On Poor Academic Attitude: A Mathematical Model With Optimal Control
Kwabena Appiagyei Asare, M. A. Boateng, Rhydal Esi Eghan
Source abstract
This study develops and analyzes a compartmental mathematical model to describe the spread of poor academic attitude among senior high school students. The population is divided into five compartments: susceptible ( S ), exposed ( E ), active poor attitude ( A ), partially reformed ( R p ), and fully reformed ( R f ). The poor attitude reproduction number is derived using the next‐generation matrix method. The poor attitude‐free equilibrium is shown to be locally and globally asymptotically stable when , whereas the poor attitude‐endemic equilibrium is stable when . Bifurcation analysis revealed that the system exhibits a forward transcritical bifurcation at . Sensitivity analysis identifies the transmission rate and reform rate as the most influential parameters. An optimal control problem is formulated with two time‐dependent controls representing sensitization programs and counseling interventions. Pontryagin′s maximum principle is applied to derive the necessary optimality conditions. The findings provide a theoretical framework for understanding how poor academic attitudes spread through peer interactions and how interventions can be designed to manage them.
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