wav_spectra2D_Sweden.dat from Emergence of oscillations in a simple epidemic model with demographic data

A simple susceptible–infectious–removed epidemic model for smallpox, with birth and death rates based on historical data, produces oscillatory dynamics with remarkably accurate periodicity. Stochastic population data cause oscillations to be sustained rather than damped, and data analysis regarding the oscillations provides insights into the same set of population data. Notably, oscillations arise naturally from the model, instead of from a periodic forcing term or other exogenous mechanism that guarantees oscillation: the model has no such mechanism. These emergent natural oscillations display appropriate periodicity for smallpox, even when the model is applied to different locations and populations. The model and datasets, in turn, offer new observations about disease dynamics and solution trajectories. These results call for renewed attention to relatively simple models, in combination with datasets from real outbreaks.一款基于历史人口出生率与死亡率数据构建的简易天花易感-感染-移除（Susceptible-Infectious-Removed, SIR）流行病模型，能够生成具有高度精准周期性的振荡动力学行为。随机人口数据可令振荡持续存续而非逐渐衰减，针对此类振荡的数据分析亦可反哺同一套人口数据集的研究。尤为关键的是，此类振荡是模型自然涌现的结果，而非依赖预设的周期强迫项或其他可保障振荡发生的外生机制——本模型本身并不具备此类机制。即便将该模型应用于不同地区与不同人群，这类自然涌现的振荡仍能呈现出契合天花疫情的周期性特征。该模型与配套数据集，亦可为疾病动力学与模型解轨线的研究提供全新观测视角。本研究结果呼吁学界重新重视结合真实疫情暴发数据集构建的简易流行病模型。