[1]王爱丽.具有饱和接种率的传染病模型的稳定性[J].江西师范大学学报(自然科学版),2014,(05):526-530.
　WANG Ai-li.The Stability of an Epidemic Model with Saturation Vaccination[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(05):526-530.
点击复制

具有饱和接种率的传染病模型的稳定性()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年05期
页码:
526-530
栏目:
出版日期:
2014-10-31

文章信息/Info

Title:
The Stability of an Epidemic Model with Saturation Vaccination
作者:
王爱丽
宝鸡文理学院数学系,陕西 宝鸡,721013
Author(s):
WANG Ai-li
关键词:
饱和接种率; 传染病模型; 全局稳定性
Keywords:
saturation vaccination; epidemic model; global stability
分类号:
O175
文献标志码:
A
摘要:
考虑到实践中有一部分人不愿意接种疫苗，引入1个阈值参数，建立了1个具有饱和接种率的传染病模型，以刻画资源有限情况下的接种策略。定义了模型的基本再生数，讨论了无病平衡点和地方病平衡点的存在性以及全局稳定性。结果表明：一方面人群中不愿接种者的比例影响疾病的消除与否以及不能消除时染病者的比例；另一方面可以适当增加存储疫苗的数量，使得当疾病不能被消除时，染病者的数量可以稳定在一个医疗条件允许的预先设定的水平。
Abstract:
A threshold parameter is introduced to represent some individuals will not vaccinate. An epidemic model with saturation vaccination is proposed to describe the vaccination policy with limited resources. The basic reproduc-tion number is defined. The existence and global stability of disease-free equilibrium as well as endemic equilibrium is investigated. The results obtained in this work indicates that the proportion of those willing not vaccinate plays an important role in whether the disease dies out or not and the ratio of infecteds when the disease persists. It also im-plies that the ratio of infecteds could stabilize at a previously specified level by increasing the amount of vaccines if it is impossible to eradicate.

参考文献/References:

[1] Anderson R,May R.Infectious disease of humans,dynamics and control [M].Oxford:Oxford University Press,1995.
[2] Keeling M J,Rohani P.Modeling infectious diseases in human and animals [M].Princeton:Princeton University Press,2008.
[3] 赵君平.一类具有一般非线性隔离函数和潜伏年龄SEIRS传染病模型稳定性分析 [J].江西师范大学学报:自然科学版,2011,35(5):464-470.
[4] 马知恩,周义仓,王稳地.传染病动力学的数学建模与研究 [M].北京:科学出版社,2004.
[5] Wang Wendi.Backward bifurcation of an epidemic model with treatment [J].Math Biosci,2006,201(1):58-71.
[6] 万辉,李永凤.一类传染病模型的Bagdanov-Takens 分支分析 [J].南京师大学报:自然科学版,2012,35(4):7-13.
[7] Li Yongfeng,Cui Jingan.The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage [J].Comm Nonl Sci Nume Simu,2009,14(5):2353-2365.
[8] Greenhalgh D,Khan Q J A,Lewis F I.Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity [J].Nonl Anal TMA,2005,63(6):779-788.
[9] Xiao Yanni,Tang Sanyi.Dynamics of infection with nonlinear incidence in a simple vaccination model [J].Nonlinear Anal,RWA,2010,11(5):4154-4163.
[10] Buonomo B.On the optimal vaccination strategies for horizontally and vertically transmitted infectious diseases [J].J Biol Syst,2011,19(2):263-279.
[11] Onofrio A d'.Stability properties of pulse vaccination strategy in SEIR epidemic model [J].Math Bios,2002,179(1):57-72.
[12] Wang Aili,Xiao Yanni.Sliding bifurcation and global dynamics of a Filippov epidemic model with vaccination [J].Internat J Bifur Chaos,2013,23(8):1-32.
[13] Stone L,Shulgin B,Agur Z.Theoretical examination of the pulse vaccination policy in the SIR epidemic model [J].Math Comp Mode,2000,31(4):207-215.
[14] Hui Jing,Chen Lansun.Impulsive vaccination of SIR epidemic models with nonlinear incidence rates [J].Disc Cont Dyna Syst,2004,4(3):595-605.
[15] Arino J,Mccluskey C C,Driessche P V D.Global results for an epidemic model with vaccination that exhibits backward bifurcation [J].SIAM J Appl Math,2003,64(1):260-276.

备注/Memo

备注/Memo:
陕西省教育厅科研计划(2010JK399)；宝鸡文理学院重点科研计划课题(ZK11129)
更新日期/Last Update: 1900-01-01