Japan_Hida_spdeaths.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.

一款基于历史数据确定出生率与死亡率的简易天花易感-感染-移除（Susceptible-Infectious-Removed, SIR）流行病模型，可生成具备极高精准周期性的振荡动力学特征。随机种群数据会使振荡持续存续而非衰减，针对此类振荡开展的数据分析，还可反向挖掘出对应种群数据集的相关信息。值得注意的是，振荡是该模型自然涌现的结果，并非依赖于可强制产生振荡的周期强迫项或其他外生机制——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域与不同种群场景，这类自然涌现的振荡仍能呈现出与天花疫情相适配的合理周期性。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。本研究结果表明，结合真实疫情暴发数据集开展相对简易的流行病模型研究，值得学界重新给予关注。