Mathematical Model of Potato virus y disease spread with Optimal control

Potato virus Y (PVY) is an aphid-borne plant virus that causes substantial yield losses in potato production. Control measures of the viral infection are both limited and expensive. A proper use of mixed-cropping strategy can reduce the spread of PVY. In this paper, we formulate and analyze a mathematical model of PVY spread in a mixed-cropping system. Then, we extend the model to an optimal control problem by considering use of mineral oil, insecticide and farmer’s level of field inspection for infected plants. The analytic results show that the basic reproduction number ℜ0, a threshold parameter that decides properties of the dynamics. The disease free equilibrium is stable if ℜ0 < 1 and unstable when ℜ0 > 1. It is found that ℜ0, and hence, the disease dynamics is highly sensitive to the representative parameters of density the non-host plant and its quality in attracting vectors. The model exhibits forward bifurcation at ℜ0 = 1. The study of optimal control problem suggests that mixed-cropping combined with either mineral oil or insecticide is the best to control the disease. Furthermore, simulation results show that mixed-cropping can be used as an alternative strategy and can reduce the need of mineral oil or insecticide.