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《Journal of Guangdong University of Technology》 2008-03
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A SIRS Epidemic Model with Varying Population Size and Its Controlling Strategies

Gao Jing-guang,Sun You-fa,Zhang Cheng-ke(Faculty of Economics and Management,Guangdong University of Technology,Guangzhou 510520,China)  
A SIRS infectious disease model with immigration,birth and death,vertical transmission,and isolation,is studied.According to the global asymptotical stability conditions of the disease-free equilibrium,the integrated strategy for controlling the disease—first isolating the infected individuals,then limiting the liquidity of the susceptible and controlling the vertical transmission,and at last making a tradeoff between annihilating the disease with no terms and the underlying expenses before taking any measures,is derived.Finally,the effectiveness of the controlling strategy is validated by the numerical simulations.
【Fund】: 国家自然科学基金资助项目(70771029);; 广东省自然科学基金资助项目(07001795);; 广东省哲学社会科学“十一五”规划学科共建项目(06GO03);; 广东工业大学博士启动基金资助项目(063032)
【CateGory Index】: R183
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【Citations】
Chinese Journal Full-text Database 3 Hits
1 ZHANG Shuang-de~1, ZHANG Xi-hong~2, HAO Hai~1(1.Basic Department, Chinese People's Armed Police Forces Medical College, Tianjin 300162,China;2.Basic Department, Changzhi Medical College,Changzhi 046000,China);A SIRS Infections Disease Model with Stage-Structure and Isolation[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2005-04
2 CHEN Jun-jie PAN Guo-wei ( Department of Mathematics, Zhejiang University, Hangzhou Zhejiang 310029 China) ( Department of Physics, Zhejiang University, Hangzhou Zhejiang 310029 China);A Dynamic Model for Diseases with Nonpermanent Immunity in a Variable Size Population[J];Journal of Biomathematics;2003-04
3 LI Jian-quan~(1,2),ZHANG Juan~1,MA Zhi-en~1(1.Department of Applied Mathematics,Xi'an Jiaotong University,Xi'an 710049,P.R.China;2.Telecommunication Engineering Institute,Air Force Engineering University,Xi'an 710077,P.R.China);Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration[J];Applied Mathematics and Mechanics;2004-04
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 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
2 ZOU Qina,b,GAO Shu-jinga,b(a.School of Mathematics and Computer Science;b.Key Laboratory of Numerical Simulation Technology of Jiangxi Province,Gannan Normal University Ganzhou 341000,China);Global Analysis of SIS Epidemic Model with Vertical Infections[J];Journal of Gannan Normal University;2009-03
3 SHI Lian-rong,YOU Xiong,SHU Xin,WANG Yan-bo(1.College of Sciences,Nanjing Agricutueal University,Nanjing 210095,China);An SIVS Epidemic Model wih Vertical Transmission where the Disease Can Recrudesce in the Chronic Phase[J];Journal of Gansu Sciences;2007-04
4 GU Zheng1,2,YOU Xiong2 (1.School of Economics and Management,Nanjing Agricultural University,China;2.Science College,Nanjing Agricultural University 210095);The numerical simulation on the rate of farmers participating of risk management based on the dynamics of infectious diseases[J];Journal of Guizhou University(Natural Science Edition);2008-04
5 CHEN Yong-xue(College of Computer and Information,Fujian Agriculture and Forestry University,Fuzhou,Fujian 350002,China);Global analysis of an SEQS avian influenza model[J];Journal of Fujian Agriculture and Forestry University(Natural Science Edition);2010-02
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 ZHANG Hui,FENG Feng1(Department of Basic Courses,the Second Artillery Engineering College,Xi'an 710025,P.R.China;Department of Applied Mathematics and Physics,Xi'an Institute of Posts of Telecom1,Xi'an 710121,P.R.China);Global Stability of a SIS Epidemic Model with Vertical Transmission[J];Science Technology and Engineering;2010-01
8 LIU Xiao-yu1,2,LI Dong-mei1,WANG Hui1(1.School of Applied Science,Harbin University of Science and Technology,Harbin 150080,China;2.Harbin Financial College,Harbin 150030,China);Stability Analysis of an Epidemic Model with Inflectious Force in Latent Period and Inflected Period[J];Journal of Harbin University of Science and Technology;2009-06
9 DU Jun-hua1,2,LIU Xiao-yu1(1.College of Applied Science,Harbin University of Science and Technology,Harbin 150080,China;2.Department of Mathematics,Qiqihar University,Heilongjiang Qiqihar 161006,China);Stability analysis of an epidemic model with a generate contact rate[J];Journal of Qiqihar University(Natural Science Edition);2008-03
10 DONG Shu-zhuan(Dept of Math.Yuncheng University,Yuncheng Shanxi 044000,China);Global Stability of an Epidemic Model with Vacccination and Quarantine[J];Mathematics in Practice and Theory;2007-20
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 FONG Bei-xiang (Department of Mathematics, Fudan University, Shanghai 200433, China);The Globle Existence and Uniqueness of the Solution of a Kind of ODE SIRS Model[J];Journal of Fudan University;2001-06
2 CHEN JUNJIE ZHANG NANSONG(Research Center of Biometrics, Zhejiang University, HangZhou 310029);AN HIV/AIDS TRANSMISSION MODEL WITH INFECTIOUS STAGES AND CONSTANT RECRUITMENT[J];Acta Mathematicae Applicatae Sinica;2002-03
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