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《Journal of Yunnan University(Natural Sciences Edition)》 2008-S2
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A nonautonomous SEIR epidemic model with vertical transmission

DING Ling-fen,LI Jian-li (Department of Mathematics,Hunan Normal University,Changsha 410081,China)  
A nonautonomous SEIR epidemic model with vertical transmission is studied.Under quite weak assumptions,the sufficient condition on the uniformly strong persistence of the disease is established,and the sufficient condition on the extinction of the disease is obtained.
【Fund】: 国家自然科学基金资助项目资助项目(10571050);; 湖南省教育厅青年项目(07B041);; 湖南师范大学青年优秀人才培养计划项目
【CateGory Index】: O175.1
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【Citations】
Chinese Journal Full-text Database 1 Hits
1 LIU Yan-ping (College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China);Persistence and Extinction for a Non-autonomous SIR Epidemic Model with Vertical Transmitted Diseases[J];Journal of Xinjiang University (Natural Science Edition);2005-03
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 SHI Rui-feng,LIU Ying-dong(School of Science,Beijing Jiaotong University,Beijing 100044,China);Global Stability on Constant Equilibria of A SIRS Model with Diffusion Terms[J];Journal of Beijing Jiaotong University;2006-06
2 YIN Rong-rong,HU Zhi-xing(School of Applied Science,University of Science and Technology Beijing,Beijing 10083,China);STABILITY OF AN EPIDEMIC MODEL FOR NONLINEAR INFECTIOUS RATE WITH VACCINATION AND QUARANTINE[J];Journal of Beijing Technology and Business University(Natural Science Edition);2009-03
3 XUE Ying1,2,XIONG Zuo-liang1(1.Department of Mathematics,Nanchang University,Nanchang Jiangxi 330047,China;2.Department of Basic Science,Logistical Engineering University of PLA,Chongqing 400016,China);A Kind of SEIR Epidemic Model with Impulsive Vaccinationand Class Age-Structure[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-01
4 GUO Jin-sheng1,2,LI Xiao-yan3(1.College of Mathematics,Physics & Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;2.Department of Mathematics,Hexi University,Zhangye 734000,China;3.Department of Mathematics,Lanzhou City University,Lanzhou 730070,China);A Qualitative Analysis of an Epidemic Model with Bilinear Incidence Rat[J];Journal of Chongqing Institute of Technology(Natural Science Edition);2008-02
5 XU Yan-li 1,2(1.Department of Mathematics and Computer Science,Hunan normal University,Changsha 410081,China;2.Department of Mathematics,Xiangnan University,Chenzhou 423000,China);Global Stability of SIQR Model with Vaccination,Quarantine and Non-linear Incidence Rate βSI/H+I[J];Journal of Xiangnan University;2009-02
6 HUA Lai-qing 1 , XIONG Lin-ping 1* ,SHEN Guang-rong 2 ,MENG Hong 1 ,HU Ya-ping 3 ,ZHAO Sheng-rong 4 (1. Department of Health Statistics, Facuty of Health Service,Second Military Medical University, Shanghai 200433, China; 2. School of Agriculture and Biology, Shanghai Jiaotong University,Shanghai 201101; 3. Agro-technical Extension of Pudong New District of Shanghai,Shanghai 201201; 4. Agro-technical Extension of Songjiang District of Shanghai, Shanghai 201613);Application of an autoregressive model in cucumber downy mildew disease forecasting[J];Academic Journal of Second Military Medical University;2005-06
7 Qu Linbo Han Ruizhu (School of Economics and Management,Southeast University,Nanjing 210096);Analysis of biology dangerous source diffusing dynamics model in population migration[J];Journal of Southeast University(Natural Science Edition);2007-S2
8 XU Wen-xiong~1 ZHANG Tai-lei~2 XU Zong-ben~1 (1-School of Science,Xi'an Jiaotong University,Xi'an 710049;2-College of Mathematics and System Seciences,Xinjiang University,Urumqi 830046);Global Stability for a Non-linear High Dimensional Autonomous Differential System SEIQR Model in Epidemiology[J];Chinese Journal of Engineering Mathematics;2007-01
