A model for the control of the mosaic virus disease in Jatropha curcas plantations

Jatropha curcas is a plant with a variety of potential and ecological applications. The seeds of this plant contain a high amount of oil that can be used to obtain a better quality of alternative fuel biodiesel. But the Jatropha plants are seriously affected by the mosaic virus (Begomovirus) that is carried by infected vector whiteflies. It severely affects the Jatropha plants by causing leaf damage, yellowing leaves and sap drainage. In particular, it attacks its fruits considerably reducing the production of seeds. In this paper, we formulate a model for the dynamics of this disease and its possible control via insecticide spraying. We identify the parameters that are most important for vector-borne disease control. Pontryagin minimum principle is employed to minimize the cost of spraying. The findings indicate that the optimal spraying policy does not require insecticide application during the first ten days of the epidemic outbreak and that instead the spraying must be continued for the following three months to eradicate the disease.