Dynamics and prevention of gemini virus infection in red chili crops studied with generalized fractional operator: Analysis and modeling

Abstract The gemini virus, a major obstacle to red chili production, is exacerbated by yellow virus propagation. This study explores the potential of an epidemic model using generalized fractal fractional operators to observe dynamics and develop prevention strategies to control infections. The fractional-ordering system is analyzed quantitatively and qualitatively, including positiveness, boundedness, unique solution, and reproductive analysis under equilibrium points to ensure bounded and positive solutions. The proposed model’s uniqueness is demonstrated through global effects analysis using Lipschitz and linear growth techniques, and local and global stability was assessed using the Lyapunov function and the first derivative test. The study utilizes a two-level Lagrange polynomial, specifically the Mittag–Leffler kernel, to explore the impact of fractional operators on plant diseases. The fractional-order model’s behavior is verified through numerical simulations at disease-free and equilibrium points, and results are compared to demonstrate its efficacy and memory effect. The study visually illustrates the impact of various proposed operators on the proposed red chilli model, providing numerical data for each operator with varying fractional parameters. By comparing non-integer orders to integer orders, we obtain a more comparable result to support its stance. The study found that the fractal fractional operator is more effective than the usual integer order for disease eradication because it efficiently reduces gemini virus infection rates by lowering the fractional-order parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="italic">ϑ</m:mi> </m:math> {\vartheta } . This study will allow us to develop mitigating techniques for afflicted plants and gain a better understanding of the virus’s behavior.