Jump to Content
Your Recent History
View Cart
Logged Out Log In
SIAM J. Appl. Math. 68, pp. 1665-1687 (23 pages)
A Mathematical Model for the Control and Eradication of a Wood Boring Beetle Infestation
Alerts
Alert Me When Cited
Alert Me When Corrected
Tools
Download Citation
Add to MyScitation
Blog This Article
Print-Friendly
Research Toolkit
Share
Email Abstract
Connotea
CiteULike
del.icio.us
BibSonomy
Tweet this Article
Add to FacebookWe propose a mathematical model for an infestation of a wooded area by a beetle species in which the larva develop deep in the wood of living trees. Due to the difficulties of detection, we presume that only a certain proportion of infested trees will be detected and that detection, if it happens, will occur only after some delay, which could be long. An infested tree once detected is immediately cut down and burned. The model is stage structured and contains a second time delay, which is the development time of the beetle from egg to adult. There is a delicate interplay between the two time delays due to the possibility in one case for a larva to mature even in a tree destined for destruction. We present conditions sufficient for infestation eradication and discuss the significance of the conditions, particularly in terms of the proportion of infested trees that need to be detected and removed. If the infestation is successfully eradicated, there are always a number of trees that completely escape infestation, and we compute lower bounds and an approximation for this number. Finally, we present the results of some numerical simulations.
© 2008 Society for Industrial and Applied Mathematics
RELATED DATABASES
To view database links for this article,
you need to log in.
KEYWORDS
PUBLICATION DATA
ARTICLE DATA
History
Received November 08, 2006
Accepted March 17, 2008
Published online June 25, 2008
Accepted March 17, 2008
Published online June 25, 2008
Digital Object Identifier
For access to fully linked references, you need to log in.
ALL SIAM Content
Scitation
Google Scholar