  We develop a mathematical model, based on a system of ordinary differential
equations, to the upshot of farming alertness in crop pest administration,
bearing in mind plant biomass, pest, and level of control. Main qualitative
analysis of the proposed mathematical model, akin to both pest-free and
coexistence equilibrium points and stability analysis, is investigated. We show
that all solutions of the model are positive and bounded with initial
conditions in a certain significant set. The local stability of pest-free and
coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we
prove that when a threshold value is less than one, then the pest-free
equilibrium is locally asymptotically stable. To get optimum interventions for
crop pests, that is, to decrease the number of pests in the crop field, we
apply optimal control theory and find the corresponding optimal controls. We
establish existence of optimal controls and characterize them using
Pontryagin's minimum principle. Finally, we make use of numerical simulations
to illustrate the theoretical analysis of the proposed model, with and without
control measures.
