论文标题
蒙特卡洛方法使用gompertz功能建模19号死亡和感染
A Monte Carlo approach to model COVID-19 deaths and infections using Gompertz functions
论文作者
论文摘要
这项研究描述了通过Monte Carlo方法的Covid-19死亡和感染的动力学。据世卫组织称，分析包括来自美国，巴西，墨西哥，英国，印度和俄罗斯的死亡数据，该数据构成了截至2020年8月7日，死亡人数最多/已确认的案件的四个国家。通过映射$χ^2 $值，将Gompertz函数拟合到每天平均确认死亡的数据。模型参数的不确定性，方差和协方差是通过传播计算的。美国和印度每天平均死亡的合适功能具有上升趋势，前者的增长率更高，不确定性较大。对于墨西哥，英国和俄罗斯来说，拟合与斜率下降的模式一致。对于巴西来说，我们发现了一个微妙的趋势，但存在很大的不确定性。与第二个数据相比，美国，英国和印度的数据显示出第一个峰值，增长率更高，这表明了卫生措施的非药物干预措施的好处，而社会距离则使曲线变平。对于美国而言，第三个高峰似乎很合理，很可能与最近的放松政策有关。两个高度重叠的Gompertz函数具有相似的增长率，这表明了大流行蔓延的两步过程。该模型预测的95％CI（$ \ times 10^3 $）为8月31日，2020年8月31日的CI是160至220、110至130、130、59至62、59至62、46.6至47.3、54至54至54至54至63和63和63和63和63和63和63和16.0，分别为美国，美国，巴西，墨西哥，英国，印度和俄罗斯，分别为美国我们对感染患病率的估计与美国和巴西进行的血清学研究的一些初步报告是合理的。该方法代表了一个有效的框架，以根据实际数据估算感染曲线的线形和相关参数的不确定性。
This study describes the dynamics of COVID-19 deaths and infections via a Monte Carlo approach. The analyses include death's data from USA, Brazil, Mexico, UK, India and Russia, which comprise the four countries with the highest number of deaths/confirmed cases, as of Aug 07, 2020, according to the WHO. The Gompertz functions were fitted to the data of weekly averaged confirmed deaths per day by mapping the $χ^2$ values. The uncertainties, variances and covariances of the model parameters were calculated by propagation. The fitted functions for the average deaths per day for USA and India have an upward trend, with the former having a higher growth rate and quite huge uncertainties. For Mexico, UK and Russia, the fits are consistent with a slope down pattern. For Brazil we found a subtle trend down, but with significant uncertainties. The USA, UK and India data shown a first peak with a higher growth rate when compared to the second one, demonstrating the benefits of non-pharmaceutical interventions of sanitary measures and social distance flattening the curve. For USA, a third peak seems quite plausible, most likely related with the recent relaxation policies. Brazil's data are satisfactorily described by two highly overlapped Gompertz functions with similar growth rates, suggesting a two-steps process for the pandemic spreading. The 95% CI for the total number of deaths ($\times 10^3$) predicted by the model for Aug 31, 2020 are 160 to 220, 110 to 130, 59 to 62, 46.6 to 47.3, 54 to 63 and 16.0 to 16.7 for USA, Brazil, Mexico, UK, India and Russia, respectively. Our estimates for the prevalences of infections are in reasonable agreement with some preliminary reports from serological studies carried out in USA and Brazil. The method represents an effective framework to estimate the line-shape of the infection curves and the uncertainties of the relevant parameters based on the actual data.
