KMS Of Academy of mathematics and systems sciences, CAS
| A new mathematical model for optimal control strategies of integrated pest management | |
| Meng, Xinzhu; Song, Zhitao; Chen, Lansun | |
| 2007-06-01 | |
| Source Publication | JOURNAL OF BIOLOGICAL SYSTEMS
 |
| ISSN | 0218-3390 |
| Volume | 15Issue:2Pages:219-234 |
| Abstract | 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. |
| Keyword | SI epidemic model impulsive effect biological and mechanical control periodic solution economic threshold |
| Language | 英语 |
| WOS Research Area | Life Sciences & Biomedicine - Other Topics ; Mathematical & Computational Biology |
| WOS Subject | Biology ; Mathematical & Computational Biology |
| WOS ID | WOS:000248241500008 |
| Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/5111 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Meng, Xinzhu |
| Affiliation | 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 |
| Recommended Citation 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. |
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