论文标题
COVID-19大流行的随机隔室模型必须具有时间相关的不确定性
Stochastic compartmental models of COVID-19 pandemic must have temporally correlated uncertainties
论文作者
论文摘要
隔间模型是流行病学中重要的定量工具，使我们能够预测传染病的过程。但是，模型参数（例如疾病的感染率）被不确定性带来了，这激发了随机隔室模型的发展和使用。在这里，我们首先表明，将不确定性视为白噪声的常见随机模型从根本上存在缺陷，因为它错误地暗示着更大的参数不确定性将导致消除该疾病。然后，我们基于对每个人的联系的合理假设进行了对不确定性的原则建模。使用中央限制定理和DOOB定理在高斯马尔可夫过程中，我们证明相关的Ornstein-Uhlenbeck过程是对感染率中不确定性进行建模的合适工具。我们使用COVID-19大流行的隔室模型以及来自Johns Hopkins University Covid-19数据库的美国数据来证明我们的结果。特别是，我们表明，白噪声随机模型系统地低估了Covid-19的Omicron变体的严重性，而Ornstein-Uhlenbeck模型正确地预测了该变体的过程。此外，使用性传播疾病的SIS模型，我们为受感染个体的渐近分布提供了精确的封闭式解决方案。该分析结果表明，白噪声模型低估了由于不现实的噪声引起的过渡而低估了大流行的严重程度。我们的结果强烈支持在传染病隔室模型中建模不确定性的时间相关性的需求。
Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modeling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob's theorem on Gaussian Markov processes, we prove that the correlated Ornstein-Uhlenbeck process is the appropriate tool for modeling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the Ornstein-Uhlenbeck model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the asymptotic distribution of infected individuals. This analytic result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modeling of uncertainties in compartmental models of infectious disease.
