Full-Text Search：
《Journal of Biomathematics》 2004-02

## Hepatitis Epidemic Models with Proportional and Pulse Vaccination

XU Jie ZHOU Yi-cang (Department of Mathematics, Shanghai Maritime University, Shanghai 200135 China) ( Science College, Xi'an Jiaotong University, Xi'an Shanxi 710049 China)
Vaccination is an important strategy for the elimination of infectious diseases. Two mathematical SIR models with proportional vaccination and pulse vaccination are formulated in this paper. The dynamical behavior of these models are studied, and the basic reproductive numbers σ0 and σ1 are defined. For proportional model it is proved that the disease free equilibrium is globally asymptotically stable if σ0 1, and it is unstable if σ0 ;the endemic equilibrium is globally asymptotically stable if σ0 1. For pulse model,it is proved that the disease free periodic solution is stable if σ1 1, and it is unstable if σ1 ; the endemic periodic solution is stable if σ11 and p is sufficiently small.
【CateGory Index】： O242.1
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
 【References】
 Chinese Journal Full-text Database 8 Hits
 1 YANG Guang,ZHANG Qing-ling,LIU Pei-yong(School of Sciences,Northeastern University,Shenyang 110004,China.);Mathematical Model of Hepatitis B and Its Control[J];Journal of Northeastern University(Natural Science);2007-03 2 ZHANG Ping1, 2, 3, ZHANG Bai1, Peter M. ATKINSON4 (1. Northeast Institute of Geography and Agricultural Ecology, CAS, Changchun 130012, China; 2. Graduate School of the Chinese Academy of Sciences, Beijing 100039, China; 3. Geo-Exploration Science & Technology College, Jilin University, Changchun 130026, China; 4. Department of Geography, University of Southampton, Southampton SO17 1BJ, UK);Modelling Framework on Urbanization's Effect on the Infectious Disease Transmission: A Case Study on Southampton of UK[J];Acta Geographica Sinica;2007-02 3 GUO Xiao-jun LI Da-zhi (School of Sciences,Nantong University,Nantong 226007,China);Stability Analysis on a Class of SIQR Epidemic Dynamical Model with Vaccination and Isolated Items[J];Journal of Nantong University(Natural Science Edition);2008-04 4 GONG Zhang-rong,SHENG Wan-cheng,ZHANG Hong-zhi(School of Sciences,Shanghai University,Shanghai 200444,China);Stability of a Type of SI_1I_2R_1R_2 Epidemic Model[J];Journal of Shanghai University(Natural Science Edition);2006-05 5 FU Jingchao (College of Sciences,Northeastern Dianli University,Jilin 132012;The School of Information Science and Engineering,Northeastern University,Shenyang 110004) JING Yuanwei (The School of Information Science and Engineering,Northeastern University,Shenyang 110004) ZHANG Zhonghua (College of Sciences,Northeastern Dianli University,Jilin 132012) ZHANG Siying (College of Sciences,Northeastern Dianli University,Jilin 132012;The School of Information Science and Engineering,Northeastern University,Shenyang 110004);THE TWO SIRS EPIDEMICAL MODELS WITH VERTICAL INFECTION AND VACCINATION IN THE EASILY INFECTED GROUPS[J];Journal of Systems Science and Mathematical Sciences;2009-04 6 LIANG Ju-hua~(1,2) TANG San-yi~1 (1 College of Mathematics and Information Science,Shanzi Normal University,Xi'an Shanxi 710062 China) (2 Department of Mathematics,Zhoukou Normal University,Zhoukou Henan 466001 China);Discrete Host-Pathogen Models with Integrated Control Tactics[J];Journal of Biomathematics;2008-02 7 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 8 YANG Guang~1 LIU Xiao~2 (1 School of Mathematics and Systems Science,Shenyang Normal University Shenyang Liaoning 110004 China) (2 Liaodong University,Dandong Liaoning 118003 China);Calculation of the Basic Reproductive Number R_0 and Control Strategy[J];Journal of Biomathematics;2008-04
 【Citations】
 Chinese Journal Full-text Database 1 Hits
 1 JIN Zhen, PAN Jinxiao (Department of Mathematics, North China Institute of Technology, Taiyua n 030051);Dynamic Models of Infectious Diseases in Continuous Vaccination[J];Journal of Basic Science and Engineering;2001-Z1
