论文标题

建模COVID-19-我是一个动态的先生(D),并应用于印度数据

Modelling COVID-19 -- I A dynamic SIR(D) with application to Indian data

论文作者

Bhattacharjee, Madhuchhanda, Bose, Arup

论文摘要

我们使用自适应动态三个隔室(带有四个状态)SIR(d)模型提出了一个流行病学模型。我们的方法类似于精神上的非参数曲线拟合,并自动适应了关键的外部因素,例如干预措施,同时保留了标准SIR(d)模型的简约性质。通过在所选的滞后期间最小化感染,回收和死亡人数的正方形的骨料残差总和来获得模型参数的初始动态时间估计。然后,应用了几何更平滑的方法来获得最终的估计时间序列。这些估计值用于获得该大流行的关键特征的动态时间鲁棒估计,即“繁殖数”。我们说明了2020年3月14日至8月31日的印度共同数据数据的方法。36个州和联合领土的时间序列数据图显示了流行病的预后存在区域间变化。这也是由基础参数的估计值(包括36个区域的繁殖数字)所估算出来的。因此,在国家汇总数据上的动态或其他方式的先生(D)模型不适合稳健的局部预测。该模型的估计时间序列使我们能够每天,每周以及长期预测,包括预测频段的构建。我们在实际数据和模型之间在区域层面预测数据之间获得了出色的一致性。我们对当前繁殖数量的估计估计在三个地区(安得拉邦,马哈拉施特拉邦和北方邦),在13个地区的1.5至2之间。这些区域中的每个区域都经历了一个个体轨迹,该轨迹通常涉及冲击的初始阶段,然后涉及相对稳定的繁殖数。

We propose an epidemiological model using an adaptive dynamic three compartment (with four states) SIR(D) model. Our approach is similar to non-parametric curve fitting in spirit and automatically adapts to key external factors, such as interventions, while retaining the parsimonious nature of the standard SIR(D) model. Initial dynamic temporal estimates of the model parameters are obtained by minimising the aggregate residual sum of squares across the number of infections, recoveries, and fatalities, over a chosen lag period. Then a geometric smoother is applied to obtain the final time series of estimates. These estimates are used to obtain dynamic temporal robust estimates of the key feature of this pandemic, namely the "reproduction number". We illustrate our method on the Indian COVID-19 data for the period March 14 - August 31, 2020. The time series data plots of the 36 states and union territories shows a clear presence of inter-regional variation in the prognosis of the epidemic. This is also bourne out by the estimates of the underlying parameters, including the reproduction numbers for the 36 regions. Due to this, an SIR(D) model, dynamic or otherwise, on the national aggregate data is not suited for robust local predictions. The time series of estimates of the model enables us to carry out daily, weekly and also long term predictions, including construction of predictive bands. We obtain an excellent agreement between the actual data and the model predicted data at the regional level. Our estimates of the current reproduction number turn out to be more than 2 in three regions (Andhra Pradesh, Maharashtra and Uttar Pradesh) and between 1.5 and 2 in 13 regions. Each of these regions have experienced an individual trajectory, which typically involves initial phase of shock(s) followed by a relatively steady lower level of the reproduction number.

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