A new mathematical model for optimal control strategies of integrated pest management

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	A new mathematical model for optimal control strategies of integrated pest management
	Meng, Xinzhu ; Song, Zhitao ; Chen, Lansun
	2007-06-01
发表期刊	JOURNAL OF BIOLOGICAL SYSTEMS
ISSN	0218-3390
卷号	15 期号:2 页码:219-234
摘要	A state-dependent impulsive SI epidemic model for integrated pest management (IPM) is proposed and investigated. We shall examine an optimal impulsive control problem in the management of an epidemic to control a pest population. We introduce a small amount of pathogen into a pest population with the expectation that it will generate an epidemic and that it will subsequently be endemic such that the number of pests is no larger than the given economic threshold (ET), so that the pests cannot cause economic damage. This is the biological control strategy given in the present paper. The combination strategy of pulse capturing (susceptible individuals) and pulse releasing (infective individuals) is implemented in the model if the number of pests (susceptible) reaches the ET. Firstly, the impulsive control problem is to drive the pest population below a given pest level and to do so in a manner which minimizes a weighted sum of the cost of using the control. Hence, for a one time impulsive effect we obtain the optimal strategy in terms of total cost such that the number of pests is no larger than the given ET. Secondly, we show the existence of periodic solution with the number of pests no larger than ET, and by using the Analogue of the Poincare Criterion we prove that it is asymptotically stable under a planned impulsive control strategy. Further, the period T of the periodic solution is calculated, which can be used to estimate how long the pest population will take to return back to its pre-control level. The main feature of the present paper is to apply an SI infectious disease model to IPM, and some pests control strategies are given.
关键词	SI epidemic model impulsive effect biological and mechanical control periodic solution economic threshold
语种	英语
WOS研究方向	Life Sciences & Biomedicine - Other Topics ; Mathematical & Computational Biology
WOS类目	Biology ; Mathematical & Computational Biology
WOS记录号	WOS:000248241500008
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5111
专题	中国科学院数学与系统科学研究院
通讯作者	Meng, Xinzhu
作者单位	1.Shandong Univ Sci & Technol, Coll Sci, Qingdao 266510, Peoples R China 2.Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China 3.Acad Sinica, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Meng, Xinzhu,Song, Zhitao,Chen, Lansun. A new mathematical model for optimal control strategies of integrated pest management[J]. JOURNAL OF BIOLOGICAL SYSTEMS,2007,15(2):219-234.
APA	Meng, Xinzhu,Song, Zhitao,&Chen, Lansun.(2007).A new mathematical model for optimal control strategies of integrated pest management.JOURNAL OF BIOLOGICAL SYSTEMS,15(2),219-234.
MLA	Meng, Xinzhu,et al."A new mathematical model for optimal control strategies of integrated pest management".JOURNAL OF BIOLOGICAL SYSTEMS 15.2(2007):219-234.