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Reaction-diffusion modeling of the spread of spruce budworm in boreal ecosystem

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Abstract

Boreal forest in Canada has two main recurrent disturbances: one is fire and the other one is spruce budworm. The defoliation by spruce budworm, Choristoneura fumiferana (Clem.) (Lepidoptera: Tortricidae) was first started in British Columbia of Canada in 1957 near Liard River. Budworm outbreaks were observed in the 1960’s to 1970’s and from the mid 1980’s to the present. Spruce budworm disturbance is one of the major issues of the forest management because of the potential losses of timber and non-timber resources in the boreal forest. To develop a sustainable management of the boreal ecosystem, mathematical modeling approaches for the budworm outbreak have been progressed. For this understanding, we propose a single species reaction-diffusion model appended with Holling type II functional response. In this paper, our main goal is to understand the spreading phenomenon of spruce budworm and subsequently identify its spreading velocity. In order to determine the spreading velocity, we focus on the one-dimensional traveling wave solutions of the model. Our results suggest that the minimal speed of traveling wave solutions can exhibit the spreading velocity of the spruce budworm in boreal forests.

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Acknowledgements

The author would like to thank Professor Masayasu Mimura for his valuable suggestions and encouragement to conduct this research.

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  1. Department of Mathematics, Jahangirnagar University, Dhaka, 1342, Bangladesh

    M. Humayun Kabir

  2. Center for Mathematical Modeling and Applications (CMMA), Meiji University, Tokyo, 164-8525, Japan

    M. Humayun Kabir

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Correspondence to M. Humayun Kabir.

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Kabir, M.H. Reaction-diffusion modeling of the spread of spruce budworm in boreal ecosystem. J. Appl. Math. Comput. 66, 203–219 (2021). https://doi.org/10.1007/s12190-020-01427-3

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  • DOI: https://doi.org/10.1007/s12190-020-01427-3

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