Mathematical Modelling of the Impacts of Morning Fatigue on Academic Performance: A Case Study of Federal University Wukari, Taraba State

Abstract

Several authors have researched the phenomenon of sleep deprivation among students. In their studies, we discovered that they did not consider morning fatigue. So, we decided to fill the gap in the literature by using mathematical models to study the impact of morning fatigue. The aim is to develop mathematical modelling for the impact of morning fatigues on the academic performances of the students, a case study of the Federal University Wukari in Taraba State. In this project work, we formulated a mathematical model based on a system of ordinary differential equations to study the impact of morning fatigue on academic performance. We tested the model for existence and uniqueness and discovered that the model exists and that it is unique. The basic reproduction number was computed using the next-generation matrix approach. Questionnaires were distributed to 400 students and the data for this research were collected from the responses of the students. The result of the basic reproduction number shows that morning fatigue can be controlled. Using the Routh-Hurwitz criterion for local stability, the fatigue-free equilibrium (FFE) states of the model were established and proved to be locally asymptotically stable. Sensitivity analysis was then carried out to determine which parameters should be targeted by control intervention strategies of which the result shows that an increase in the acceptance of the control measure rate leads to a reduction in the prevalence of fatigue. Finally, a numerical simulation of the model was carried out and the result shows that Morning fatigue has a great impact on the academic performance of students. This means that there is a need for students to avoid reading till daybreak which in turn brings morning fatigue.