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

Abstract

Rice blast, caused by the pathogenic fungus Magnapor the oryzae, poses a significant threat to rice pro-duction, especially in regions like Kenya where rice is both a staple food and a key economic commodity. This study introduces a comprehensive mathematical model designed to investigate the dynamics of rice blastre-infection following fungicide application on infected crops. The model is formulated as a system of ordi-nary differential equations (ODEs) that categorizes the rice population into five compartments: Susceptible, Protected, Infected, Recovered, and Secondary Infected. The positivity and boundedness of solutions were established, ensuring that the model is both mathematically and biologically well-posed. Using the stability theory of differential equations, the model was analyzed, and the basic reproduction numberR0was derivedvia the Next Generation Matrix method. The existence of both the Disease-Free Equilibrium (DFE) and the Endemic Equilibrium Point (EEP) was demonstrated. Stability analysis revealed that the DFE is locally and globally stable whenR0<1, and unstable whenR0>1. Conversely, the EEP is locally asymptotically stablewhenR0>1. Sensitivity analysis identified the fungicide application rate (π) as the most influential pa-ra meter in reducing rice blast re-infection. Numerical simulations were conducted to support the analytical findings, demonstrating that effective fungicide use can substantially decrease disease prevalence, there by enhancing rice yield and promoting sustainable agricultural practices. This study contributes meaningfully to the field of plant disease modeling and provides a robust framework for future research into the epidemiology and management of crop diseases.