Mathematical modeling and analysis for the transmission dynamics of wheat yellow rust disease

Wheat is one of the most significant crops grown worldwide and serves as both an important source of food for consumers and a means of income for farmers. However, the fungus that causes wheat yellow rust (WYR) seriously damages the world's wheat production, especially in developing countries. In this study, we proposed and analyzed a compartmental mathematical model to describe the transmission dynamics of WYR disease on wheat crops. For the proposed model, the existence and uniqueness, the positivity and boundedness of the solutions are explained. The two equilibrium points, namely disease-free and endemic equilibrium points are demonstrated, and the basic reproduction number is evaluated using the next-generation matrix approach. The Routh Hurwitz stability criteria and center manifold theory are used to analyze the local stability of the equilibrium points and the existence of forward bifurcation, respectively. The global stability of the equilibrium points are also established using Lyapunov's approach. A sensitivity analysis of the model is also carried out. To validate our analytical results, MATLAB software is utilized to conduct several numerical simulations and generate graphical representations of the results. The findings of this study suggest that effective use of fungicides can significantly prevent the spread of WYR disease.