Bulletin of Mathematical Biology

, Volume 67, Issue 1, pp 115–135 | Cite as

Integrated pest management models and their dynamical behaviour

  • Sanyi TangEmail author
  • Yanni Xiao
  • Lansun Chen
  • Robert A. Cheke


Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than certain critical values. The effects of pest resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for this periodic solution is given and the ET is evaluated for given parameters.We also show that in some cases control costs can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration using mathematical models that an IPM strategy is more effective than classical control methods.


Periodic Solution Natural Enemy Mathematical Biology Integrate Pest Management Pest Population 
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Copyright information

© Society for Mathematical Biology 2005

Authors and Affiliations

  • Sanyi Tang
    • 1
    Email author
  • Yanni Xiao
    • 2
  • Lansun Chen
    • 3
  • Robert A. Cheke
    • 4
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK
  3. 3.Academy of Mathematics and System Sciences, Chinese Academy of SciencesBeijingPR China
  4. 4.Natural Resources InstituteUniversity of GreenwichKentUK

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