Spatio-temporal dynamics of the vector-born plant disease model

In this manuscript, the reaction-diffusion vector-borne plant disease model is considered. Plants are a crucial part of the ecosystem because they provide food and oxygen for living organisms. If the disease is spread out in an area, then there is the possibility of starvation for animals and human beings. The need of the hour is to consider such models and their results which provides the opportunity for the decision makers to prepare policy for the betterment of human mankind. The underlying model is numerically investigated by an implicit finite difference scheme. The positivity of the governing model is also established. The Taylor series is employed to check the consistency. Linear stability of the implicit scheme is also derived. The positivity of the scheme is also derived by using the M-matrix and induction method. There are two equilibrium points namely disease free and endemic. 2D and 3D plots are drawn for the different choices of the parameters and both equilibrium points are successfully gained. It is evident from the simulations that results are consistent with the continuous model, results preserve the positive behavior for the whole domain. Numerical simulations confirm the efficacy of the method and validate the theoretical findings.