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Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control

Bulletin of Mathematical Biology volume 70, pages 769–784 (2008)Cite this article

Abstract

Understanding the dynamics of spruce budworm population is very important for the protection of spruce and balsam fir trees of North American forests, and a full understanding of the dynamics requires careful consideration of the individual physiological structures that is essential for outbreak control. A model as a delay differential equation is derived from structured population system, and is validated by comparing simulation results with real data from the Green River area of New Brunswick (Canada) and with the periodic outbreaks widely observed. Analysis of the equilibrium stability and examination of the amplitudes and frequencies of periodic oscillations are conducted, and the effect of budworm control strategies such as mature population control, immature population control and predation by birds are assessed. Analysis and simulation results suggest that killing only budworm larvae might not be enough for the long-term control of the budworm population. Since the time required for development during the inactive stage (from egg to second instar caterpillar) causes periodic outbreak, a strategy of reducing budworms in the inactive stage, such as removing egg biomass, should also be implemented for successful control.

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Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Naveen K. Vaidya

  2. Center for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Jianhong Wu

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  1. Naveen K. Vaidya
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  2. Jianhong Wu
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Correspondence to Naveen K. Vaidya.

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Vaidya, N.K., Wu, J. Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control. Bull. Math. Biol. 70, 769–784 (2008). https://doi.org/10.1007/s11538-007-9278-x

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  • DOI: https://doi.org/10.1007/s11538-007-9278-x

Keywords

  • Delay differential equation
  • Larvae
  • Outbreak control
  • Predation
  • Spruce budworm
  • Structured populations