# An integrated mathematical model for optimizing integrated pest management strategies against rice tungro virus disease

## TL;DR

This paper develops a mathematical model to find the best strategies for controlling rice tungro virus disease using pest management techniques.

## Contribution

The novelty lies in integrating multiple pest control methods into a mathematical model to optimize rice tungro disease management.

## Key findings

- The non-endemic equilibrium is stable when the basic reproduction number $R_0$ is less than 1.
- Insecticide-induced mortality rate and natural enemy recruitment rate are key parameters in controlling the disease.
- Combining roguing, refugia planting, insecticide use, and natural enemies is the most effective strategy.

## Abstract

One of the main obstacles in rice cultivation is rice tungro disease, caused by the combined infection of Rice Tungro Spherical Virus (RTBV) and Rice Tungro Spherical Virus (RTSV), which are transmitted by green leafhopper vectors (Nephotettix virescens) through a semi-persistent mode of transmission. Control of this disease can be carried out using roguing, insecticide application, and the planting of refugia plants. Each control strategy has its advantages and disadvantages. Thus, analysis is needed to determine the most effective approach. Mathematically, one way to evaluate the effectiveness of these control methods is by developing a mathematical model of the spread of rice tungro disease that considers the characteristics of the viruses, the presence of vector and natural enemies, roguing, refugia planting, and insecticide use. Dynamic and sensitivity analyses, along with optimal control strategies, were conducted based on the model. The results indicate that the non-endemic equilibrium point is locally asymptotically stable if \documentclass[12pt]{minimal}
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\begin{document}$$R_0<1$$\end{document}, with key influencing parameters being the insecticide-induced mortality rate \documentclass[12pt]{minimal}
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\begin{document}$$(\mu _2)$$\end{document} and the natural enemy recruitment rate \documentclass[12pt]{minimal}
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\begin{document}$$(\xi )$$\end{document}. Numerical simulations suggest that combining roguing, refugia planting, and insecticide application while utilizing natural enemies is the most efficient control strategy.