Dynamical analysis of fractional plant disease model with curative and preventive treatments. (November 2022) - Shaw, Pawan Kumar; Kumar, Sunil; Momani, Shaher; Hadid, Samir
Abstract: Food security has become a major concern as the human population grows. Agriculture is crucial in this environment. The majority of staple meals are derived from plants. Plant diseases, on the other hand, can lower food production and quality. In this paper, two stage plant disease (TSPD) dynamics can be studied using a fractional order model. Here we used two fractional operator: Caputo fractional derivative (CFD) and Caputo–Fabrizio fractional derivative (CFFD) each of arbitrary order ϖ ∈ ( 0, 1 ] . We evaluate the effects of curative and preventive treatments on plant disease transmission dynamics in the concerned model. We demonstrate that this model has non-negative solutions, which is desirable in population dynamics. For the suggested model, we discuss the stability of a disease-free and endemic equilibrium. For numerical simulation, we used generalized fractional RK2 scheme, Adams–Bashforth Moulton (ABM) scheme, and three step fractional Adam–Bashforth scheme (ABS) to visualize the outcomes of the concerned model. We discovered that combining curative and preventive treatment can help to reduce the number of diseased plants. Highlights: Food security has become a major concern as the human population grows. The majority of staple meals are derived. We demonstrate that this model has non-negative solutions. We conclude that the idea of fractional provides better results.