Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21655
Title: A mathematical model for the spatial spread and biocontrol of the asian longhorned beetle
Authors: Gourley, SA
Lou, Y 
Keywords: Age structure
Asian longhorned beetle
Biocontrol
Delay
Persistence
Stability
Issue Date: 2014
Publisher: Society for Industrial and Applied Mathematics Publications
Source: Siam journal on applied mathematics, 2014, v. 74, no. 3, p. 864-884 How to cite?
Journal: SIAM Journal on Applied Mathematics 
Abstract: We propose a mathematical model, of four coupled delay differential equations, for control of the Asian longhorned beetle Anoplophora glabripennis by one of its natural predators, the cylindrical bark beetle Dastarcus longulus or another predator with similar characteristics. It is a predator prey interaction at the larval rather than adult level which creates interesting modeling challenges. We specify the birth rate only for A. glabripennis and calculate the birth rate of the control agent D. longulus by keeping track of its consumption of larval A. glabripennis biomass and using the idea of conversion of biomass. We prove rigorous results on the stability of equilibria and on persistence of D. longulus, and we make an assessment of the kinds of characteristics that enable D. longulus, or any similar control agent, to effectively control A. glabripennis. A pest such as A. glabripennis will destroy its habitat and must continually find new host trees. Even though our model does not have explicit spatial dependence, we may use it to make some inferences about the likely spatial spread of an infestation.
URI: http://hdl.handle.net/10397/21655
ISSN: 0036-1399
DOI: 10.1137/130939304
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