Abstract and Applied Analysis

Optimal Control Policies of Pests for Hybrid Dynamical Systems

Baolin Kang, Mingfeng He, and Bing Liu

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We improve the traditional integrated pest management (IPM) control strategies and formulate three specific management strategies, which can be described by hybrid dynamical systems. These strategies can not only effectively control pests but also reduce the abuse of pesticides and protect the natural enemies. The aim of this work is to study how the factors, such as natural enemies optimum choice in the two kinds of different pests, timings of natural enemy releases, dosages and timings of insecticide applications, and instantaneous killing rates of pesticides on both pests and natural enemies, can affect the success of IPM control programmes. The results indicate that the pests outbreak period or frequency largely depends on the optimal selective feeding of the natural enemy between one of the pests and the control tactics. Ultimately, we obtain the only pest x 2 needs to be controlled below a certain threshold while not supervising pest x 1 .

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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 574541, 16 pages.

First available in Project Euclid: 27 February 2014

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Kang, Baolin; He, Mingfeng; Liu, Bing. Optimal Control Policies of Pests for Hybrid Dynamical Systems. Abstr. Appl. Anal. 2013 (2013), Article ID 574541, 16 pages. doi:10.1155/2013/574541. https://projecteuclid.org/euclid.aaa/1393512063

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  • S. Finch and R. H. Collier, “Integrated pest management in field vegetable crops in northern Europe–-with focus on two key pests,” Crop Protection, vol. 19, no. 8-10, pp. 817–824, 2000.
  • M. P. Bange, S. A. Deutscher, D. Larsen, D. Linsley, and S. Whiteside, “A handheld decision support system to facilitate improved insect pest management in Australian cotton systems,” Computers and Electronics in Agriculture, vol. 43, no. 2, pp. 131–147, 2004.
  • V. Bisignanesi and M. S. Borgas, “Models for integrated pest management with chemicals in atmospheric surface layers,” Ecological Modelling, vol. 201, no. 1, pp. 2–10, 2007.
  • S. M. Hashemi, S. M. Hosseini, and C. A. Damalas, “Farmers' competence and training needs on pest management practices: participation in extension workshops,” Crop Protection, vol. 28, no. 11, pp. 934–939, 2009.
  • J. F. Strand, “Some agrometeorological aspects of pest and disease management for the 21st century,” Agricultural and Forest Meteorology, vol. 103, no. 1-2, pp. 73–82, 2000.
  • J. M. Yorobe, R. M. Rejesus, and M. D. Hammig, “Insecticide use impacts of Integrated Pest Management (IPM) Farmer Field Schools: evidence from onion farmers in the Philippines,” Agricultural Systems, vol. 104, no. 7, pp. 580–587, 2011.
  • B. Liu, Y. J. Zhang, and L. S. Chen, “The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management,” Nonlinear Analysis: Real World Applications, vol. 6, no. 2, pp. 227–243, 2005.
  • Y. J. Zhang, B. Liu, and L. S. Chen, “Dynamical behavior of Volterra model with mutual interference concerning IPM,” Mathematical Modelling and Numerical Analysis, vol. 38, no. 1, pp. 143–155, 2004.
  • B. Liu, Y. J. Zhang, and L. Chen, “The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management,” Nonlinear Analysis: Real World Applications, vol. 6, no. 2, pp. 227–243, 2005.
  • X. Meng, J. Jiao, and L. Chen, “The dynamics of an age structured predator-prey model with disturbing pulse and time delays,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 547–561, 2008.
  • X. Meng, Z. Song, and L. Chen, “A new mathematical model for optimal control strategies of integrated pest management,” Journal of Biological Systems, vol. 15, no. 2, pp. 219–234, 2007.
  • J.-J. Jiao and L.-S. Chen, “Nonlinear incidence rate of a pest management SI model with biological and chemical control concern,” Applied Mathematics and Mechanics, vol. 28, no. 4, pp. 541–551, 2007.
  • B. Liu, Z. D. Teng, and L. Chen, “Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 347–362, 2006.
  • S. Tang, G. Tang, and R. A. Cheke, “Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases,” Journal of Theoretical Biology, vol. 264, no. 2, pp. 623–638, 2010.
  • H. K. Baek, “Qualitative analysis of Beddington-DeAngelis type impulsive predator-prey models,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1312–1322, 2010.
  • D. T. Dimitrov and H. V. Kojouharov, “Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response,” Applied Mathematics and Computation, vol. 162, no. 2, pp. 523–538, 2005.
  • R. K. Naji and A. T. Balasim, “On the dynamical behavior of three species food web model,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1636–1648, 2007.
  • B. Ermentrout, Simulating: Analyzing and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2002.
  • M. Genkai-Kato and N. Yamamura, “Unpalatable prey resolves the paradox of enrichment,” Proceedings of the Royal Society B, vol. 266, no. 1425, pp. 1215–1219, 1999.
  • D. D. Baĭnov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific, New York, NY, USA, 1993.
  • D. D. Bainov and P. S. Simeonov, System With Impulsive Effect: Stability, Theory and Applications, John Wiley & Sons, New York, NY, USA, 1989.
  • V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, London, UK, 1989.
  • E. E. Werner and D. Hall, “Optimal foraging and the size selection of prey by the bluegill sunfish (Lepomis macrochirus),” Ecology, vol. 55, pp. 1216–1232, 1974.
  • J. R. Ruberson, H. Nemoto, and Y. Hirose, “Pesticides and conservation of natural enemies in pest management,” in Conservation Biological Control, P. Barbosa, Ed., pp. 207–220, Academic Press, New York, NY, USA, 1998.
  • H. Wang, “Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems,” Journal of Nonlinear Science, vol. 21, no. 5, pp. 747–783, 2011.
  • E. Teramoto, K. Kawasaki, and N. Shigesada, “Switching effect of predation on competitive prey species,” Journal of Theoretical Biology, vol. 79, no. 3, pp. 303–315, 1979.
  • http://www.chinadaily.com.cn/china/.
  • http://www.ecns.cn/cns-wire/2012/08-17/22255.shtml.