Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme

Abstract

Food security is a basic human right that guarantees humans an adequate amount of nutritious food. However, plant viruses and agricultural pests cause real damage to food sources, leading to negative impacts on meeting the human right of obtaining a sufficient amount of food. Understanding infectious disease dynamics can help us to design appropriate control and prevention strategies. Although cassava is among the most produced and consumed crops and greatly contributes to food security, cassava mosaic disease causes a decrease in photosynthesis and reduces cassava yield, resulting in a lack of crops. This paper developed a fractional model for cassava mosaic disease (CMD) dynamics based on the Caputo–Fabrizio (CF) fractional derivative to decrease cassava plant infection. We used fixed-point theory to study the existence of a unique solution in the form of the CMD model. A stability analysis of the model was conducted by using fixed-point theory and the Picard technique. A new numerical scheme was proposed for solving the nonlinear system of a fractional model in the sense of the CF-derivative and applied to obtain numerical simulations for a fractional model of the dynamics of CMD. The obtained results are described using figures that show the dynamics and behaviors of the compartments of CMD, and it is concluded that decreasing the population of whitefly vectors can prevent cassava plants from becoming infected better than increasing the recovery rate of the infected cassava plants.