[1]韦春妙,庞建华,陆双扬,等.具有饱和发生率的次优免疫反应传染病模型分析[J].南京师范大学学报(自然科学版),2016,39(01):48.
 Wei Chunmiao,Pang Jianhua,Lu Shuangyang,et al.Analysis of a Sub-Optimal Immune Reaction EpidemiologicalModel with Saturation Incidence[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(01):48.
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具有饱和发生率的次优免疫反应传染病模型分析()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第39卷
期数:
2016年01期
页码:
48
栏目:
数学
出版日期:
2016-03-31

文章信息/Info

Title:
Analysis of a Sub-Optimal Immune Reaction EpidemiologicalModel with Saturation Incidence
作者:
韦春妙庞建华陆双扬惠 静
广西科技大学理学院,广西 柳州 545006
Author(s):
Wei ChunmiaoPang JianhuaLu ShuangyangHui Jing
School of Science,Guangxi Universty of Science and Technology,Liuzhou 545006,China
关键词:
次优免疫反应传染病模型基本再生数全局稳定性
Keywords:
Sub-optimal immune reactionepidemiological modelreproduction numberglobal stability
分类号:
O129
文献标志码:
A
摘要:
本文建立了一类具有饱和发生率,能反映次优免疫反应传播机制的传染病动力学模型,通过引入参数[σ],将经典的SIS模型和SIRS模型连接起来,该模型既能反映SIS模型和SIRS模型的动力学形态,又能反映一类介于这两类模型之间的次有免疫反应的传染病模型的动力学形态. 通过对模型的分析,确定了模型各类平衡点存在的阈值条件,通过构造Dulac函数和利用线性系统的局部稳定性定理,得到了各平衡点全局稳定的条件. 研究结果表明,对于具有饱和发生率的传染病模型,经典的SIS模型和SIRS模型具有相同的动力学形态,但其染病高峰时间和感染人数有明显的区别.
Abstract:
In this paper,an epidemiological model with saturation incidence rate which can reflect sub-optimal immune reaction propagation mechanism is investigated. This model corresponds to a transition between SIR and SIS model frameworks by a parameter. It shows that saturation incidence rate leads to rich dynamic behaviors,and the threshold of the existence of various equilibria are found. By means of constructing Dulac function and combing with the local stability of the corresponding linear system,we can obtain the conditions of global stability of equilibria. Furthermore,we are pleasantly surprised to find that between the SIS and SIR models there are very similar dynamics with saturation incidence rate,but it is obviously discriminate that the date when the endemic equilibrium becomes and the number of individuals will be infected between SIS and SIRS models.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2015-01-29. 
基金项目:国家自然科学基金(11401117和11201236)、广西自然科学基金(2012GXNSFAA053011)、广西高校科研项目(YB2014203)、广西科技大学科学基金(校科自1419206). 
通讯联系人:庞建华,博士,副教授,研究方向:生物数学. E-mail:pjh968@126.com
doi:10.3969/j.issn.1001-4616.2016.01.008
更新日期/Last Update: 2016-03-30