Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application

One of the main obstacles in rice cultivation is tungro disease, caused by Rice Tungro Spherical Virus (RTSV) and Rice Tungro Bacilliform Virus (RTBV), which are transmitted by green leafhopper vectors ( Nephotettix virescens ). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if R 0 < 1 . At the same time, the parameters that greatly influence the spread of this disease are parameters μ , μ 2 , and ϕ for local sensitivity analysis and α , a , β , b , ϕ , and μ 2 for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease.