潜伏期具有传染性的水痘模型的分析  

Analysis of a Varicella Model Incorporating Infectious Force in Latent Period

作　　者：陈亚东 燕振阳 王厚强 鲁文龙 刘璐菊[1] 

机构地区：[1]河南科技大学数学与统计学院,河南 洛阳

出　　处：《自然科学》2020年第3期196-205,共10页Open Journal of Nature Science

基　　金：河南科技大学大学生研究训练计划(SRTP)项目(项目编号:2019202);河南科技大学青年学术带头人科研项目(项目编号:13490002)。

摘　　要：研究了一类潜伏期具有传染性的水痘模型,并考虑复发,隔离以及接种疫苗的因素。得到了水痘模型的基本再生数,利用李雅普诺夫第二方法证明水痘模型的全局动力学性态完全由基本再生数所控制。即当基本再生数小于1时,水痘病毒会在人群中逐渐消失;当基本再生数大于1时,水痘病毒不会绝灭并且在人群中形成地方病。A varicella model with infectious force during the latent period has been considered with the factors of relapse, quarantine and vaccination taken into account. The basic reproduction number of the varicella model is obtained, and the varicella model’s global dynamics are completely controlled by the basic reproduction number by using the second method of Lyapunov. If the basic reproduction number is under one, the varicella virus gradually disappears in the population;while if the basic reproduction number is above one, the varicella virus does not eradicate and becomes an endemic disease in the population.

关 键 词：水痘模型 基本再生数 地方病平衡点 李雅普诺夫第二方法 全局渐近稳定的 

分 类 号：R18[医药卫生—流行病学]