A Mathematical Model for Effective Fungicide Use in Rice Blast Re-Infection

Rice blast, caused by the pathogenic fungus Magnaporthe oryzae, represents a critical challenge to rice production, particularly in regions such as Kenya where rice serves as a staple food and a vital economic resource. This study presents a comprehensive mathematical model aimed at elucidating the dynamics of rice blast re-infection following the application of fungicides on infected crops. The model was developed from a system of Ordinary Differential Equations that divides rice population into five classes: Susceptible, Protected, Infected,Recovered and the Secondary infected.Positivity and boundedness of solutions was established that the model was mathematically and biologically meaningful.The model was analysed using the stability theory of differential equations.The Basic reproduction number $R_O$ was developed using Next Generation Matrix.The existence of DFE and EEP was determined.Stability analysis of the model showed that DFE is both locally and globally stable when $R_O$<1 and unstable when $R_O$>1 while EEP is locally asymptotically stable when $R_O$>1.Sensitivity analysis of the model parameters showed that the parameter $\pi$(Rate of fungicide application) is the most sensitive parameter in reducing rice blast re-infection.Numerical simulation was done to validate the analytical results.The results demonstrate that judicious fungicide application can significantly reduce the prevalence of rice blast, leading to enhanced rice yields and improved sustainability in agricultural practices. This study not only contributes to the existing body of knowledge on plant disease management but also provides a robust framework for future investigations into the epidemiology of crop diseases.