Optimal Chemical Control Based on τ-Periodic Solution Models in Pest Management

Abstract:

For the issue of the optimal chemical control method in agricultural pests, impulsive differential equations theory is applied to establish and analyze both the pest management model of spraying pesticides and the corps effectiveness model; for -periodic solution models, in order to make the residual pesticide dosage in crops and the dosage of spraying minimum, control pest number under the economic damage threshold, optimal control theory is employed to determine the optimal pesticide dosage and spraying interval. So, a best method about controlling agricultural pests via pesticide is given. Finally, Numerical Simulation is used to explain the implement of this method.

• Periodical: Advanced Materials Research (Volumes 1079-1080)
• Pages: 720-723
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1079-1080.720
• Online since: December 2014
• Authors: Guang Yang*
• Keywords: Corps Effectiveness Model, Impulsive Differential Equation, Optimal Chemical Control, Pest Comprehensive Management, Pest Management Model

References

[1] P. D. N. Srinivasu, B. S. R.V. Prasad. Time optimal control of an additional food provided predator–prey system with applications to pest management and biological conservation [J]. J. Math. Biol. 2010, 60(4): 591–613.

DOI: 10.1007/s00285-009-0279-2

[2] Ya-Zhong, Luo, Guo-Jin Tang, Hai-yang Li. Optimization of multiple-impulse minimum-time rendezvous with impulse constraints using a hybrid genetic algorithm[J]. Aerospace Science and Technology. 2006, 10(6): 534–540.

DOI: 10.1016/j.ast.2005.12.007

[3] Angelova J, Dishliev A. Optimization problems for one-impulsive models from population dynamics [J]. Nonlinear Analysis, 2000, 39(4): 483-497.

DOI: 10.1016/s0362-546x(98)00216-8

[4] N. McRobert, G. Hughes and S. Savary. Integrated approaches to understanding and control of diseases and pests in field crops [J]. Australasian Plant Pathology 2003, 32(2): 167-180.

DOI: 10.1071/ap03026

[5] Zhisheng Shuai, Ling Bai, Ke Wang. Optimization problems for general simple population with n-impulsive harvest [J]. Journal of Mathematical Analysis and Applications. 2007, 329(1): 634–646.

DOI: 10.1016/j.jmaa.2006.07.010

[6] L. Bai, Z. Shuai, K. Wang. Optimal impulsive harvest policy for an autonomous system [J]. Taiwanese J. Math. 2004, 8 (2): 245–258.

DOI: 10.11650/twjm/1500407626

[7] Juhua Liang, Sanyi Tang. Optimal dosage and economic threshold of multiple pesticide applications for pest control [J]. Mathematical and Computer Modelling, 2010, 51（5-6）：487-503.

DOI: 10.1016/j.mcm.2009.11.021

[8] Tang, Sanyi, Xiao, Yanni and Cheke, Robert A. Dynamical analysis of plant disease models with cultural control strategies and economic thresholds [J]. Mathematics and Computers in Simulation. 2010, 80(5): 894-921.

DOI: 10.1016/j.matcom.2009.10.004