摘要
为研究无症状病人对疾病传播的影响,本文研究了一类带有无症状病人的SISIa传染病模型,得出基本再生数和平衡点的存在性.通过选取恰当的Lyapunov函数和Dulac函数,利用Lasalle不变性原理和Bendixson-Dulac原理证明平衡点的全局渐近稳定性,并且发现此模型在边界平衡点会出现折分支和Bogdanov-Takens分支现象.由此可见,无症状病人在传染病传播过程中会导致系统产生复杂的动力学性态.
To study the impact of asymptomatic patients on disease transmission,this article studies a class of S-IS-Ia infectious diseases with asymptomatic patients model.Existence of basic regeneration number and equilibrium point are obtained.By choosing appropriate Lyapunov function and Dulac function,the global asymptotic stability of the equilibrium is proved by using Lasalle invariance principle and Bendixson-Dulac principle.It is also found that the model will show the bifurcation branch and Bogdanov-Takens branch phenomenon at the boundary equilibrium.It can be seen that asymptomatic patients will cause complex dynamics in the system during the transmission of infectious diseases.
作者
刘彬彬
于辛雅
齐龙兴
LIU Binbin;YU Xinya;QI Longxing(School of Mathematical Sciences,Anhui University,Hefei,China 230601,China)
出处
《应用数学学报》
CSCD
北大核心
2021年第5期703-721,共19页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(11401002,11771001)
安徽省自然科学基金(2008085MA02)
安徽省质量工程重点项目(2020jyxm0103)
安徽省高等学校自然科学基金(KJ2018A0029)资助。
