- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 428453, 25 pages
Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies
1College of Science, Shandong University of Science and Technology, Qingdao 266510, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
3State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China
Received 28 December 2011; Accepted 6 February 2012
Academic Editor: Khalida Inayat Noor
Copyright © 2012 Tongqian Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. J. Roberts, D. Schimmelpfennig, E. Ashley, M. Livingston, M. Ash, and U. Vasavada, “The value of plant disease early-warning systems: a case study of USDA’s soybean rust coordinated framework,” Economic Research Service 18, United States Department of Agriculture, 2006.
- J. M. Thresh and R. J. Cooter, “Strategies for controlling cassava mosaic disease in Africa,” Plant Pathology, vol. 54, pp. 587–614, 2005.
- J. Dubern, “Transmission of African cassava mosaic geminivirus by the whitefly (Bemisia tabaci),” Tropical Science, vol. 34, pp. 82–91, 1994.
- R. W. Gibson, V. Aritua, E. Byamukama, I. Mpembe, and J. Kayongo, “Control strategies for sweet potato virus disease in Africa,” Virus Research, vol. 100, no. 1, pp. 115–122, 2004.
- R. W. Gibson, J. P. Legg, and G. W. Otim-Nape, “Unusually severe symptoms are a characteristic of the current epidemic of mosaic virus disease of cassava in Uganda,” Annals of Applied Biology, vol. 128, no. 3, pp. 479–490, 1996.
- R. A. C. Jones, “Determining threshold levels for seed-borne virus infection in seed stocks,” Virus Research, vol. 71, no. 1-2, pp. 171–183, 2000.
- R. A. C. Jones, “Using epidemiological information to develop effective integrated virus disease management strategies,” Virus Research, vol. 100, no. 1, pp. 5–30, 2004.
- F. Van Den Bosch, M. J. Jeger, and C. A. Gilligan, “Disease control and its selection for damaging plant virus strains in vegetatively propagated staple food crops; a theoretical assessment,” Proceedings of the Royal Society B, vol. 274, no. 1606, pp. 11–18, 2007.
- F. van den Bosch and A. de Roos, “The dynamics of infectious diseases in orchards with roguing and replanting as control strategy,” Journal of Mathematical Biology, vol. 35, no. 2, pp. 129–157, 1996.
- M. S. Suen and M. J. Jeger, “An analytical model of plant virus disease dynamics with roguing and replanting,” Journal of Applied Ecology, vol. 31, no. 3, pp. 413–427, 1994.
- J. C. Zadoks and R. D. Schein, Epidemiology and Plant Disease Management, Oxford University, New York, NY, USA, 1979.
- S. Sankaran, A. Mishra, R. Ehsani, and C. Davis, “A review of advanced techniques for detecting plant diseases,” Computers and Electronics in Agriculture, vol. 72, pp. 1–13, 2010.
- S. Fishman, R. Marcus, H. Talpaz, et al., “Epidemiological and economic models for the spread and control of citrus tristeza virus disease,” Phytoparasitica, vol. 11, pp. 39–49, 1983.
- J. Holt and T. C. B. Chancellor, “A model of plant virus disease epidemics in asynchronously-planted cropping systems,” Plant Pathology, vol. 46, no. 4, pp. 490–501, 1997.
- J. E. van der Plank, Plant Diseases: Epidemics and Control, Wiley, New York, NY, USA, 1963.
- S. Tang, Y. Xiao, and R. A. Cheke, “Dynamical analysis of plant disease models with cultural control strategies and economic thresholds,” Mathematics and Computers in Simulation, vol. 80, no. 5, pp. 894–921, 2010.
- X. Meng and Z. Li, “The dynamics of plant disease models with continuous and impulsive cultural control strategies,” Journal of Theoretical Biology, vol. 266, no. 1, pp. 29–40, 2010.
- K. L. Cooke, “Stability analysis for a vector disease model,” The Rocky Mountain Journal of Mathematics, vol. 9, no. 1, pp. 31–42, 1979.
- J. J. Jiao and L. S. Chen, “Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators,” International Journal of Biomathematics, vol. 1, no. 2, pp. 197–208, 2008.
- S. Gao, Z. Teng, and D. Xie, “The effects of pulse vaccination on SEIR model with two time delays,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 282–292, 2008.
- P. Yongzhen, L. Changguo, and C. Lansun, “Continuous and impulsive harvesting strategies in a stage-structured predator-prey model with time delay,” Mathematics and Computers in Simulation, vol. 79, no. 10, pp. 2994–3008, 2009.
- S. Gao, L. Chen, J. J. Nieto, and A. Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol. 24, no. 35-36, pp. 6037–6045, 2006.
- T. Zhang, X. Meng, and Y. Song, “The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments,” Nonlinear Dynamics, vol. 64, no. 1-2, pp. 1–12, 2011.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191, Academic Press, Boston, Mass, USA, 1993.
- H. L. Smith, Monotone Dynamical Systems, vol. 41, American Mathematical Society, Providence, RI, USA, 1995.
- X.-Q. Zhao and X. Zou, “Threshold dynamics in a delayed SIS epidemic model,” Journal of Mathematical Analysis and Applications, vol. 257, no. 2, pp. 282–291, 2001.