Abstract and Applied Analysis
Volume 2012 (2012), Article ID 428453, 25 pages
http://dx.doi.org/10.1155/2012/428453
Research Article

Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies

Tongqian Zhang,1 Xinzhu Meng,2,3 Yi Song,1 and Zhenqing Li3

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.

Abstract

Delayed plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are presented and investigated. Firstly, we consider continuous cultural control strategy in which continuous replanting of healthy plants is taken. The existence and local stability of disease-free equilibrium and positive equilibrium are studied by analyzing the associated characteristic transcendental equation. And then, plant disease model with impulsive replanting of healthy plants is also considered; the sufficient condition under which the infected plant-free periodic solution is globally attritive is obtained. Moreover, permanence of the system is studied. Some numerical simulations are also given to illustrate our results.