Mathematical Model of Effect of Yellow Virus on Tomato Plants Through Bemisia tabaci Insects Using Verticillium lecanii Fungus

Abstract

The Yellow virus is a virus that causes tomato plants to die. The insect vector Bemisia tabaci spreads this virus. The goal of this study is to identify the shape of a mathematical model of the influence of yellow virus on tomato plants via the insect Bemisia tabaci and the fungus Verticilliun lecanii, as well as to interpret the results of the mathematical model analysis. This is referred to as basic research. This study employs a descriptive method in which theories are analysed in relation to the topics to be discussed, and these theories are based on a literature review. Stability analysis is carried out using Routh-Hurwitz criteria. It indicates that the disease-free equilibrium point is asymptotically stable when Λ_t=μ_tN and the endemic equilibrium point is asymptotically stable for d₁>e₁, d₂>e₂ and a1>(a₁)²+(a₃)²a₀)/(a₃a₂ ). The model simulation shows that if the efficacy of Verticillium lecanii is high, the population of infected tomato plants, as well as the population of Bemisia tabaci, will go extinct.