Impact of social media on academics: a fractional order mathematical model

Due to the COVID pandemic and lockdown, usage of social platforms increased for academic and non-academic purposes. As a result, students are at significant risk of developing social media addiction, so techniques to control social media addiction throughout society are required. There are several positive and negative ways in which social media affects the academic performance of a student. Most of the mathematical models exclude the past of an individual, which is critical for controlling social media consumption. Hence, this study offers a fractional-order mathematical model to analyze the impact of social media on academics. There are two equilibrium points for the proposed model: social web-free and endemic equilibrium. Based on an evaluation of the threshold value, the social web-free equilibrium point is globally asymptotically stable whenever the threshold value is less than one. Endemic equilibrium points exist when the threshold value is greater than 1. Additionally, numerical simulations have been performed to examine changes in population dynamics and validate analytical outcomes. In summary, the findings of this research reveal that social media addiction decreases as the order of the derivative decreases, demonstrating the high efficiency of a fractional-order model over an integer-order model.

受新冠疫情（COVID pandemic）与封控政策影响，人们出于学术与非学术目的对社交平台的使用频次显著攀升。这使得学生群体罹患社交媒体成瘾症的风险大幅提升，因此全社会亟需有效的社交媒体成瘾防控手段。社交媒体对学生学业表现的影响兼具正负两面性。现有多数数学模型均未考虑个体的既往行为特征，而这一因素对管控社交媒体使用行为至关重要。有鉴于此，本研究构建了一个分数阶（fractional-order）数学模型，用于分析社交媒体对学业表现的影响。所提出的模型存在两类平衡点：无社交网络平衡点与地方病平衡点。通过对阈值的分析可知，当阈值小于1时，无社交网络平衡点全局渐近稳定；当阈值大于1时，则存在地方病平衡点。此外，本研究开展了数值模拟实验，以探究种群动态变化规律并验证解析结果的正确性。综上，本研究结果表明，社交媒体成瘾程度随导数阶数的降低而减弱，这也印证了分数阶模型相较于整数阶模型具备更高的应用效能。