Fractional Order Modeling the Gemini Virus in <i>Capsicum annuum</i> with Optimal Control

Abstract

In this article, a fractional model of the Capsicum annuum (C. annuum) affected by the yellow virus through whiteflies (Bemisia tabaci) is examined. We analyzed the model by equilibrium points, reproductive number, and local and global stability. The optimal control methods are discussed to decrease the infectious B. tabaci and C. annuum by applying the Verticillium lecanii (V. lecanii) with the Atangana–Baleanu derivative. Numerical results described the population of plants and comparison values of using V. lecanni. The results show that using 60% of V. lecanni will control the spread of the yellow virus in infected B. tabaci and C. annuum in 10 days, which helps farmers to afford the costs of cultivating chili plants.

Keywords

• fractional calculus
• stability analysis
• Atangana–Baleanu fractional derivative
• optimal control
• mathematical models
• yellow virus