具有垂直传播及感染期的乙肝传播模型

doi:10.3969/j.issn.1000-1565.2017.06.002

河北大学学报(自然科学版) ›› 2017, Vol. 37 ›› Issue (6): 567-571.DOI: 10.3969/j.issn.1000-1565.2017.06.002

具有垂直传播及感染期的乙肝传播模型

陶玉杰¹,冯贺平²

收稿日期:2017-02-17 发布日期:2017-11-25
作者简介:陶玉杰(1975—),女,吉林通化人,吉林通化师范学院副教授,主要从事微分方程及应用控制方面的研究. E-mail:369387310@qq.com
基金资助:
吉林省教育厅资助项目(吉教科合字［2015］441)

Hepatitis B virus infection model with vertical transmission and infection period

TAO Yujie¹,FENG Heping²

1.Department of Mathematics, Tonghua Normal University, Tonghua 134000, China; 2.Intelligent Engineering Department, Hebei Software Institute, Baoding 071000, China

Received:2017-02-17 Published:2017-11-25

摘要/Abstract

摘要： 研究具有垂直传播和感染期的乙肝病毒感染模型,考虑了发生率函数为非线性时模型的性质,以乙肝的平均感染期作为时滞,利用Routh-Hurwite判别法得到了系统的疾病消失的平衡点局部渐近稳定的条件,找到了基本再生数R₀,通过构造Lyapunov函数,证明了地方病平衡点的全局渐近稳定性.

关键词: 乙肝模型, 时滞, 全局渐近稳定, 非线性发生率, 垂直传播

Abstract: Hepatitis B virus infection model with vertical transmission and infection period were studied.By consider the epidemic models with nonlinear incidence rate,making infection period as time delay,and making use of Routh-Hurwite criterion to prove that condition of disease-free equilibrium is local asymptotic stability,we obtained a basic reproductive number R₀ and proved the global asymptotic stability of endemic equilibrium by using the Lyapunov functional method.

Key words: HBV epidemic model, time delay, global asymptotic stability, nonlinear incidence rate, vertical transmission

中图分类号:

O175

陶玉杰,冯贺平. 具有垂直传播及感染期的乙肝传播模型[J]. 河北大学学报(自然科学版), 2017, 37(6): 567-571.

TAO Yujie,FENG Heping. Hepatitis B virus infection model with vertical transmission and infection period[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(6): 567-571.

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具有垂直传播及感染期的乙肝传播模型

Hepatitis B virus infection model with vertical transmission and infection period

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