A mathematical analysis of math anxiety dynamics using a classical SAS model: Bridging epidemic theory and pedagogical implications

Students' cognitive function and participation in mathematical problems are adversely affected by mathematics anxiety. This research develops and evaluates a dynamic mathematical model (SAS: Susceptible-Anxious-Susceptible) to investigate the evolution and transmission of math anxiety within students over time. The model divides students into two subgroups based on presence and absence of math anxiety. Using epidemiological modeling concepts, we derive the basic reproduction number R₀, which determines the conditions for persistence (R₀ > 1) or elimination (R₀ < 1) of anxiety. Our analysis proves that the anxiety-free equilibrium is both locally and globally asymptotically stable when R₀ < 1, while the anxiety-prevailing equilibrium is stable when R₀ > 1, with the system undergoing a transcritical bifurcation at R₀ = 1. Sensitivity analysis using Partial Rank Correlation Coefficient (PRCC) reveals that the university entrance rate (π) and social transmission rate (β) positively impact R₀, while recovery rate (α) and exit rate (μ) negatively influence it. Notably, π and μ are identified as the most influential parameters. Numerical simulations demonstrate that the population of students with mathematics anxiety is highly sensitive to changes in β and μ, while remaining relatively stable with fluctuations in π and α. These findings provide a quantitative framework for developing effective interventions, suggesting that reducing social transmission of anxiety and enhancing recovery through supportive mechanisms can significantly curb math anxiety prevalence in educational settings.