JapanHida_famine_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.

一款基于历史数据标定出生率与死亡率的简易天花易感者-感染者-移除者（Susceptible-Infectious-Removed, SIR）流行病模型，可生成具有极高精准周期性的振荡动力学行为。随机种群数据可使振荡持续维持而非衰减，而针对此类振荡的数据分析，亦能为该组种群数据本身提供研究洞见。尤为关键的是，振荡并非源于周期强迫项或其他可保障振荡产生的外源性机制，而是由该模型自然涌现而出——该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呈现出契合天花传播规律的周期性特征。该模型与配套数据集，亦为疾病传播动力学与模型解轨迹的研究提供了全新观测视角。上述研究结果呼吁学界重新关注结合真实暴发数据集构建的简易流行病模型。