Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations
Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations
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DOI：
10.1140/epjp/s13360-020-00383-y
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发表时间：
2020-04-15
影响因子：
3.4
通讯作者：
Paolozzi, Antonio
中科院分区：
文献类型：
--
作者：
Ciufolini, Ignazio;Paolozzi, Antonio
本文根据官方数据，并使用四参数高斯误差函数作为累积分布函数，对意大利新冠肺炎大流行阳性病例数随时间的演变进行了数学预测。我们分析了中国和意大利的现有数据。中国的新冠肺炎累计诊断阳性病例数随时间的演变非常接近误差函数类型的分布，即正态、高斯分布的积分。然后，我们使用这样的函数，通过对迄今可用的官方数据进行多次拟合，研究意大利阳性病例数量随时间的潜在演变。然后，我们找到了意大利每日阳性病例数量峰值出现的日期的统计预测，对应于拟合的弹性，即其二阶导数的符号变化(即从加速到减速的变化)，以及达到这种每日病例数量的大幅衰减的日期。我们还分析了中国和意大利对累积死亡人数的预测，得到了一致的结果。然后，我们进行了150次蒙特卡罗模拟，以更准确地预测上述高峰的日期以及每日阳性病例和死亡人数大幅下降的日期。虽然使用了官方数据，但这些预测是以启发式方法获得的，因为它们基于统计方法，既没有考虑一些相关问题(例如每天鼻咽拭子的数量、医疗、社会距离、病毒学和流行病学)或污染扩散的模型。
In this paper are presented mathematical predictions on the evolution in time of the number of positive cases in Italy of the COVID-19 pandemic based on official data and on the use of a function of the type of a Gauss error function, with four parameters, as a cumulative distribution function. We have analyzed the available data for China and Italy. The evolution in time of the number of cumulative diagnosed positive cases of COVID-19 in China very well approximates a distribution of the type of the error function, that is, the integral of a normal, Gaussian distribution. We have then used such a function to study the potential evolution in time of the number of positive cases in Italy by performing a number of fits of the official data so far available. We then found a statistical prediction for the day in which the peak of the number of daily positive cases in Italy occurs, corresponding to the flex of the fit, that is, to the change in sign of its second derivative (i.e., the change from acceleration to deceleration), as well as of the day in which a substantial attenuation of such number of daily cases is reached. We have also analyzed the predictions of the cumulative number of fatalities in both China and Italy, obtaining consistent results. We have then performed 150 Monte Carlo simulations to have a more robust prediction of the day of the above-mentioned peak and of the day of the substantial decrease in the number of daily positive cases and fatalities. Although official data have been used, those predictions are obtained with a heuristic approach since they are based on a statistical approach and do not take into account either a number of relevant issues (such as number of daily nasopharyngeal swabs, medical, social distancing, virological and epidemiological) or models of contamination diffusion.