Analysis of a High-Dimensional Mathematical Model for Plant Virus Transmission with Continuous and Impulsive Roguing Control

Abstract

Roguing and replanting are the most common strategies to control plant diseases and pests. How to build the mathematical models of plant virus transmission and consider the impact of roguing and replanting strategies on plant virus eradication is of great practical significance. In the present paper, we propose the mathematical models for plant virus transmission with continuous and impulsive roguing control. For the model with continuous control strategies, the threshold values for the existences and stabilities of multiple equilibria have been given, and the effect of roguing strategies on the threshold values is also addressed. Furthermore, the model with impulsive roguing control tactics is proposed, and the existence and stability of the plant-only and disease-free periodic solutions of the model are investigated by calculating several threshold values. Moreover, when selecting the design control strategy to minimize the threshold, we systematically analyze the existence of the optimal times of roguing infected plants within a replanting cycle, which is of great significance to the design and optimization of the prevention and control strategy of plant virus transmission. Finally, numerical investigations are given to reveal the main conclusions, and the biological implications of the main results are briefly discussed in the last section.

Study of Mathematical Modeling for Plant Disease Transmission: A Systematic Literature Review during 2012-2022

“…Published articles in [1] and [10] are the most cited in the autonomous system at 43 times each, whereas in the non-autonomous system, the article in [18] is the most cited at 14 times. Somehow, there are still articles that remain not been referenced, including the articles in [57,78,82]. Some possibilities caused an article has not been used as a reference, including the latest publication time, the model in the article frequently explored, and the findings not being followed up by the other studies.…”

“…The study explored the whole content in [78] because the article contained a transmission model in the non-autonomous system and is more suitable for the disease spread phenomenon. Although the article in [18] is the most often used as a reference, the contents do not precisely describe the phenomenon since the authors don't describe disease transmission as a vector-host model and represent that the disease spread directly between plants.…”

Cacao sustainability: The case of cacao swollen-shoot virus co-infection

“…Our aim in this study is to use simple differential equation models to gain useful insights about the inherent dynamics of an experimental data involving cacao swollen shoot virus from Domfeh et al [10]. Several studies have used mathematical models to study diseases transmission dynamics in plant [12][13][14][15][16][17][18], including co-infection with multiple pathogen and the resulting interactions like cross protection [12] and helper-dependent [18]. Mathematical models have also been used to understand mitigation strategies to curtail the spread of some plant pathogen [17,19].…”

“…Several studies have used mathematical models to study diseases transmission dynamics in plant [12][13][14][15][16][17][18], including co-infection with multiple pathogen and the resulting interactions like cross protection [12] and helper-dependent [18]. Mathematical models have also been used to understand mitigation strategies to curtail the spread of some plant pathogen [17,19]. Thus, we develop several models using differential equations to determine the disease transmission rate in experimental treatments with and without protective layers.…”

Study of an Epidemiological Model for Plant Virus Diseases with Periodic Coefficients

“…Periodic forcing studies are, therefore, instrumental for farmers and agricultural policymakers in strategizing crop rotations, planting schedules, and timing treatments effectively. The distinction between continuous and impulsive roguing control is a pertinent example [19]. A deeper comprehension of the periodic nature of plant virus interactions paves the way for more sophisticated control strategies.…”