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《Journal of Biomathematics》 2011-01
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Global Stability of an Epidemic Model with Vertical Transmission and Vaccination

WANG Jun-feng XUE Ya-kui (Department of Mathematics,North University of China,Shanxi Taiyuan 030051 China)  
In this paper,the SEIRS epidemic model with vertical transmission and vaccination is studied.It is proved that the global dynamics are completely determined by the basic reproduction number R_0.IfR_01,the disease-free equilibrium is global asymptotically stable and the disease always dies out.If R_01,a unique endemic equilibrium exists and is globally stable in the interior of the feasible region,and the disease persists at the endemic equilibrium state if it initially exits.At the same time,using global stability analysis of the model,it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value.It is also shown that the disease will persist within the population if the coverage level is below this threshold.
【Fund】: 国家自然科学基金(10471040);; 山西省自然科学基金(2009011005-1)
【CateGory Index】: O175.13
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【Citations】
Chinese Journal Full-text Database 3 Hits
1 CHENG Xiao-wei,HU Zhi-xing(School of Applied Science,University of Science and Technology Beijing,Beijing 100083,P.R.China);Analysis of an SIVR Model with Vertical Infection and Precautionary Vaccination[J];Science Technology and Engineering;2008-15
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 SUN Chun-li1,ZHAO Li-chun2(1.School of Science,University of Science and Technology Liaoning,Anshan 114051,China;2.Dept.of Mathematics,Anshan Normal University,Anshan 114005,China);T-S fuzzy control with hepatitis B model[J];Journal of University of Science and Technology Liaoning;2010-04
2 WANG Li-jun,SUI Xiao-hui,FENG Shou-sheng,SONG Yan (Department of Mathematics,Bohai University,Jinzhou 121013,China);Quantitative analysis of model SIR with vertical transmission and death of disease[J];Journal of Bohai University(Natural Science Edition);2009-02
3 LI Chun-yan,LI Dong-mei,YIN Xiao(Applied Science College,Harbin University of Science Technology,Harbin 150080,China);The stability analysis of the SIR epidemic models with vertical infection and continuous vaccination[J];Journal of Natural Science of Heilongjiang University;2009-06
4 LU Zhi-qi,LV Jian-feng(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China);Stability Analysis on the SIR Epidemic Model with Vertical Transmission[J];Journal of Henan Normal University(Natural Science);2010-04
5 XU Jin-rui,WANG Mei-juan,ZHANG Yong-jun (College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China);SIRS epidemical model of continuous vaccination with saturating infect rate and vertical infection[J];Journal of University of Shanghai for Science and Technology;2010-04
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7 JIAO Jian-jun~(1,2) CHEN Lan-sun~1 (1 Department of Applied Mathematics,Dalian University of Technology,Dalian Liaoning 116024 China) (2 School of Mathematics and Statistics,Guizhou College of Finance and Economics,Guiyang Guizhou 550004 China);A Pest Management SI Model with Impulsive Control Concerned[J];Journal of Biomathematics;2007-03
8 DONG Hai-ling HOU Zhen-ting WANG Bing-chang (School of Mathematics,Central South University,Changsha Hunan 410075 China);A Class of Markov-Modulated Continuous Infectious Disease Model[J];Journal of Biomathematics;2008-01
9 FU Jing-chao JING Yuan-wei ZHANG Zhong-hua ZHANG Si-ying (College of ln formatian Science and Engineering Northeastern University,Shenyang Liaoning 110004 China);The Study on the SIRS Epidemic Models with Vertical Infection and Continuous Vaccination[J];Journal of Biomathematics;2008-02
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【Secondary Citations】
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