Mathematical Model Analysis for the Transmission Dynamics of Wheat Yellow Rust Disease: In Case of Melga Woreda, Sidama Regional State, Ethiopia.

In this work, we present a mathematical model that uses real data to characterize the transmission dynamics of wheat yellow rust (WYR) disease. The model's well-posedness, such as the existence and uniqueness, the positivity, and boundedness of the solutions of the model, is examined. Additionally, the study looks at qualitative evaluations such as the existence and stability of equilibrium points and uses the next-generation matrix to derive the basic reproduction number. The Routh-Hurwitz criteria were used to assert and demonstrate the local stability of the model's WYR free and endemic equilibrium points. Lyapunov's method is also used to establish the global stability of the equilibrium point. Moreover, a sensitivity analysis of the model is carried out. Using the least squares approach, the parameters of the model are fitted with the real data obtained from Melga Woreda of Sidama Regional State, Ethiopia. Using the estimated parameters of the model, the analytical results are illustrated via numerical simulations using the MATLAB solver ode45. The key finding of our study shows that proper use of both preventive and anti-sporulant fungicides eliminates the WYR disease from wheat fields after 15 weeks.