Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order

被引：0
作者：
El-Sayed A.M.A. [1 ]
Rida S.Z. [2 ]
Gaber Y.A. [2 ]
机构：
[1] Department of Mathematics, Faculty of Science, Alexandria University, Alexandria
[2] Department of Mathematics, Faculty of Science, South Valley University, Qena
来源：
Chaos, Solitons and Fractals | 2020年 / 137卷
关键词：
Caputo fractional derivative; Fractional calculus; Fractional Euler method; Plant disease; Stability analysis;
D O I：
10.1016/j.chaos.2020.109879
中图分类号：
学科分类号：
摘要：
Plants are really important for the planet and for all living things. Plants absorb carbon dioxide and release oxygen from their leaves, which humans and other animals need to breathe. Living things need plants to live - they eat them and live on them. Therefore, understanding plant disease dynamics is important as it can provide insightful knowledge on plant disease transmission. So, in this work, we introduce the fractional order model for the plant diseases in a two-stage infection. We show that this model possesses non-negative solutions as desired in any population dynamics. We discuss the stability of a disease free and an endemic equilibrium for the proposed model. We carry out numerical solutions to demonstrate the theoretical analysis by applying the fractional Euler method (FEM). © 2020 Elsevier Ltd
引用
收藏
相关论文
共 38 条
  • [1] Vanderplank J.E., Plant disease: epidemics and control, (1963)
  • [2] Verhoeff K., Latent infection by fungi, Annu Rev Phytopathol, 12, pp. 99-107, (1974)
  • [3] Agrios G.N., Lant pathology, (1988)
  • [4] Zhang T., Meng X., Song Y., Li Z., Dynamical analysis of delayed plant disease models with continuous or impulsive cultural control strategies, Abstr Appl Anal, 2012, pp. 1-25, (2012)
  • [5] Sisterson M.S., Stenger D.C., Roguing with replacement in perennial crops: conditions for successful disease management, Phytopathology, 103, pp. 117-128, (2013)
  • [6] Luo Y., Gao S., Xie D., Dai Y., A discrete plant disease model with roguing and replanting, Adv Differ Equ, 2015, (2015)
  • [7] Blas N., David G., Dynamical roguing model for controlling the spread of tungro virus via Nephotettix Virescens in a rice field, J Phys, 893, (2017)
  • [8] Anggriani N., Yusuf M., Supriatna A.K., The effect of insecticide on the vector of rice tungro disease: insight from a mathematical model, Inf Int InterdiscipJ, 20, 9A, pp. 6197-6206, (2017)
  • [9] Anggriani N., Istifadah N., Hanifah M., Supriatna A.K., A mathematical model of protectant and curative fungicide application and its stability analysis, IOP Conf Ser, 31, (2016)
  • [10] Anggriani N., Arumi D., Hertini E., Istifadahd N.
1234