9 LIU Qi-ming1,YANG Su-min 2 (1-Basic Courses,Ordance Engineering College,Shijiazhuang 050003; 2-Department of Computer Engineering,Ordance Engineering College,Shijiazhuang 050003);Construction and Analysis of a Mathematical Model for the Computer Virus Propagation[J];Chinese Journal of Engineering Mathematics;2008-03
10 WEI Wei1,LIU Shao-ping2,SHU Yun-xing1(1.Dept.of Mathematics and Physics,Luoyang Institute of Science and Technology,Luoyang 471003,China;2.Dept.of Mathematics,Huazhong University of Science and Technology,Hubei Wuhan 430074,China);Qualitative Analyses of Pulse Vaccination in the SIR Epidemic Model with Vertical Transmission[J];College Mathematics;2008-03
China Proceedings of conference Full-text Database 1 Hits
1 MI Chuan-min~1 LIU Si-feng~1 MI Chuan-jun~2 (1.Nanjing University of Aeronautics and Astronautics,School of Economics and Management,Nanjing 210016,China;2.Beijing Institute of Technology,College of Management and Economics,Beijing 100011,China);Study on the Diffusion of Enterprise Group Internal Distress based on SEIRS Model[A];[C];2007
【Co-references】
Chinese Journal Full-text Database 9 Hits
1 WANG Xu-hui,SONG Yan,WANG Cui-jiao(Department of Mathematics,Bohai University,Jinzhou 121013,China);Analysis of a class of vertical epidemic SEI model[J];Journal of Bohai University(Natural Science Edition);2008-02
2 ZHANG Shao-lin (College of Sciences, Zhcjiang University of Science and Technology, Hangzhou Zhejiang 310023 China);The Influence of Population Movement on the Transmission Effect of Infectious Disease[J];Journal of Biomathematics;2006-02
3 YANG Jian-ya ZHANG Feng-qin (Department of Applied Mathematics,Yuncheng University,Yuncheng Shanxi 044000 China);A SIR Epidemic Model with Vertical Transmission[J];Journal of Biomathematics;2006-03
4 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
5 Ding Lingfen Li Jianli Department of Mathematics,Hunan Normal University,Changsha,Hunan 410081;A SEIR Epidemic Model with Vertical Transmission[J];Journal of Shaoxing University(Natural Science);2008-03
6 LIU Yan-ping (College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China);Persistence and Extinction for a Non-autonomous SIR Epidemic Model with Vertical Transmitted Diseases[J];Journal of Xinjiang University (Natural Science Edition);2005-03
7 GOU Qing-ming~(1,2),WANG Wen-di~11.School of Mathematics and Finance,Southwest University,Chongqing 400715,China;2.Dept.of Mathematics,Fuling Teachers College,Fuling Chongqing 408003,China;The Stability of an Epidemic Model with Dispersal[J];Journal of Southwest China Normal University(Natural Science Edition);2006-01
8 MENG Xin-zhu~(1,2) CHEN Lan-sun~2 SONG Zhi-tao~1 1.College of Science,Shandong University of Science and Technology,Qingdao 266510,Shandong Province,P.R.China; 2.Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,Liaoning Province,P.R.China;Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination[J];应用数学和力学(英文版);2007-09
9 GUO SHULI LI XUEZHI (Department of Mathematics,Xinyang Teachers College,Xinyang 464000);STABILITY OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VERTICAL TRANSMISSION[J];Acta Mathematicae Applicatae Sinica;2005-04
【Secondary Citations】
Chinese Journal Full-text Database 3 Hits
1 YANG Jian-ya ZHANG Feng-qin (Department of Applied Mathematics,Yuncheng University,Yuncheng Shanxi 044000 China);A SIR Epidemic Model with Vertical Transmission[J];Journal of Biomathematics;2006-03
2 GUO SHULI LI XUEZHI (Department of Mathematics,Xinyang Teachers College,Xinyang 464000);STABILITY OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VERTICAL TRANSMISSION[J];Acta Mathematicae Applicatae Sinica;2005-04
3 LI XUEZHI (Department of Mathematics, Xinyang Normal University, Xinyang 464000) WANG SHIFEI (Department of Information Sciences, Jiangsu Polytechnic University, Changzhou 213016);Stability of an SIS Epidemic Model with Acute and Chronic Stages[J];Acta Mathematicae Applicatae Sinica;2006-02
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