Department of Civil and Environmental Engineering, Imperial College London, London, SW7 2AZ, UK.
Sci Rep. 2023 Oct 13;13(1):17335. doi: 10.1038/s41598-023-44527-3.
We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.
我们通过展示如何将几种已记录的建筑物内空气传播疾病爆发模型视为结合量子守恒和隔室流行病学模型的方程组的特例，研究了这些模型的基本假设和适用范围的限制。我们对该系统进行了分析，深入了解了其在大时间尺度上的行为。然后，我们研究了室内爆发的特征时间尺度，展示了空间的稀释率以及与疾病相关的量子生成率、潜伏期和清除率如何用于预测爆发随时间的演变，也可用于预测其他室内空气传播爆发模型的相对性能。将该模型与更常用的模型进行了比较，在该模型中，假设环境中传染性气溶胶的浓度符合准稳态，因此无量纲量子浓度等于传染性分数。结果表明，这里提出的模型以指数方式逼近该极限，其间隔由潜伏期和清除率定义。这可用于预测病例偏离准稳态条件的最大程度。
