Figure 4.nb 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）传染病模型，可产生具备极高精准周期性的振荡动力学行为。随机种群数据会使振荡持续维持而非衰减，针对该振荡的数据分析亦可从同一组种群数据中获取有价值的研究洞见。值得注意的是，振荡是该模型自然涌现的产物，而非依赖于周期强迫项或其他可确保振荡产生的外生机制——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种群场景，这些自然涌现的振荡仍展现出契合天花传播规律的合理周期性。反过来，该模型与配套数据集也为传染病动力学与传播轨迹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传染病模型。