Description of the hyperparameters of the models.

Modeling time series has been a particularly challenging aspect due to the need for constant adjustments in a rapidly changing environment, data uncertainty, dependencies between variables, volatile fluctuations, and the need to identify ideal hyperparameters. The present study presents a Framework capable of making projections from time series related to cases and deaths by COVID-19 in the Amazonian state of Pará, in Brazil. For the first time, deep learning models such as TCN, TRANSFORMER, TFT, N-BEATS, and N-HiTS were assessed for this purpose. The ARIMA statistical model was also used in post-processing for residual adjustment and short-term smoothing of the generated forecasts. The Framework generates probabilistic forecasts, with multivariate support, considering the following variables: daily cases per day of the first symptom, cases published daily, the occurrence of deaths, deaths published daily, and percentage of daily vaccination. The generated predictions are statistically evaluated by determining the best model for 7-day moving average projections using evaluating metrics such as MSE, RMSE, MAPE, sMAPE, r2, Coefficient of Variation, and residual analysis. As a result, the generated projections showed an average error of 5.4% for Cases Publication, 8.0% for Cases Symptoms, 11.12% for Deaths Publication, and 4.6% for Deaths Occurrence, with the N-HiTS and N-BEATS models obtaining better results. In general terms, the use of deep learning models to predict cases and deaths from COVID-19 has proven to be a valuable practice for analyzing the spread of the virus, which allows health managers to better understand and respond to this kind of pandemic outbreak.

时间序列建模始终是一项极具挑战性的任务，这是因为其需要在快速变化的环境中持续调整，同时面临数据不确定性、变量间依赖关系、剧烈波动等问题，且需确定最优超参数。本研究提出了一种可针对巴西帕拉州（亚马逊区域）新冠病毒（COVID-19）确诊病例与死亡病例相关时间序列进行预测的框架。本研究首次针对该预测任务评估了时间卷积网络（Temporal Convolutional Network, TCN）、Transformer、时间融合Transformer（Temporal Fusion Transformer, TFT）、N-BEATS以及N-HiTS等深度学习模型。此外，本研究还采用自回归积分滑动平均模型（AutoRegressive Integrated Moving Average, ARIMA）对生成的预测结果开展残差修正与短期平滑的后处理操作。该框架支持多变量概率预测，所纳入的预测变量包括：首发症状出现当日新增确诊病例、每日公布确诊病例数、死亡病例发生数、每日公布死亡病例数以及每日疫苗接种率。针对生成的预测结果，本研究通过选取适用于7日移动平均预测的最优模型，并采用均方误差（Mean Squared Error, MSE）、均方根误差（Root Mean Squared Error, RMSE）、平均绝对百分比误差（Mean Absolute Percentage Error, MAPE）、对称平均绝对百分比误差（Symmetric Mean Absolute Percentage Error, sMAPE）、决定系数（Coefficient of Determination, r²）、变异系数（Coefficient of Variation）以及残差分析等评估指标开展统计性能评估。实验结果表明，所生成的预测模型在每日公布确诊病例预测上的平均误差为5.4%，首发症状确诊病例预测上的平均误差为8.0%，每日公布死亡病例预测上的平均误差为11.12%，死亡病例发生数预测上的平均误差为4.6%，其中N-HiTS与N-BEATS模型取得了最优的预测效果。总体而言，采用深度学习模型预测新冠病毒感染的确诊病例与死亡病例数，已被证实为分析病毒传播态势的有效手段，可助力卫生管理者更好地认知并应对此类新冠疫情暴发事件。