditions.
【作者单位】： 北京科技大学数理学院;
【基金】：国家自然科学基金项目(61174209,11471034)
【分类号】：O175
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