Impact of roguing and insecticide spraying on mosaic disease in Jatropha curcas

Jatropha curcas plant is greatly impaired by mosaic disease, caused by the viruses (Begomovirus), transmitted by whiteflies, which act as the vector. Roguing (i.e. removal of infected plant) and spraying of insecticides are common methods, employed in order to get rid of the disease. In this article, a mathematical model has been developed to study the mosaic disease dynamics while considering preventive measures of roguing and insecticide spraying. Sufficient conditions for the stability of equilibrium points of the system are among the results obtained through qualitative analysis. We obtain the basic reproduction number R0 and show that the disease free system is stable for R0 < 1 and unstable for R0 > 1. The region of stability of equilibrium points in different parameter spaces have also been analysed. Hopf bifurcation at the endemic steady state has been studied subsequently, as well. Finally, by formulating an optimal control problem, optimal application of roguing and spraying techniques has been determined, keeping in mind the cost effective control of the mosaic disease. Pontryagin minimum principle has been utilized to solve the optimal control problem. Numerical simulations illustrate the validity of the analytical outcomes.