JIAO Jian-jun, CHEN Lan-sun. Nonlinear Incidence Rate of a Pest Management S-I Model With Biological and Chemical Control Concern[J]. Applied Mathematics and Mechanics, 2007, 28(4): 487-496.
Citation: JIAO Jian-jun, CHEN Lan-sun. Nonlinear Incidence Rate of a Pest Management S-I Model With Biological and Chemical Control Concern[J]. Applied Mathematics and Mechanics, 2007, 28(4): 487-496.

Nonlinear Incidence Rate of a Pest Management S-I Model With Biological and Chemical Control Concern

  • Received Date: 2006-08-11
  • Rev Recd Date: 2007-01-23
  • Publish Date: 2007-04-15
  • A pest management S-I model with impulsive releases of infective pests and spraying pesticides is proposed and investigated. It was proved that all solutions of the model are uniformly ultimately bounded. The sufficient conditions of globally asymptotic stability periodic solution of pest-extinction and permanence of the model were also obtained.The approach of combining impulsive releasing infective pests with impulsive spraying pesticides provides reliable tactical basis for the practical pest management.
  • loading
  • [1]
    Falcon L A.Use of Bacteria for Microbial Control of Insects[M].New York,N Y:Academic Press,1971.
    [2]
    Burges H D,Hussey N W.Microbial Control of Insects and Mites[M].New York,N Y:Academic Press,1971,67-95.
    [3]
    Falcon L A.Problems associated with the use of arthropod viruses in pest control[J].Annu Rev Entomol,1976,[STHZ]. 21[STBZ]. :305-324.
    [4]
    Bailey N T J.The Mathematical Theory of Infectious Diseases and Its Applications[M].London:Griffin,1975,413.
    [5]
    Burges H D,Hussey N W.Microbial Control of Insections and Mites[M].New York,N Y:Academic Press,1971,861.
    [6]
    Fenner F,Ratcliffe F N.Myxomatosis[M].Cambridge:Cambridge University Press,1965,379.
    [7]
    Davis P E,Myers K,Hoy J B.Biological control among vertebrates[A].In:Huffaker C B,Messenger P S Eds.Theory and Practice of Biological Control[C].New York,N Y:Plenum Press,1976,501-519.
    [8]
    Tanada Y.Epizootiology of insect diseases[A].In:Debach P Ed.Biological Control of Insect Pests and Weeds[C].London:Chapman and Hall,1964,548-578.
    [9]
    Barclay H J.Models for pest control using predator release,habitat management and pesticide release in combination[J].J Appl Ecol,1982,19(2):337-348. doi: 10.2307/2403471
    [10]
    Paneyya J C.A mathematical model of periodically pulse chemotherapy: tumor recurrence and metastasis in a competition environment[J].Bull Math Biol,1996,58(3):425-447. doi: 10.1007/BF02460591
    [11]
    d'Onofrio A.Stability properties of pulse vaccination strategy in SEIR epidemic model[J].Math Biol,2002,179(1):57-72.
    [12]
    Van Lanteren J C.Integrated pest managemant in protected crops[A].In:Dent D Ed.Integrated Pest Management[C].London:Chapman and Hall,1995.
    [13]
    Roberts M G,Kao R R.The dynamics of an infectious disease in a population with birth pulse[J].Math Biol,1998,149(1):23-36.
    [14]
    Xiao Y N,Chen L S.A ratio-depengent predator-prey model with disease in the prey[J].Appl Math Comput,2002,131:397-414. doi: 10.1016/S0096-3003(01)00156-4
    [15]
    Xiao Y N,Chen L S.An SIS epidemic model with stage structure and a delay[J].Acta Math Appl English Series,2002,[STHZ]. 18[STBZ]. (4):607-618.
    [16]
    Xiao Y N,Chen L S,Bosh F V D.Dynamical behavior for stage-structured SIR infectious disease model[J].Nonlinear Analysis:RWA,2002,[STHZ]. 3[STBZ]. (2):175-190.
    [17]
    Xiao Y N,Chen L S.On an SIS epidemic model with stage-structure[J].Journal of System Science and Complexity,2003,16(2):275-288.
    [18]
    Lu Z H,Gang S J,Chen L S.Analysis of an SI epidemic with nonlinear transmission and stage structure[J].Acta Math Science,2003,23(4):440-446.
    [19]
    Hethcote H.The mathematics of infectious disease[J].SIAM Review,2002,42:599-653.
    [20]
    Anderson R M,May R M.Regulation and stability of host-parasite population interactions—Ⅰ Regulartory processes[J].J Anim Ecol,1978,[STHZ]. 47[STBZ]. (1):219-247.
    [21]
    Goh B S.The potential utility of control theory to pest management[J].Proc Ecol Soc,1971,6:84-89.
    [22]
    Gilbert N,Gutierrez A P,Frazer B D,et al.Ecological Relationships[M].San Francisco,Calif:W H Freeman and Co, 1976.
    [23]
    Wickwire K.Mathematical models for the control of pests and infectious diseases:a survey[J].Theoret Population Biol,1977,11(2):182-238. doi: 10.1016/0040-5809(77)90025-9
    [24]
    Anderson R,May R.Population biological of infectious diseases[M].Berlin, Heidelberg,New York: Springer,1982.
    [25]
    Anderson R,May R.Infectious Diseases of Humen: Dynamics and Control[M].Oxford:Oxford University Press,1991.
    [26]
    De Jong M C M,Diekmann O,Heesterbeek J A P.How dose tranmission depend on population size? in human infectious diseases[A].Mollison D Ed.Epidemic Models[C].Cambridge UK:Cambridge University Press,1995,84-94.
    [27]
    LIU Wei-min,Levin S A,Iwasa Y.Influence of nonlinear incidence rates upon the behavior of SIRS Epidemiological models[J].J Math Biol,1986,23(2):187-204. doi: 10.1007/BF00276956
    [28]
    LIU Wei-min,Hethcote H W,Levin S A.Dynamical behavior of epidemiological models with nonlinear incidence rates[J].J Math Biol,1987,25(4):359-380. doi: 10.1007/BF00277162
    [29]
    陈兰荪,陈健.非线性生物动力学系统[M].北京:科学出版社,1993.
    [30]
    Capasso V,Serio G.A generalization of the Kermack-Mckendrick deterministic epidemic model[J].Math Biosci,1978,42:43-61. doi: 10.1016/0025-5564(78)90006-8
    [31]
    Ruan S,Wang W.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].J Differential Equations,2003,188:135-163. doi: 10.1016/S0022-0396(02)00089-X
    [32]
    Lakshmikantham V,Bainov D D,Simeonov P.Theory of Impulsive Differential Equations[M].Singapore:World Scientific,1989.
    [33]
    Bainov D,Simeonov P.Impulsive Differential Equations:Periodic Solutions and Applications[M].Pitman Monographs and Surveys in Pure and Applied Mathematics.66.Longman Scientific Technical,1993.
    [34]
    Sangoh Bean.Management and Analysis of Biological Populations[M].Elsevier Scientific Press Company,1980.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2731) PDF downloads(762) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return