UMR CNRS 7083 Gulliver, ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France.
Laboratoire des Sciences du Climat et de l'Environnement, CEA Saclay l'Orme des Merisiers, UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay & IPSL, 91191 Gif-sur-Yvette, France.
Chaos. 2021 Oct;31(10):101107. doi: 10.1063/5.0067625.
Forecasting epidemic scenarios has been critical to many decision-makers in imposing various public health interventions. Despite progresses in determining the magnitude and timing of epidemics, epidemic peak time predictions for H1N1 and COVID-19 were inaccurate, with the peaks delayed with respect to predictions. Here, we show that infection and recovery rate fluctuations play a critical role in peak timing. Using a susceptible-infected-recovered model with daily fluctuations on control parameters, we show that infection counts follow a lognormal distribution at the beginning of an epidemic wave, similar to price distributions for financial assets. The epidemic peak time of the stochastic solution exhibits an inverse Gaussian probability distribution, fitting the spread of the epidemic peak times observed across Italian regions. We also show that, for a given basic reproduction number R, the deterministic model anticipates the peak with respect to the most probable and average peak time of the stochastic model. The epidemic peak time distribution allows one for a robust estimation of the epidemic evolution. Considering these results, we believe that the parameters' dynamical fluctuations are paramount to accurately predict the epidemic peak time and should be introduced in epidemiological models.
预测疫情情景对于许多决策者实施各种公共卫生干预措施至关重要。尽管在确定疫情的规模和时间方面取得了进展，但 H1N1 和 COVID-19 的疫情高峰期预测并不准确，高峰期相对于预测有所延迟。在这里，我们表明感染和恢复率的波动在峰值时间上起着关键作用。我们使用具有每日波动的控制参数的易感-感染-恢复模型表明，在疫情波的开始时，感染数量遵循对数正态分布，类似于金融资产的价格分布。随机解的疫情高峰期表现出反高斯概率分布，与意大利各地区观察到的疫情高峰期的传播情况相吻合。我们还表明，对于给定的基本繁殖数 R，确定性模型相对于随机模型的最可能和平均高峰期提前预测高峰期。疫情高峰期分布允许对疫情演变进行稳健估计。考虑到这些结果，我们认为参数的动态波动对于准确预测疫情高峰期至关重要，应引入到流行病学模型中。
