article · Scientific Reports
Mathematics anxiety presents a widespread challenge in higher education institutions worldwide. A Caputo fractional order mathematical model incorporating optimal control strategies analyses the dynamics of this condition among students. The mathematical evaluation confirms the non-negativity and boundedness of the system solutions, establishing both anxiety-free and anxiety-endemic equilibrium points. Local stability for both equilibria and conditions for backward bifurcation when the effective reproduction number is below one are determined, alongside the global asymptotic stability of the endemic equilibrium. Further optimal control analysis and numerical simulations examine the memory effect inherent in fractional derivatives, the general system behaviour, and the influence of specific parameters. The results establish that introducing protection measures and targeted treatment for affected students plays a fundamental role in reducing and potentially eradicating mathematics anxiety across higher education communities.
Mathematics anxiety creates substantial educational barriers for university students globally. By applying epidemiological modelling principles to an academic stressor, this work offers a rigorous framework for understanding how anxiety behaves in student communities. It clarifies how structured interventions, such as protection and treatment programmes, can be deployed systematically by educational institutions to suppress anxiety transmission and improve learning outcomes.
This early-stage theoretical research could eventually inform decision-support software or planning frameworks for university administrators, guidance counsellors, and student welfare departments. By identifying the mathematical impact of interventions, the model could aid the design of institutional support programmes. However, because the abstract focuses entirely on theoretical formulation and numerical simulations, any transition into applied institutional tools or software products remains at an early concept stage.
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Anxiety towards mathematics is the most common problem throughout nations in the world. In this study, we have mainly formulated and analyzed a Caputo fractional order mathematical model with optimal control strategies on higher institution students' anxiety towards mathematics. The non-negativity and boundedness of the fractional order dynamical system solutions have been analysed. Both the anxiety-free and anxiety endemic equilibrium points of the Caputo fractional order model are found, and the local stability analysis of the anxiety-free and anxiety endemic equilibrium points are examined. Conditions for Caputo fractional order model backward bifurcation are analyzed whenever the anxiety effective reproduction number is less than one. We have shown the global asymptotic stability of the endemic equilibrium point. Moreover, we have carried out the optimal control strategy analysis of the fractional order model. Eventually, we have established the analytical results through numerical simulations to investigate the memory effect of the fractional order derivative approach, the behavior of the model solutions and the effects of parameters on the students anxiety towards mathematics in the community. Protection and treatment of anxiety infectious students have fundamental roles to minimize and possibly to eradicate mathematics anxiety from the higher institutions.
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DOI: 10.1038/s41598-023-33961-y
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