JapanHida_alphatot_vs_delta.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.

一款针对天花的简易易感-感染-移除（Susceptible-Infectious-Removed, SIR）流行病模型，其出生率与死亡率参数基于历史数据构建，可生成具备极高精确周期性的振荡动力学特性。随机种群数据会使振荡持续存续而非衰减，针对此类振荡的数据分析则可从同一套种群数据中挖掘出富有价值的研究见解。值得注意的是，振荡是该模型自然涌现的结果，而非依赖于周期强迫项或其他可保证振荡发生的外源性机制——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种群场景，此类自然涌现的振荡仍能展现出与天花疫情匹配的适宜周期性。该模型与配套数据集反过来也为疾病动力学与模型解轨迹的研究提供了全新的观测视角。本研究结果呼吁学界重新关注结合真实疫情暴发数据集的简易流行病模型。