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.

受新冠疫情及封控措施影响，用于学术与非学术场景的社交平台使用量显著攀升。在此背景下，学生群体罹患社交媒体成瘾的风险显著升高，全社会亟需针对性的社交媒体成瘾管控手段。社交媒体对学生学业表现的影响兼具正负两面性。现有多数数学模型未考虑个体的过往行为特征，而该特征对于管控社交媒体使用行为至关重要。为此，本研究提出一款分数阶数学模型，用以剖析社交媒体对学业表现的影响。所提模型存在两类平衡点：无社交网络平衡点与地方流行平衡点。经阈值分析可知，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，则存在地方流行平衡点。此外，本研究开展数值模拟以分析种群动态变化，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降低而减弱，这也证实了分数阶模型相较于整数阶模型具有更优异的性能。