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A curative and preventive treatment fractional model for plant disease in Atangana–Baleanu derivative through Lagrange interpolation

The growth of the world populations number leads to increasing food needs. However, plant diseases can decrease the production and quality of agricultural harvests. Mathematical models are widely used to model and interpret plant diseases, showing viruses’ transmission dynamics and effects. In this paper, we investigate the dynamics of the treatments of plant diseases via the Atangana–Baleanu derivative in the sense of Caputo (ABC). We study the existence and uniqueness of solutions of curative and preventive treatment fractional model for plant disease. By using Lagrange interpolation, we give numerical simulations and investigate the results at various fractional orders under specific parameters. The results show that the increase of the roguing rate for the most infected plant or the decrease of the rate of planting in the infected area will reduce the plant disease transmissions. For balancing the plant production, the decision-makers can plant in other areas in which there are no infected cases.