Mathematical modeling and optimal control of a vector-borne rice yellow mottle virus disease

Rice yellow mottle virus causes the most important rice disease in Africa. It was first identified in 1966 in Kenya, and later it has been detected in most African countries where rice is grown. Different approaches have been carried out so far to explore the dynamics and to curtail this viral disease. Mathematical models provide a useful tool in this regard and can be used to set the appropriate controlling strategies. In this paper, we formulate a new deterministic mathematical model for the dynamics of vector-borne rice yellow mottle infection. We include control measures, namely: roguing, treatment and the use of insecticide in the model. The dynamical behaviors of such controls in the reduction of the widespread of yellow mottle virus disease in a rice field were also studied. The basic properties of the model were stated and proved accordingly. We derived the equilibrium points of the model and computed the reproduction number. The stability of disease-free equilibrium point using the Routh-Hurwitz criterion and Castillo-Chavez function was carried out separately which were found to be stable. We also determined the optimal control via Pontryagin maximum principle. For numerical simulations, we solve the optimality system using a forward-backward sweep strategy implemented in MATLAB and the results show that the use of a combination of roguing on the symptomatic infected plants and the use of insecticides on susceptible and infected grasshoppers, together with treatment of symptomatic infected plants is the most excellent technique for controlling the spread of the disease.