 【Co-citations】
 Chinese Journal Full-text Database 9 Hits
 1 JIN Zhen1,MA Zhien2,YUAN Sanling2(1Department of Mathematics, North china Institute of Technology, Taiyuan, 030051;2Department of Mathematics, Xi'an Jiaotong University, Xi'an710049);A SIR Epidemic Model with Varying Population Size[J];Chinese Journal of Engineering Mathematics;2003-03 2 LUO Rong-gui,JIANG Tao(School of Management,Wuhan University of Technology,Wuhan 430070,China);The Research of Technology Diffusion Model Based on the SIR Epidemic Model[J];Journal of Industrial Engineering and Engineering Management;2006-01 3 FAN Zhi-liang, ZHANG Ju-ping(Dept. of Applied Mathematics, North China Institute of Technology, Taiyuan 030051, China);A Class of The Combination of SIR and SIS Epidemic Modelwith Immigrants of Constant[J];Journal of North China Institute of Technology;2004-02 4 FAN Zhi-liang(Dept. of Applied Mathematics, North China Institute of Technology, Taiyuan 030051, China);A SIR Epidemic Model with Infectious Rate β(N)and Exponential Born[J];;2004-06 5 FAN Zhi-liang,ZHANG Ju-ping(Dept.of Mathematics,North University of China,Taiyuan 030051,China);A SIR Epidemic Model with an Infectious Rate β(N)[J];Journal of North University of China(Natural Science Edition);2006-02 6 FAN Zhi-liang,ZHANG Ju-ping (School of Science,North University of China,Taiyuan 030051,China);Global Stability of an SIR Epidemic Model with General Contact Rate[J];Journal of North University of China(Natural Science Edition);2007-01 7 GUO Hong-jian~1,XIANG Zhong-yi~2,SONG Xin-yu~1(1.Editorial Department of Journal,Xinyang Normal University,Xinyang 464000,China;2.Department of Mathematics,Hubei Institute for Nationalities,Enshi 445000,China);A Kind of SIRS Epidemic Model with Satured Incidence and Impulsive Vaccination[J];Journal of Hubei Institute for Nationalities(Natural Science Edition);2006-02 8 GUO Xiao-jun LI Da-zhi (School of Sciences,Nantong University,Nantong 226007,China);Stability Analysis on a Class of SIQR Epidemic Dynamical Model with Vaccination and Isolated Items[J];Journal of Nantong University(Natural Science Edition);2008-04 9 JIA Jian-wen(School of Mathematics and Computer Science, Shanxi Teacher′s University, Linfen, Shanxi 041004, China);Study of a Kind SIR Epidemic Model with Nonlinear Incidence Rate[J];Journal of Shanxi Teachers University(Natural Science Edition);2004-04
 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 10 Hits
 1 ZHAO Wei, ZHAO Jia-kun(Science College, Xi'an Jiaotong University, Xi'an71--49,China);Epidemic model of the proportional vaccination about Hepatitis B[J];Pure and Applied Mathematics;2003-04 2 ZHANG Yu-juan~(*1,2), CHEN Lan-sun~1, SUN Li-hua~1 ( 1.Dept. of Appl. Math., Dalian Univ. of Technol., Dalian 116024, China; 2.Dept. of Math., Anshan Norm. Univ., Anshan 114005, China );Analysis of a class of predator-prey system with impulsive effect[J];Journal of Dalian University of Technology;2004-05 3 LI Xia, YEH Anthony Gar-On ( Guangzhou Institute of Geography, Guangzhou 510070, China; Centre of Urban Planning and Environmental Management, University of Hong Kong, Hong Kong, China);Neural-network-based Cellular Automata for Realistic and Idealized Urban Simulation[J];Acta Geographica Sinica;2002-02 4 HE Chunyang, CHEN Jin, SHI Peijun, FAN Yida (Key Laboratory of Environmental Change and Natural Disaster,Ministry of Education of China,Beijing Normal University;Institute of Resources Science,Beijing Normal University,Beijing100875, China);City Expansion Model of Metropolitan Area in China:a Case Study of Beijing[J];Acta Geographica Sinica;2003-02 5 LIU Xiaoping, LI Xia, AI Bin, TAO Haiyan, WU Shaokun, LIU Tao (School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China);Multi-agent Systems for Simulating and Planning Land Use Development[J];Acta Geographica Sinica;2006-10 6 HE Chun yang, CHEN Jin, SHI Pei jun, YU Zhang tao (Key Laboratory of Environmental Change and