Abstract
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.
Highlights
Pest control is a worldwide problem in agricultural and forest ecosystem management, where mathematical modeling has an important impact [1, 2, 3]
In [20], Pathak and Maiti develop a mathematical model on pest control with a virus as a control agent
We investigate the stability of the fourth equilibrium point
Summary
Pest control is a worldwide problem in agricultural and forest ecosystem management, where mathematical modeling has an important impact [1, 2, 3]. In [20], Pathak and Maiti develop a mathematical model on pest control with a virus as a control agent They consider the mutual relations going on an ecosystem where a virus influences a pest population nosh on a plant, the final creature unaltered by the virus. Biological pesticides, which are exactly the most ordinary control mechanisms used in integrated pest administration based control outlines They assume the speed of flattering aware is comparative to the number of vulnerable pests in the meadow. A compartmental model is developed with ordinary differential equations to study the force of farming awareness-based optimum interventions for crop pest control (Section 2). We end up the paper with discussion and conclusions (Section 6)
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