[1]白 婵,万 辉.一个传染病模型中的后向分支问题（英文）[J].南京师范大学学报(自然科学版),2017,40(03):5.[doi:10.3969/j.issn.1001-4616.2017.03.002]
　Bai Chan,Wan Hui.Backward Bifurcation in an Epidemic Model[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(03):5.[doi:10.3969/j.issn.1001-4616.2017.03.002]
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一个传染病模型中的后向分支问题（英文）()
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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40卷
期数:
2017年03期
页码:
5
栏目:
·数学·
出版日期:
2017-09-30

文章信息/Info

Title:
Backward Bifurcation in an Epidemic Model
文章编号:
1001-4616(2017)03-0005-08
作者:
白 婵; 万 辉
江苏省大规模复杂系统数值模拟重点实验室,南京师范大学数学科学学院,江苏 南京 210023
Author(s):
Bai Chan; Wan Hui
Jiangsu Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
关键词:
免疫接种; 传染病模型; 医疗资源; 平衡点; 稳定性; 后向分支
Keywords:
vaccination; epidemic model; medical resource; equilibrium; stability; backward bifurcation
分类号:
175.12
DOI:
10.3969/j.issn.1001-4616.2017.03.002
文献标志码:
A
摘要:
为了研究在考虑免疫接种情况下有限的医疗资源对疾病传播的影响,我们建立了一个带有特殊恢复率的SIVS传染病模型,研究了模型的基本动力学性质并对后向分支进行了详细的证明. 结果表明,有限的医疗资源会导致重要的动力学性质,比如双稳现象等. 后向分支意味着,即使基本再生数小于1模型依然可能会有稳定的地方病平衡点,基本再生数不能完全反映疾病流行与否. 此时,人们应该注意疾病爆发时的初始状态. 研究结果同时表明,充足的医疗资源和服务对于疾病的消除与控制非常重要. 另外,文章也分析了免疫接种的影响.
Abstract:
In this paper,we formulate a SIVS epidemic model with special recovery rate to study the impact of limited medical resource on the transmission dynamics of diseases with vaccination. The basic investigation of the model has been finished. The backward bifurcation has been proved precisely. It is shown that limited medical resource leads to vital dynamics,such as bistability. Backward bifurcation implies that even if the basic reproduction number is smaller than unity,there may be a stable endemic equilibrium and the basic reproductive number itself is not enough to describe whether a disease will prevail or not and we should pay more attention to the initial conditions. It is also shown that sufficient medical services and medicines are very important for the disease control and eradication. Besides,the impact of vaccination has been explored too.

参考文献/References:

[1] CUI J,MU X,WAN H. Saturation recovery leads to multiple endemic equilibria and backward bifurcation[J]. Journal of theoretical biology,2008,254:275-283.
[2]KRIBS Z C,VELASCO H J. A simple vaccination model with multiple endemic states[J]. Math Biosci,2000,164:183-201.
[3]LIU X,TAKEUCHI Y,IWAMI S. SVIR epidemic models with vaccination strategies[J]. Journal of theoretical biology,2008,253:1-11.
[4]LI J,ZHAO Y,ZHU H. Bifurcation of an SIS model with nonlinear contact rate[J]. J Math Anal Appl,2015,432:1 119-1 138.
[5]LI G,LI G F. Bifurcation analysis of an SIR epidemic model with the contact transmissions function[J]. Abstract and applied analysis,2014,Article ID 930541.
[6]MAGPANTAY F M G,RIOLO M A,DOMENECH de CELLS M,et al. Epidemiological consequences of imperfect vaccines for immunizing Iinfection[J]. SIAM Journal on applied mathematics,2014,74:1 810-1 830.
[7]ERIKA R,ERIC A,GERARDO G. Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment[J]. Mathematics and computers in simulation,2016,121:109-132.
[8]SHAN C,ZHU H. Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds[J]. J differential equations,2014,257:1 662-1 688.
[9]SHAN C,ZHU H. Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources[J]. J differential equations,2016,260:4 339-4 365.
[10]WAN H,CUI J. Rich Dynamics of an epidemic model with saturation recovery[J]. Journal of applied mathematics,2013,Article ID 314958,9 pages.
[11]XIAO Y,TANG S. Dynamics of infection with nonlinear incidence in a simple vaccination model[J]. Nonlinear analysis:real world applications,2010,11:4 154-4 163.
[12]ZHOU T,ZHANG W,LU Q. Bifurcation analysis of an SIS epidemic model with saturated incidence rate and saturated treatment function[J]. J applied mathematics and computation,2014,226:288-305.
[13]VAN DEN DRIESSCHE P,WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental model of disease transmission[J]. J Math Biosci,2002,180:29-48.
[14]CASTILLO C C,SONG B. Dynamical models of tuberculosis and their applications[J]. Mathematical biosciences and enginieering,2004(1):361-404.

相似文献/References:

[1]万辉,李永凤.一个传染病模型的Bogdanov-Takens分支分析(英文)[J].南京师范大学学报(自然科学版),2012,35(04):7.
　Wan Hui,Li Yongfeng.Bogdanov-Takens Bifurcation Analysis of an Epidemic Model[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(03):7.
[2]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.
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备注/Memo

备注/Memo:
Received data:2017-04-13.
Foundation item:Supported by Jiangsu Overseas Research and Training Program for University Prominent Young & Middle-aged Tachers and Presidents; the NSF of the Jiangsu Higher Education Committee of China(15KJD110004); Project Founded by PAPD of Jiangsu Higher Education Institutions.
Corresponding author:Wan Hui,associate professor,majored in mathematical biology. E-mail:wanh2046@163.com
更新日期/Last Update: 2017-09-30