Skip to main content
SpringerLink
Log in

Threshold conditions for integrated pest management models with pesticides that have residual effects

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

Impulsive differential equations (hybrid dynamical systems) can provide a natural description of pulse-like actions such as when a pesticide kills a pest instantly. However, pesticides may have long-term residual effects, with some remaining active against pests for several weeks, months or years. Therefore, a more realistic method for modelling chemical control in such cases is to use continuous or piecewise-continuous periodic functions which affect growth rates. How to evaluate the effects of the duration of the pesticide residual effectiveness on successful pest control is key to the implementation of integrated pest management (IPM) in practice. To address these questions in detail, we have modelled IPM including residual effects of pesticides in terms of fixed pulse-type actions. The stability threshold conditions for pest eradication are given. Moreover, effects of the killing efficiency rate and the decay rate of the pesticide on the pest and on its natural enemies, the duration of residual effectiveness, the number of pesticide applications and the number of natural enemy releases on the threshold conditions are investigated with regard to the extent of depression or resurgence resulting from pulses of pesticide applications and predator releases. Latin Hypercube Sampling/Partial Rank Correlation uncertainty and sensitivity analysis techniques are employed to investigate the key control parameters which are most significantly related to threshold values. The findings combined with Volterra’s principle confirm that when the pesticide has a strong effect on the natural enemies, repeated use of the same pesticide can result in target pest resurgence. The results also indicate that there exists an optimal number of pesticide applications which can suppress the pest most effectively, and this may help in the design of an optimal control strategy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barclay HJ (1982) Models for pest control using predator release, habitat management and pesticide release in combination. J Appl Ecol 19: 337–348

    Article  Google Scholar 

  • Barlow ND, Moller H, Beggs JR (1996) A model for the effect of Sphecophaga vesparum as a biological control agent of the common wasp in New Zealand. J Appl Ecol 33: 31–34

    Article  Google Scholar 

  • Beddington JR, Free CA, Lawton JH (1978) Characteristics of successful natural enemies in models of biological control of insect pests. Nature 273: 513–519

    Article  Google Scholar 

  • Blower SM, Dowlatabadi H (1994) Sensitivity and uncertainty analysis of complex-models of disease transmission? An HIV model, as an example. Int Stat Rev 62: 229–243

    Article  MATH  Google Scholar 

  • Bor Jeffrey YC (1995) Optimal pest management and economic threshold. Agric Syst 49: 113–133

    Article  Google Scholar 

  • Debach P (1974) Biological control by natural enemies. Cambridge University Press, London

    Google Scholar 

  • Heinrichs EA, Mochida O (1985) From secondary to major pest status: the case of insecticide-induced rice brown planthopper, Nilaparvata lugens, resurgence. Prot Ecol 7: 201–218

    Google Scholar 

  • Jones WA, Greenberg SM, Legaspi JR (1999) The effect of varying Bemisia argentifolii and Eretmocerus mundus ratios on parasitism. BioControl 44: 13–28

    Article  Google Scholar 

  • Liu XN, Chen LS (2004) Global dynamics of the periodic logistic system with periodic impulsive perturbations. J Math Anal Appl 289: 279–291

    Article  MathSciNet  MATH  Google Scholar 

  • Liu B, Chen LS (2004) The periodic competing Lotka-Volterra model with impulsive effect. Math Med Biol 38: 1505–1523

    Google Scholar 

  • Marino S, Ian B, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254: 178–196

    Article  Google Scholar 

  • Mckay MD, Beckman RJ, Conover WJ (1979) Comparison of 3 methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21: 239–245

    MathSciNet  MATH  Google Scholar 

  • Neuenschwander P, Herren HR (1988) Biological control of the Cassava Mealybug, Phenacoccus manihoti, by the exotic parasitoid Epidinocarsis lopezi in Africa. Phil Trans R Soc Lond B 318: 319–333

    Article  Google Scholar 

  • Panetta JC (1995) A logistic model of periodic chemotherapy. Appl Math Lett 8: 83–86

    Article  MATH  Google Scholar 

  • Parker FD (1971) Management of pest populations by manipulating densities of both host and parasites through periodic releases. In: Huffaker CB (ed) Biological control. Plenum Press, New York

    Google Scholar 

  • Pedigo LP, Higley LG (1992) A new perspective of the economic injury level concept and environmental quality. Am Entomol 38: 12–20

    Google Scholar 

  • Raupp MJ, Holmes JJ, Sadof C, Shrewsbury P, Davidson JA (2001) Effects of cover sprays and residual pesticides on scale insects and natural enemies in urban forests. J Arboric 27: 203–214

    Google Scholar 

  • Reed GL, Jensen AS, Riebe J, Head G, Duan JJ (2001) Transgenic Bt potato and conventional insecticides for Colorado Beetle management: comparative efficacy and non-target impacts. Entomologia Experimentalies et Applicata 100: 89–100

