Stability analysis for yellow virus disease mathematical model of red chili plants

Abstract

One of the main obstacles in the cultivation of red chili plants (Capsicum annuum) is the yellow virus disease caused by the Gemini virus. The virus is transmitted through insect vectors which can be controlled using insect pathogenic fungi (Verticillium lecanii). To understand the dynamics of the spread of the yellow virus in Capsicum annuum (C. annuum), we have formulated and analyzed a mathematical model of plant disease. From this model, the value of the Basic Reproduction Number (ℜ0) is presented, which is an essential quantity in an epidemiological model. The obtaining results indicate that when the value of ℜ0 is greater than one, the endemic equilibrium point is asymptomatically stable. However, if the value of ℜ0 is smaller than one, then the endemic equilibrium point is unstable. Also, we provide numerical simulations to illustrate the results.