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.

加拿大的北方森林经常受到两种主要干扰：一种是火灾，另一种是云杉芽虫。云杉芽虫Choristoneura fumiferana（Clem。）（鳞翅目：Tortricidae）的落叶始于1957年在加拿大不列颠哥伦比亚省利亚德河附近。在1960年代到1970年代以及1980年代中期到现在都观察到了虫暴发。由于北方森林中木材和非木材资源的潜在损失，云杉芽虫干扰是森林管理的主要问题之一。为了发展对北方生态系统的可持续管理，已经对for虫暴发进行了数学建模。为了理解，我们提出了带有Holling II型的单物种反应扩散模型功能反应。在本文中，我们的主要目标是了解云杉芽虫的扩散现象，并随后确定其扩散速度。为了确定扩展速度，我们集中在模型的一维行波解上。我们的结果表明，行波解的最小速度可以表现出云杉芽虫在北方森林中的扩散速度。