中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (2): 155-160.doi: 10.13471/j.cnki.acta.snus.2019.02.020

• 论文 • 上一篇    

一类具有饱和发生率和潜伏期的SEIR模型的稳定性

豆中丽1,王锐2   

  1. 1. 重庆工商大学融智学院,重庆 400055;
    2. 重庆大学数学科学学院,重庆 401331
  • 收稿日期:2018-06-11 出版日期:2019-03-25 发布日期:2019-03-25

The stability of a SEIR model with saturate incidence and latency

DOU Zhongli1, WANG Rui2   

  1. 1.Rongzhi College, Chongqing Technology and Business University, Chongqing 400055, China;
    2. School of Mathematics Science, Chongqing University, Chongqing 401331, China
  • Received:2018-06-11 Online:2019-03-25 Published:2019-03-25

摘要:

对一类具有饱和发生率和潜伏期的SEIR传染病模型进行研究,确定决定疾病灭绝或者持续存在的基本再生数,分析模型平衡点的存在性。首先,通过构造适当的Lyapunov函数,证明了无病平衡点的全局稳定性;另外,运用复合矩阵判定定理分析了地方病平衡点的渐近稳定性;最后,利用竞争系统定理,证明了地方病平衡点的全局稳定性。

关键词: 基本再生数, 稳定性, 复合矩阵, 竞争系统

Abstract:

A SEIR infectious disease model with saturated incidence and latency is studied. The basic number of regeneration that determines extinction or persistence of diseases is determined. The existence of the model‘s equilibrium point is analyzed. Firstly, the global stability of disease-free equilibrium point is proved by constructing the Lyapunov function appropriately. Then, the asymptotic stability of local diseases-equilibrium point is analyzed by using the composite matrix judgment theorem. Finally, the global stability of local diseases-equilibrium point is proved by applying the competition system theorem.

Key words: reproduction number, stability, composite matrix, competitive system

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