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

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.

[1]  N. Rose,et al.  Differential Equations With Applications , 1967 .

[2]  Kenneth L. Cooke,et al.  Stability analysis for a vector disease model , 1979 .

[3]  J. Zadoks,et al.  Epidemiology and plant disease management , 1979 .

[4]  J. Dubern.  Transmission of African cassava mosaic geminivirus by the whitefly (Bemisia tabaci). , 1994 .

[5]  Man-Suen Chan,et al.  An analytical model of plant virus disease dynamics with roguing and replanting. , 1994 .

[6]  F. van den Bosch,et al.  The dynamics of infectious diseases in orchards with roguing and replanting as control strategy , 1996 .

[7]  J. Legg,et al.  Unusually severe symptoms are a characteristic of the current epidemic of mosaic virus disease of cassava in Uganda , 1996 .

[8]  Johnson Holt,et al.  A model of plant virus disease epidemics in asynchronously‐planted cropping systems , 1997 .

[9]  R. Jones,et al.  Determining 'threshold' levels for seed-borne virus infection in seed stocks. , 2000, Virus research.

[10]  Xiao-Qiang Zhao,et al.  Threshold Dynamics in a Delayed SIS Epidemic Model , 2001 .

[11]  Roger A. C. Jones,et al.  Using epidemiological information to develop effective integrated virus disease management strategies. , 2004, Virus research.

[12]  Emmanuel Byamukama,et al.  Control strategies for sweet potato virus disease in Africa. , 2004, Virus research.

[13]  R. Cooter,et al.  Strategies for controlling cassava mosaic virus disease in Africa , 2005 .

[14]  M. Hirsch,et al.  4. Monotone Dynamical Systems , 2005 .

[15]  Shujing Gao,et al.  Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. , 2006, Vaccine.

[16]  David Schimmelpfennig,et al.  The Value of Plant Disease Early-Warning Systems: A Case Study of USDA's Soybean Rust Coordinated Framework , 2006 .

[17]  C A Gilligan,et al.  Disease control and its selection for damaging plant virus strains in vegetatively propagated staple food crops; a theoretical assessment , 2007, Proceedings of the Royal Society B: Biological Sciences.

[18]  Zhidong Teng,et al.  The effects of pulse vaccination on SEIR model with two time delays , 2008, Appl. Math. Comput..

[19]  H. Talpaz,et al.  Epidemiological and economic models for spread and control of citrus tristeza virus disease , 1983, Phytoparasitica.

[20]  Jianjun Jiao,et al.  GLOBAL ATTRACTIVITY OF A STAGE-STRUCTURE VARIABLE COEFFICIENTS PREDATOR-PREY SYSTEM WITH TIME DELAY AND IMPULSIVE PERTURBATIONS ON PREDATORS , 2008 .

[21]  Lansun Chen,et al.  Continuous and impulsive harvesting strategies in a stage-structured predator-prey model with time delay , 2009, Math. Comput. Simul..

[22]  Zhenqing Li,et al.  The dynamics of plant disease models with continuous and impulsive cultural control strategies. , 2010, Journal of theoretical biology.

[23]  Sanyi Tang,et al.  Dynamical analysis of plant disease models with cultural control strategies and economic thresholds , 2010, Math. Comput. Simul..

[24]  Reza Ehsani,et al.  Review: A review of advanced techniques for detecting plant diseases , 2010 .

[25]  Yi Song,et al.  The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments , 2011 .

[26]  Y. Kuang.  Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[27]  Van der Plank.  Plant Diseases: Epidemics and Control , 2013 .