Natural Disaster, Ministry of Education, Beijing Normal University; Institute of Resources Science, Beijing Normal University, Beijing 100875,China)\$\$\$\$;STUDY ON THE SPATIAL DYNAMIC CITY MODEL BASED ON CA(CELLULAR AUTOMATA)MODEL[J];Advance In Earth Sciences;2002-02 7 ZHOU Ling-li, HU Xin-li, SUN Chuan-jiao (1. School of Science,Xi' an Jiaotong University,Xi' an 710049; 2. Institute of Math, and Phy.,XAUEST, Xi' an 710048,China);Asymptotic analysis of a SIS model with pulse vaccination[J];Basic Sciences Journal of Textile Universities;2003-02 8 LIU Hanwu,XU Jie,LIU Qiming(1Science College, Hebei University of Science & Technology, Shijiazhuang 050018;2Faculty of Science, Xi'an Jiaotong University, Xi'an 710049;3Ordnance Engineering College, Shijiazhuang 050003);Age-structured SIS Communicable Disease Model with Continuous Vaccination[J];Chinese Journal of Engineering Mathematics;2002-04 9 LI Jian-quan1 , WANG Feng1, MA Zhi-en1 ,2 (1- Xi’an Jiaotong University, Xi’an 710049; 2- Air Force Engineering University, Xi’an 710077 );Analysis of Global Stability for an Epidemic Model with Quarantine[J];Chinese Journal of Engineering Mathematics;2005-01 10 XU Wen-xiong, ZHANG Zhong-hua (School of Sciences, Xi'an Jiaotong University, Xi'an710049);Global Stability of SIR Epidemiological Model with Vaccinal Immunity and Bilinear Incidence Rates[J];College Mathematies;2003-06
 【Secondary References】
 Chinese Journal Full-text Database 9 Hits
 1 LV Xiao-guo et al(College of Science,Nantong University,Nantong,Jiangsu 226007);Prediction Analysis on Vegetable Production Value of Farm[J];Journal of Anhui Agricultural Sciences;2009-16 2 LV Xiao-guo et al (College of Science,Nantong University,Nantong,Jiangsu 226007);Statistical Analysis on Influencing Factors of Agriculture Production Value[J];Journal of Anhui Agricultural Sciences;2009-17 3 LV Xiao-guo et al(Science school of Nantong University,Nantong,Jiangsu 226007);Predicting Agricultural Output Value with a "Discount" Seasonal Index Method[J];Journal of Anhui Agricultural Sciences;2009-26 4 ZHANG Hui(School of Sciences,Nantong University,Nantong 226007,China);The Stability for a Class of Epidemic Model with Population Change[J];Journal of Nantong University(Natural Science Edition);2009-02 5 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 6 LI Lu-ping1,2,JIA Jian-wen2(1.School of Mathematical and Computer Science,Shanxi Datong University,Datong 037009,China)(2.School of Mathematical and Computer Science,Shanxi Normal University,Linfen 041004,China);The Periodic Solution of a SIR Epidemic Model with Periodic Vertical Infection Rate[J];Mathematics in Practice and Theory;2009-12 7 ZHAO Ting-ting TANG San-yi~* (College of Mathematics and Information Science,Shaanxi Normal University,Xi'an Shanxi 710062 China);Plant Disease Control with Economic Threshold[J];Journal of Biomathematics;2009-03 8 YANG Guang (Shenyang normal university School of Mathematics and Systems Science,Shenyang Liaoning China);Isolate Control of SIR Epidemics Model[J];Journal of Biomathematics;2009-03 9 Han Chaofeng, Chen Zhongxin (Institute of Agricultural Resources and Regional Planning, the Chinese Academy of Agricultural Sciences, Key Laboratory of Resources Remote Sensing and Digital Agriculture, Ministry of Agriculture, Beijing 100081);Models for Driving Forces of Land Use/Cover Change: A Review[J];Chinese Agricultural Science Bulletin;2008-04
Similar Journals
 > Basic Sciences Journal of Textile Universities > Journal of Shaanxi University of Science & Technology(Natural Science Edition) > Chinese Journal of Engineering Mathematics > Journal of Taiyuan Normal University(Natural Science Edition) > Journal of Xiamen University(Natural Science) > Journal of Jilin Institute of Chemical Technology > Journal of Fuzhou University(Natural Science Edition) > Journal of North University of China(Natural Science Edition) > Journal of Nanchang University(Engineering & Technology) > Journal of Biomathematics