Bulletin of Mathematical Biology

, Volume 75, Issue 11, pp 2167–2195 | Cite as

Adaptive Release of Natural Enemies in a Pest-Natural Enemy System with Pesticide Resistance

  • Juhua Liang
  • Sanyi Tang
  • Robert A. Cheke
  • Jianhong Wu
Original Article


Integrated pest management options such as combining chemical and biological control are optimal for combating pesticide resistance, but pose questions if a pest is to be controlled to extinction. These questions include (i) what is the relationship between the evolution of pesticide resistance and the number of natural enemies released? (ii) How does the cumulative number of natural enemies dying affect the number of natural enemies to be released? To address these questions, we developed two novel pest-natural enemy interaction models incorporating the evolution of pesticide resistance. We investigated the number of natural enemies to be released when threshold conditions for the extinction of the pest population in two different control tactics are reached. Our results show that the number of natural enemies to be released to ensure pest eradication in the presence of increasing pesticide resistance can be determined analytically and depends on the cumulative number of dead natural enemies before the next scheduled release time.


IPM Pest resistance Frequency of pesticide applications Biological control Dynamic threshold Cumulative number of deaths 



This work was supported by the Fundamental Research Funds for the Central Universities (GK201104009), and by the National Natural Science Foundation of China (NSFC, 11171199), and by the International Development Research Centre.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anP.R. China
  2. 2.European Centre for Integrated Pest Management, Natural Resources InstituteUniversity of Greenwich at MedwayChathamUK
  3. 3.Centre for Disease Modelling, York Institute for Health ResearchYork UniversityTorontoCanada

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