Mathematical Modelling And Bifurcation Analysis Of Vector-Borne Diseases Of Crop Biomass

Abstract

This study presents mathematical modelling and bifurcation analysis of vector-borne crop diseases by incorporating non-linear saturation rate of Holling type II. A mathematical model is developed by taking into account the logistic crop growth and vector dynamics. Before showing the existence of two equilibrium points (the disease-free and the endemic), the basic properties of the model are discussed and then the expression for basic reproduction number is obtained by using the next generation matrix method. Furthermore, bifurcation analysis is done by using the centre manifold theory. Sensitivity analysis is performed for the basic reproduction number which is shown with the help of a bar chart. Model parameters with positive sensitivity indices significantly impact the spread of crop diseases, while those with negative indices have a lesser effect. Numerical simulations are done and the results are displayed graphically to justify the analytical findings. This model aids in developing strategies to control vector-borne diseases in crops, enhancing productivity and food security.