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《Journal of Dalian University of Technology》 2007-03
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Analysis of SIRS model with saturated contact rate and pulse vaccination

PANG Guo-ping1,2,TAO Feng-mei1,3,CHEN Lan-sun1(1.Dept.of Appl.Math.,Dalian Univ.of Technol.,Dalian 116024,China; 2.Dept.of Math.& Comput.Sci.,Yulin Norm.Univ.,Yulin 537000,China;3.Dept.of Math.,Anshan Norm.Univ.,Anshan 114005,China)  
In order to constitute the reasonable immune vaccination strategy and prevent the infectious diseases from arising and spreading effectively,the dynamical behavior of a SIRS model with saturated contact rate and pulse vaccination is investigated.Using Floquet theory and comparison theorem of impulsive differential equation,the existence and globally asymptotically stability of infection-free periodic solution are proven.Using bifurcation theory,the bifurcation parameter for the existence of positive periodic solution is obtained.The result indicates that the disease will die out if θθ(or ττ),whereas the system is uniformly persistent if ττ0,which means that after some period of time the disease will become endemic.
【Fund】: 国家自然科学基金资助项目(1047111710526015);; 广西壮族自治区教育厅科研资助项目(2006243);; 玉林师范学院重点科研资助项目(2007YJZD08)
【CateGory Index】: O175
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【References】
Chinese Journal Full-text Database 1 Hits
1 ZHAO Wen-cai,MENG Xin-zhu(College of Science,Shandong University of Science and Technology, Qingdao 266510,Shandong Province,China);Impulsively Vaccinating SIRS Epidemic Model with Logistic Death Rate[J];Journal of Jilin University(Science Edition);2009-06
【Citations】
Chinese Journal Full-text Database 1 Hits
1 (This paper is consecrated to the medical workers who devoted their lives to the cause of flighting against SARS) JIN Zhen\+1, MA Zhien\+2 (1. Dept. of Applied Mathematics, North China Institute of Technology, Taiyuan 030051, China; 2. Dept. of Applied Mathematics, Xi′an Jiaotong University, Xi′an 710049, China);The SIR Epidemical Models with Continuousand Impulsive Vaccinations[J];Journal of North China Institute of Technology;2003-04
【Co-citations】
Chinese Journal Full-text Database 6 Hits
1 Liu Ming Zhao Lindu Cheng Ting (School of Economics and Management,Southeast University,Nanjing 210096,China);Integrated and dynamic optimization control of multi-level anti-bioterrorism emergency logistics network[J];Journal of Southeast University(Natural Science Edition);2007-S2
2 Li Zhi Han Ruizhu Liu Ming (School of Economics and Management,Southeast University,Nanjing 210096,China);Analysis of synergetic dynamics model of emergency rescue network in anti-bioterrorism system[J];Journal of Southeast University(Natural Science Edition);2007-S2
3 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
4 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
5 ZHOU Yan-li1,WANG He-qiao2,WANG Mei-juan2,XU Chang-yong2 (1.College of Medical Instrumentation,University of Shanghai for Science and Technology,Shanghai 200093,China;2.Colloge of Science,University of Shanghai for Science and Technology,Shanghai 200093,China);SIQR epidemical model with impulsive vaccination[J];Journal of University of Shanghai for Science and Technology;2007-01
6 ZHU Hui1,2,XIONG Zuo-liang1(1.Department of Mathematics,Nanchang University,Nanchang 330031,China;2.Department of Computing Science,Huaiyin Institute of Technology,Huaian 223002,China);An SIV Epidemic Model with Impulsive Vaccination and Nonlinear Incidence Rate[J];Journal of Nanchang University(Engineering & Technology Edition);2007-01
【Co-references】
Chinese Journal Full-text Database 3 Hits
1 DONG Lin (School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China);Qualitative Analysis of an Epidemic Model with Quarantine Items[J];Journal of Fujian Normal University(Natural Science Edition);2008-05
2 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
3 XIANG Zhong-yi(Department of Mathematics,Hubei Institute for Nationalities,Enshi 445000,China);Impulsive Vaccination of SIR Epidemic Models with Incidence Rates[J];Journal of Hubei Institute for Nationalities(Natural Science Edition);2006-01
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