Eco-epidemiological Model and Optimal Control Analysis of Tomato Yellow Leaf Curl Virus Disease in Tomato Plant

IF 1.2 Q2 MATHEMATICS, APPLIED
B. Kahsay, O. Makinde
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引用次数: 0

Abstract

The purpose of this study is to analyze the impact of control strategies, namely, insecticide spray, roguing of a diseased tomato plant, and protective netting to protect tomato plant from tomato yellow leaf curl virus disease (TYLCVD). For this, we formulate and analyze a simple deterministic model for the transmission dynamics of TYLCVD that incorporates these control strategies. We initially take into account the constant control case, we calculate the basic reproduction number, and we investigate the existence and stability of the disease-free and endemic equilibria. We use the Kamgang-Sallet stability to ensure that the disease-free equilibrium point is globally asymptotically stable when the reproduction number R 0 is less than one. This indicates that TYLCVD dies out independent of the initial size of the tomato population. For R 0 < 1 , the disease-free equilibrium becomes unstable, and the endemic equilibrium is globally asymptotically stable. This indicates that TYLCVD propagates. In the nonconstant control case, we use Pontryagin’s maximum principle to derive the necessary conditions for the optimal control of the disease. Our findings show that all the combined efforts of two out of three strategies can significantly reduce the power of infectivity of the disease except the combination of the use of insecticide spray and rouging infected tomato plants. Besides our numerical simulations show, the implementation of the combination of roguing diseased plants and protective netting has a similar effect in minimizing or eliminating TYLCV as the use of all strategies. Hence, as resources are always in scarce, we recommend policymakers to adapt the combination of the use of roguing diseased tomato plants and protective netting to eradicate the disease.
番茄黄曲叶病毒病在番茄植株中的生态流行病学模型及最优控制分析
本研究的目的是分析控制策略的影响,即杀虫剂喷雾、对患病番茄植株的roguing和保护网以保护番茄植株免受番茄黄叶卷曲病毒病(TYLCVD)的影响。为此,我们为TYLCVD的传输动力学制定并分析了一个简单的确定性模型,该模型包含了这些控制策略。我们最初考虑了恒定控制情况,计算了基本繁殖数,并研究了无病和地方病平衡的存在性和稳定性。我们使用Kamgang-Sallet稳定性来确保当繁殖数R0小于1时,无病平衡点是全局渐近稳定的。这表明TYLCVD的死亡与番茄种群的初始规模无关。对于R0<1,无病平衡变得不稳定,地方病平衡是全局渐近稳定的。这表明TYLCVD正在传播。在非恒定控制的情况下,我们使用Pontryagin的最大值原理来推导疾病最佳控制的必要条件。我们的研究结果表明,除了使用杀虫剂喷雾和对受感染的番茄植株进行消毒外,三种策略中的两种组合可以显著降低疾病的传染性。此外,我们的数值模拟表明,在最小化或消除TYLCV方面,将病株和防护网相结合的实施与使用所有策略具有相似的效果。因此,由于资源总是稀缺的,我们建议政策制定者调整对患病番茄植物进行改良和使用防护网的组合,以根除这种疾病。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Applied Mathematics
Journal of Applied Mathematics MATHEMATICS, APPLIED-
CiteScore
2.70
自引率
0.00%
发文量
58
审稿时长
3.2 months
期刊介绍: Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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