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A mathematical model for biocontrol of the invasive weed Fallopia japonica

Gourley, SA, Li, J and Zou, X (2016) A mathematical model for biocontrol of the invasive weed Fallopia japonica Bulletin of Mathematical Biology, 78 (8). pp. 1678-1702.

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Abstract

We propose a mathematical model for biocontrol of the invasive weed Fallopia japonica using one of its co-evolved natural enemies, the Japanese sap-sucking psyllid Aphalara itadori. This insect sucks the sap from the stems of the plant thereby weakening it. Its diet is highly specific to F. japonica. We consider a single isolated knotweed stand, the plant’s size being described by time dependent variables for total stem and rhizome biomass. It is the larvae of A. itadori that damage the plant most, so the insect population is described in terms of variables for the numbers of larvae and adults, using a stage-structured modelling approach. The dynamics of the model depends mainly on a parameter h, which measures how long it takes for an insect to handle (digest) one unit of F. japonica stem biomass. If h is too large then the model does not have a positive equilibrium and the plant biomass and insect numbers both grow together without bound, though at a lower rate than if the insects were absent. If h is sufficiently small then the model possesses a positive equilibrium which appears to be locally stable. The results based on our model imply that satisfactory long term control of the knotweed F. japonica using the insect A. itadori is only possible if the insect is able to consume and digest knotweed biomass sufficiently quickly; if it cannot then the insect can only slow down the growth which is still unbounded.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Gourley, SAUNSPECIFIEDUNSPECIFIED
Li, JUNSPECIFIEDUNSPECIFIED
Zou, XUNSPECIFIEDUNSPECIFIED
Date : August 2016
Identification Number : 10.1007/s11538-016-0195-8
Copyright Disclaimer : © The Author(s) 2016. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 18 Jul 2016 09:41
Last Modified : 15 Nov 2016 10:22
URI: http://epubs.surrey.ac.uk/id/eprint/811237

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