Stability analysis and optimal control for leaf brown spot disease of rice

Leaf brown spot, caused by fungi, is a terrible plant disease, and it can significantly reduce the quality and quantity of rice. In this paper, we developed the model based on leaf brown spot disease development and considered a preventive treatment using botanical fungicide. In addition, we develop a model with suitable optimal control strategies. The result shows disease-free equilibrium is asymptotically stable when $R_0>1$. In contrast, the endemic equilibrium is asymptotically stable when $R_0>1$. The obtained optimal control to can reduce the number of infected plants compared to that without control. In addition, the analytical results were confirmed by numerical simulations of the occurrence of the theoretical results.