Optimal Control of Tungro Disease Spread by Considering Growth Phase and Roguing Control

Abstract

Tungro disease poses a serious threat to rice cultivation, as it is caused by a viral infection transmitted by green leafhoppers. This study develops a mathematical model to describe the spread of tungro disease by incorporating plant growth phases and control measures such as roguing. The model divides the system into two subpopulations: plants (susceptible and infected in both vegetative and generative phases) and vectors (susceptible and infected). Dynamic analysis identifies two equilibrium conditions, namely a disease-free state and an endemic state. The disease-free equilibrium is stable when the basic reproduction number is less than one, whereas the endemic equilibrium becomes stable when the reproduction number exceeds one. Sensitivity analysis using the Partial Rank Correlation Coefficient method shows that the infectivity rate and the roguing rate are the most influential parameters affecting disease transmission. An optimal control framework based on Pontryagin’s Maximum Principle is then applied to determine the most effective roguing and vector control strategies. Simulation results indicate that applying roguing during the vegetative phase markedly reduces the number of infected plants and suppresses disease spread. These findings demonstrate that combining dynamic modeling, sensitivity analysis, and optimal control provides an effective and efficient strategy for managing tungro disease in rice crops.