Publication Date



mountain pine beetle, chemotaxis, reaction-diffusion transport, nonlinear dynamical systems, numerical simulation


Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education


This article presents existing mathematical models associated with mountain pine beetle populations in lodgepole pine forests, whose reproductive cycle requires the destruction of colonized host trees, decreasing timber availability/quality, and providing fuel sources for wildfires. With the existence of a positive-feedback loop with environmental warming, the need for intervention and management is clear. However, the legislative responses to the focusing events from our 2000-2010 North American epidemics are characterized as under-leveraged. While the reasons for this are multifaceted, increasing the capacity of STEM-informed individuals to take part in quantitative modeling of the underlying ecosystem generates awareness and provides pathways connecting the ``how'' of public land management to the ``what'' and ``why'' of policy creation. To this end, we survey existing mathematical models for the mountain pine beetle, ranging from a simple planar model to a chemotactic model involving pheromone/kairomone signaling between beetles and host trees. The latter can be localized to a host tree characterized by a nonlinear system of ordinary differential equations whose solution is reasonable to approximate numerically.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.