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Title: Farming awareness based optimum interventions for crop pest control
Author: Abraha, Teklebirhan
Al Basir, Fahad
Obsu, Legesse Lemecha
Torres, Delfim F. M.
Keywords: Mathematical modeling of ecological systems
Holling type-II functional response
Optimal control
Pontryagin's minimum principle
Numerical simulations
Issue Date: 2021
Publisher: AIMS Press
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.
Peer review: yes
DOI: 10.3934/mbe.2021272
ISSN: 1551-0018
Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

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