Liang, Juhua, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2012) An integrated pest management model with delayed responses to pesticide applications and its threshold dynamics. Nonlinear Analysis: Real World Applications, 13 (5). pp. 2352-2374. ISSN 1468-1218 (doi:https://doi.org/10.1016/j.nonrwa.2012.02.003)

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Abstract

Pulse-like pest management actions such as spraying pesticides and killing a pest instantly and the release of natural enemies at critical times can be modelled with impulsive differential equations. In practice, many pesticides have long-term residual effects and, also, both pest and natural enemy populations may have delayed responses to pesticide applications. In order to evaluate the effects of the duration of the residual effectiveness of pesticides and of delayed responses to pesticides on a pest management strategy, we developed novel mathematical models. These combine piecewise-continuous periodic functions for chemical control with pulse actions for releasing natural enemies in terms of fixed pulse-type actions and unfixed pulse-type actions. For the fixed pulse-type model, the stability threshold conditions for the pest eradication periodic solution and permanence of the model are derived, and the effects of key parameters including killing efficiency rate, decay rate, delayed response rate, number of pesticide applications and number of natural enemy releases on the threshold values are discussed in detail. The results indicate that there exists an optimal releasing period or an optimal number of pesticide applications which maximizes the threshold value. For unfixed pulse-type models, the effects of the killing efficiency rate, decay rate and delayed response rate on the pest outbreak period, and the frequency of control actions are also investigated numerically.

Item Type:	Article
Additional Information:	[1] First published online: 3 March 2012. [2] Published in print: October 2012.
Uncontrolled Keywords:	residual effect of pesticide, delayed response to pesticide application, IPM, threshold condition, economic threshold
Subjects:	S Agriculture > S Agriculture (General) S Agriculture > SB Plant culture
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > Natural Resources Institute Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Related URLs:	Publisher Organisation Organisation
Last Modified:	27 Jun 2014 10:13
URI:	http://gala.gre.ac.uk/id/eprint/7874

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