    Article  Google Scholar 

  • Residual effects of pesticides (2010). http://www.bedbugbattleplan.com/

  • Roughgarden J (1979) Theory of population genetics and evolutionary ecology: an introduction. MacMillan, New York

    Google Scholar 

  • Ruberson JR, Nemoto H, Hirose Y (1998) Pesticides and conservation of natural enemies in pest management. In: Barbosa P (ed) Conservation biological control. Academic Press, New York, pp 207–220

    Chapter  Google Scholar 

  • Schaalje GB (1990) Dynamic models of pesticide effectiveness. Environ Entomol 19: 439–447

    Google Scholar 

  • Schmutterer H (1988) Potential of azadirachtin-containing pesticides for integrated pest control in developing and industrialized countries. J Insect Phys 34: 713–719

    Article  Google Scholar 

  • Tang SY, Chen LS (2002) Density-dependent birth rate, birth pulses and their population dynamic consequences. J Math Bio 44: 185–199

    Article  MathSciNet  Google Scholar 

  • Tang SY, Chen LS (2003) Multiple attractors in stage-structured population models with birth pulses. Bull Math Biol 65: 479–495

    Article  Google Scholar 

  • Tang SY, Cheke RA (2005) Stage-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences. J Math Biol 50: 257–292

    Article  MathSciNet  MATH  Google Scholar 

  • Tang SY, Xiao YN, Chen LS, Cheke RA (2005) Integrated pest management models and their dynamical behaviour. Bull Math Biol 67: 115–135

    Article  MathSciNet  Google Scholar 

  • Tang SY, Xiao YN, Cheke RA (2008) Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak. Theor Popul Biol 73: 181–197

    Article  MATH  Google Scholar 

  • Tang SY, Cheke RA (2008) Models for integrated pest control and their biological implications. Math Biosci 215: 115–125

    Article  MathSciNet  MATH  Google Scholar 

  • Tang SY, Xiao YN, Cheke RA (2009) Effects of predator and prey dispersal on success or failure of biological control. Bull Math Biol 71: 2025–2047

    Article  MathSciNet  MATH  Google Scholar 

  • Tang SY, Tang GY, Cheke RA (2010) Optimum timing for integrated pest management: Modelling rates of pesticide application and natural enemy releases. J Theor Biol 264: 623–638

    Article  Google Scholar 

  • Udayagiri S, Norton AP, Welter SC (2000) Integrating pesticide effects with inundative biological control: interpretation of pesticide toxicity curves for Anaphes iole in strawberries. Entomologia Experimentalis et Applicata 95: 87–95

    Article  Google Scholar 

  • Van Lenteren JC (1995) Integrated pest management in protected crops. In: Dent D (ed) Integrated pest management. Chapman & Hall, London, pp 311–320

    Google Scholar 

  • van Lenteren JC (2000) Measures of success in biological control of arthropods by augmentation of natural enemies. In: Wratten S, Gurr G (eds) Measures of success in biological control. Kluwer Academic Publishers, Dordrecht, pp 77–89

    Chapter  Google Scholar 

  • Van Lenteren JC, Woets J (1988) Biological and integrated pest control in greenhouses. Ann Rev Ent 33: 239–250

    Article  Google Scholar 

  • Volterra V (1926) Fluctuation in abundance of a species considered mathematically. Nature 118: 558–560

    Article  MATH  Google Scholar 

  • Waage JK, Hassell MP (1982) Parasitoids as biological control agents-a fundamental approach. Parasitology 84: 241–268

    Article  Google Scholar 

  • Waage JK, Hassell MP, Godfray HCJ (1985) The dynamics of pest-parasitoid-insecticide interactions. J Appl Ecol 22: 825–838

    Article  Google Scholar 

  • Zacharda M, Hluchy M (1991) Long-term residual efficacy of commercial formulations of 16 pesticides to Typhlodromus pyri Scheuten (Acari: Phytoseiidae) inhabiting commercial vineyards. Exp Appl Acaro 13: 27–40

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China

    Sanyi Tang & Juhua Liang

  2. Department of Mathematics and Physics, Chongqing Jiaotong University, Chongqing, 400074, People’s Republic of China

    Yuanshun Tan

  3. Natural Resources Institute, University of Greenwich at Medway, Central Avenue, Chatham Maritime, Kent, ME4 4TB, UK

    Robert A. Cheke

Authors
  1. Sanyi Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juhua Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuanshun Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert A. Cheke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanyi Tang.

Additional information

S. Tang is supported by the National Natural Science Foundation of China NSFC 10871122, 11171199 and by the Fundamental Research Funds for the Central Universities GK201003001. R.A. Cheke is grateful to the University of Greenwich for support under project E0171.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tang, S., Liang, J., Tan, Y. et al. Threshold conditions for integrated pest management models with pesticides that have residual effects. J. Math. Biol. 66, 1–35 (2013). https://doi.org/10.1007/s00285-011-0501-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-011-0501-x

Keywords

Mathematics Subject Classification (2000)

Search

Navigation