The rise and fall of ideas’ popularity
本文提出一个基于SIRS流行病学模型的改进模型，通过引入动态恢复率来模拟思想流行度的自然兴衰，解释了社会饱和与兴趣重燃导致的快速波动，适用于营销、技术采纳和政治运动等领域。
In the dynamic landscape of contemporary society, the popularity of ideas, opinions, and interests fluctuates rapidly. Traditional dynamical models in social sciences often fail to capture this inherent volatility, attributing changes to exogenous shocks rather than intrinsic features of the system. This paper introduces a novel, tractable model that simulates the natural rise and fall of ideas’ popularity, offering a more accurate representation of real-world dynamics. Building upon the SIRS (Susceptible, Infectious, Recovered, Susceptible) epidemiological model, we incorporate a feedback mechanism that allows the recovery rate to vary dynamically based on the current state of the system. This modification reflects the cyclical nature of idea adoption and abandonment, driven by social saturation and renewed interest. Our model successfully captures the rapid and recurrent shifts in popularity, providing valuable insights into the mechanisms behind these fluctuations. This approach offers a robust framework for studying the diffusion dynamics of popular ideas, with potential applications across various fields such as marketing, technology adoption, and political movements.