Investigating the efficacy of insecticides in controlling the spread of tungro virus in rice plants: a mathematical modeling approach

Abstract

The rise in population and robust economic expansion have led to a heightened need for food, energy, and water resources. In such circumstances, food security becomes an indispensable necessity for human survival. However, while striving to uphold food security, we frequently encounter the challenge of crop failure due to pest infestations, particularly green planthoppers. These infestations can lead to a reduction in both the quality and quantity of crop yields, and they also have the potential to disseminate the destructive tungro disease virus, further compromising crop health. Utilizing a mathematical modeling approach, a complex five-dimensional nonlinear system of differential equations is formulated to depict the intricate dynamics between rice plants and planthopper pests in the transmission of the tungro virus. This approach is adopted to investigate the effectiveness of control measures in curtailing the transmission of the tungro virus via planthopper pests. The model includes two control measures, which are the application of insecticides and the removal of infected plants, aimed at mitigating the virus’s transmission. We conducted stability analysis and derived the basic reproduction number formula (R₀) to examine the qualitative behavior of the model. Furthermore, the stability of the interior equilibrium was analyzed using the Monte Carlo method, allowing for a robust evaluation of system dynamics under varying parameter uncertainties. As the basic reproduction number is influenced by the two aforementioned controls and endemic conditions emerge when this number exceeds one, we performed a sensitivity analysis to assess the impact of these control measures on reducing the R₀ value and infected compartment. Subsequently, we conducted an optimal control investigation to assess the efficacy of implementing these two control measures by developing various scenarios. Our results indicate that implementing both insecticide application and the removal of infected plants together is considerably more effective than implementing these control measures separately.