具有阈值控制的植物病虫害模型的全局动力学分析
Global Dynamics Analysis of a Plant Disease Model with Threshold Control
DOI: 10.12677/AAM.2025.141044, PDF,   
作者: 杨 梦：长沙理工大学数学与统计学院，湖南 长沙
关键词: Filippov系统；植物病虫害；阈值控制；全局动力学；Filippov System； Plant Diseases； Threshold Control； Global Dynamics
摘要: 本文研究了一类分段光滑的植物病虫害模型，通过研究感染个体的数量在单位时间内的变化，以 决定是否采取移除措施。 利用 F ilippov 理论、非光滑 Lyap-unov 函数等方法，根据基本再生数的 取值情况，讨论系统的无病平衡点、 地方病平衡点的全局动力学行为。 最后，采用数值仿真的方 法展示了全局动力学。
Abstract: This paper studies the global dynamics of a class of piecewise smooth plant disease model, by studying the change in the number of infected individuals per unit time, to determine whether removal measures should be taken. Based on the value of the basic reproduction number and combined with Filippov theory, non-smooth Lyapunov function and other methods, discussing the global dynamical behaviors of the disease- free equilibrium and the endemic equilibrium of the system. Finally, using numerical simulation to show global dynamics.
文章引用：杨梦. 具有阈值控制的植物病虫害模型的全局动力学分析[J]. 应用数学进展, 2025, 14(1): 453-461. https://doi.org/10.12677/AAM.2025.141044

参考文献

[1] Jeger, M.J., Seal, S.E. and Van den Bosch, F. (2006) Evolutionary Epidemiology of Plant Virus Disease. In: Advances in Virus Research, Elsevier, 163-203.
https://doi.org/10.1016/s0065-3527(06)67005-x
[2] van den Bosch, F. and de Roos, A.M. (1996) The Dynamics of Infectious Diseases in Orchards with Roguing and Replanting as Control Strategy. Journal of Mathematical Biology, 35, 129- 157.
https://doi.org/10.1007/s002850050047
[3] Marcus, R., Talpaz, H. and Bar-Joseph, M. (1989) A Model for the Spread and Control of Citrus Tristeza Virus Disease. Journal of Applied Statistics, 16, 315-320.
https://doi.org/10.1080/02664768900000039
[4] Chan, M. and Jeger, M.J. (1994) An Analytical Model of Plant Virus Disease Dynamics with Roguing and Replanting. The Journal of Applied Ecology, 31, 413-427.
https://doi.org/10.2307/2404439
[5] Fishman, S. and Marcus, R. (1984) A Model for Spread of Plant Disease with Periodic Re- movals. Journal of Mathematical Biology, 21, 149-158.
https://doi.org/10.1007/bf00277667
[6] Luo, Y., Gao, S., Xie, D. and Dai, Y. (2015) A Discrete Plant Disease Model with Roguing and Replanting. Advances in Difference Equations, 2015, 12.
https://doi.org/10.1186/s13662-014-0332-3
[7] Wang, J., Zhang, X., Wang, J. and Sun, Q. (2019) Dynamics of a Nonautonomous Plant Disease Model with General Nonlinear Incidence Rate and Time-Varying Impulse. Journal of Applied Mathematics and Physics, 7, 2518-2530.
https://doi.org/10.4236/jamp.2019.710171
[8] Thresh, J.M. and Owusu, G.K. (1986) The Control of Cocoa Swollen Shoot Disease in Ghana: An Evaluation of Eradication Procedures. Crop Protection, 5, 41-52.
https://doi.org/10.1016/0261-2194(86)90037-2
[9] Fishman, S., Marcus, R., Talpaz, H., Bar-Joseph, M., Oren, Y., Salomon, R., et al. (1983) Epidemiological and Economic Models for Spread and Control of Citrus Tristeza Virus Disease. Phytoparasitica, 11, 39-49.
https://doi.org/10.1007/bf02980710
[10] Thresh, J.M. and Cooter, R.J. (2005) Strategies for Controlling Cassava Mosaic Virus Disease in Africa. Plant Pathology, 54, 587-614.
https://doi.org/10.1111/j.1365-3059.2005.01282.x
[11] Gibson, R.W. and Aritua, V. (2002) The Perspective of Sweetpotato Chlorotic Stunt Virus in Sweetpotato Production in Africa: A Review. African Crop Science Journal, 10, 281-310.
https://doi.org/10.4314/acsj.v10i4.27531
[12] van den Bosch, F., Jeger, M.J. and Gilligan, C.A. (2006) 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: Biological Sciences, 274, 11-18.
https://doi.org/10.1098/rspb.2006.3715
[13] Dong, C., Xiang, C., Xiang, Z. and Yang, Y. (2022) Global Dynamics of a Filippov Epidemic System with Nonlinear Thresholds. Chaos, Solitons Fractals, 163, Article 112560.
https://doi.org/10.1016/j.chaos.2022.112560
[14] Xiao, Y., Xu, X. and Tang, S. (2012) Sliding Mode Control of Outbreaks of Emerging Infectious Diseases. Bulletin of Mathematical Biology, 74, 2403-2422.
https://doi.org/10.1007/s11538-012-9758-5
[15] Wang, J., Zhang, F. and Wang, L. (2016) Equilibrium, Pseudoequilibrium and Sliding-Mode Heteroclinic Orbit in a Filippov-Type Plant Disease Model. Nonlinear Analysis: Real World Applications, 31, 308-324.
https://doi.org/10.1016/j.nonrwa.2016.01.017
[16] Filippov, A.F. (1988) Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers.
[17] 王佳伏, 徐忠齐, 黄立宏. 具有不连续控制策略的SIQR传染病模型的全局动力学分析[J]. 应用数学学报, 2023, 46(6): 998-1011.
[18] 黄立宏, 郭振远, 王佳伏. 右端不连续微分方程理论与应用[M]. 北京: 科学出版社, 2011.
[19] Bacciotti, A. and Ceragioli, F. (1999) Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions. ESAIM: Control, Optimisation and Calculus of Variations, 4, 361-376.
https://doi.org/10.1051/cocv:1999113

为你推荐
Baidu
map