Optimal control issues in plant disease with host demographic factor and botanical fungicides

Indonesian Operations Research Association - International Conference on Operations Research 2017

Anggriani, N.^1 ; Mardiyah, M.^1 ; Istifadah, N.^2 ; Supriatna, A.K.^1

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang km 21, Jatinangor

45363, Indonesia^1

Department of Plant Pathology, Faculty of Agriculture, Padjadjaran University, Indonesia^2

关键词: Analytical results;    Basic reproduction number;    Demographic factors;    Endemic equilibrium;    Infectious period;    Largest eigenvalues;    Optimal controls;    Preventive treatments;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/332/1/012036/pdf
DOI  :  10.1088/1757-899X/332/1/012036

来源: IOP

【 摘 要 】

In this paper, we discuss a mathematical model of plant disease with the effect of fungicide. We assume that the fungicide is given as a preventive treatment to infectious plants. The model is constructed based on the development of the disease in which the monomolecular is monocyclic. We show the value of the Basic Reproduction Number (BRN)0of the plant disease transmission. The BRN is computed from the largest eigenvalue of the next generation matrix of the model. The result shows that in the region where0greater than one there is a single stable endemic equilibrium. However, in the region where0less than one this endemic equilibrium becomes unstable. The dynamics of the model is highly sensitive to changes in contact rate and infectious period. We also discuss the optimal control of the infected plant host by considering a preventive treatment aimed at reducing the infected host plant. The obtaining optimal control shows that it can reduce the number of infected hosts compared to that without control. Some numerical simulations are also given to illustrate our analytical results.