Japan_Hida_cont_R0_3.05_mu_16.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，可生成具备极高周期准确性的振荡动力学行为。随机人口数据会使振荡持续存续而非衰减，针对该振荡的数据分析可加深对同一组人口数据的认知。值得注意的是，振荡是模型自然涌现的结果，而非依赖于可保障振荡产生的周期强迫项或其他外生驱动机制——该模型本身并未内置此类机制。即便将该模型应用于不同地区与不同人群，其涌现出的自然振荡仍能匹配天花的合理周期性特征。该模型及其配套数据集则为疾病动力学与模型解轨线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疫情暴发数据集的简易流行病模型。