Sweden_beta_period_95sig.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.

本研究针对天花构建了一款基于历史数据设定出生率与死亡率的简易易感者-感染者-移除者（susceptible–infectious–removed）流行病模型，该模型可生成具有极高精确周期性的振荡动力学行为。随机种群数据可使振荡持续存续而非衰减，针对振荡开展的数据分析亦能为该套种群数据本身提供研究洞见。值得注意的是，振荡是该模型自发涌现的结果，而非依赖周期性强迫项或其他可确保振荡发生的外生机制——本模型并未内置此类机制。即便将该模型应用于不同地区与不同种群场景，这类自发涌现的自然振荡仍能呈现出契合天花疫情特征的周期性。反过来，该模型及其配套数据集可为疾病动力学与模型解轨迹的研究提供全新观测视角。本研究结果呼吁学界重新关注结合真实疫情暴发数据集构建的简易流行病模型。