This paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

中文翻译：

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英语教育数学模型的质性

本文提出了一个数学模型，用于检验传统和现代教育计划的影响。我们计算两个复制数。通过使用查韦斯和宋定理，我们证明了发生了反向分叉。此外，我们使用复合矩阵研究了边界平衡点和共存平衡点的存在，局部和全局稳定性以及共存平衡点的全局稳定性。