Piecewise Modeling the Accumulated Daily Growth of COVID-19 Deaths: The Case of the State of São Paulo,Brazil

The pandemic scenery caused by the new coronavirus, called SARS-CoV-2, increased interest in statistical models capable of projecting the evolution of the number of cases (and associated deaths) due to COVID-19 in countries, states and/or cities. This interest is mainly due to the fact that the projections may help the government agencies in making decisions in relation to procedures of prevention of the disease. Since the growth of the number of cases (and deaths) of COVID-19, in general, has presented a heterogeneous evolution over time, it is important that the modeling procedure is capable of identifying periods with different growth rates and proposing an adequate model for each period. Here, we present a modeling procedure based on the fit of a piecewise growth model for the cumulative number of deaths. We opt to focus on the modeling of the cumulative number of deaths because, other than for the number of cases, these values do not depend on the number of diagnostic tests performed. In the proposed approach, the model is updated in the course of the pandemic, and whenever a “new” period of the pandemic is identified, it creates a new sub-dataset composed of the cumulative number of deaths registered from the change point and a new growth model is chosen for that period. Three growth models were fitted for each period: exponential, logistic and Gompertz models. The best model for the cumulative number of deaths recorded is the one with the smallest mean square error and the smallest Akaike information criterion (AIC) and Bayesian information criterion (BIC) values. This approach is illustrated in a case study, in which we model the number of deaths due to COVID-19 recorded in the State of São Paulo, Brazil. The results have shown that the fit of a piecewise model is very effective for explaining the different periods of the pandemic evolution.     

耦合不同年龄层接触模式的新冠肺炎传播模型

搜集广东省自1月23日到2月16日期间944例新冠肺炎样本信息.对确诊人群进行年龄特征分析,将人群分为儿童组(0—5岁)、青少年组(6—19岁)、中青年组(20—64岁)、老年组(65岁及以上),耦合不同年龄层的接触模式,建立离散年龄结构新冠肺炎模型,得出模型的基本再生数及最终规模.通过蒙特卡罗数值算法(MCMC)辨识模型的参数、拟合累计病例数、计算消亡时间、感染峰值及到达时间等有关生物量.研究发现中青年人群感染人数最多;相比于居家模式,社区模式下中青年人群感染峰值上升41%,峰值推迟一周到达.通过分析不同年龄层的最终规模在对应年龄层的占比,发现老年人的易感性较高,青少年的易感性相对较低.在居家模式下,若各年龄层患者能及时就诊,住院峰值将进一步减少,但住院高峰将提前一周到达.此模型可揭示个体接触行为对新冠肺炎的传播的影响,定量评价居家隔离措施的有效性.     

新型冠状病毒肺炎疫情确诊病例的统计分析及自回归建模

基于安徽省卫生健康委员会截至2020年2月19日公布的800余例新型冠状病毒肺炎病例信息,根据病例中公布的接触史构建确诊患者间的有向传播关系,发现源传染患者中男性居多,被传染患者中女性居多.从病例信息中可知,安徽省新型冠状病毒肺炎疫情的发展从初期的具有武汉居住或接触史的输入病例转入后期本地传播为主的小范围社区传播,且严格的防控隔离措施有效切断了社区内的进一步传播.源传染患者与被传染患者的确诊时间间隔可用G分布拟合,确诊时间间隔的中位数为2 d,平均值为2.67 d.基于有向传播关系的统计特点,构建安徽省疫情发展后期的自回归传播模型,模型仿真结果与疫情发展数据符合.对除湖北省的全国确诊病例数据同样采取自回归建模与仿真,结果仍与疫情发展数据符合.这一发现为控制疫情在湖北省以外区域的防控提供了参考:通过严格的防控措施和隔离措施,疫情在湖北省之外的传播具有很大的黏滞性,多为家庭程度的密切接触传播,且能有效控制新型冠状病毒肺炎在当地的传播深度,有效控制了疫情的蔓延.     

Understanding the Impact of Walkability,Population Density,and Population Size on COVID-19 Spread: A Pilot Study of the Early Contagion in the United States

The novel coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global event that has been challenging governments, health systems, and communities worldwide. Available data from the first months indicated varying patterns of the spread of COVID-19 within American cities, when the spread was faster in high-density and walkable cities such as New York than in low-density and car-oriented cities such as Los Angeles. Subsequent containment efforts, underlying population characteristics, variants, and other factors likely affected the spread significantly. However, this work investigates the hypothesis that urban configuration and associated spatial use patterns directly impact how the disease spreads and infects a population. It follows work that has shown how the spatial configuration of urban spaces impacts the social behavior of people moving through those spaces. It addresses the first 60 days of contagion (before containment measures were widely adopted and had time to affect spread) in 93 urban counties in the United States, considering population size, population density, walkability, here evaluated through walkscore, an indicator that measures the density of amenities, and, therefore, opportunities for population mixing, and the number of confirmed cases and deaths. Our findings indicate correlations between walkability, population density, and COVID-19 spreading patterns but no clear correlation between population size and the number of cases or deaths per 100 k habitants. Although virus spread beyond these initial cases may provide additional data for analysis, this study is an initial step in understanding the relationship between COVID-19 and urban configuration.     

Determining the minimum embedding dimension of nonlinear time series based on prediction method

Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension. Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.     

2013年长江下游降水低频分量延伸期预报的扩展复数自回归模型

用长江下游降水低频分量和全球850 hPa低频经向风主成分,建立扩展复数自回归模型(ECAR),对2013年1—12月长江下游降水低频分量进行延伸期逐日变化预报试验.结果表明,20—30 d时间尺度的长江下游低频降水预测时效可达43 d左右,能较好地预测与暴雨过程对应的低频分量的非线性增长过程,预报能力明显优于自回归模型(AR).这种通过构造主要低频序列组成的扩展复数矩阵(ECM)进行复数自回归(CAR)建模的ECAR方法,也为展现气候系统内部分量之间相互作用的动力学过程提供了崭新的描述.基于全球环流主要20—30 d振荡型的发展和演变,对于提前27 d预报长江下游地区2013年10月上旬后期大暴雨过程很有帮助,其中南半球热带外环流20—30 d振荡是影响2013年夏秋季长江下游地区延伸期强降水变化的一个主要因子.     

Research on Risk Contagion among Financial Submarkets in China Based on Complex Networks

As the COVID-19 outbreak has an impact on the global economy, there will be interest in how China’s financial markets function during the outbreak. To investigate the path of risk contagion in China’s financial sub-markets before and after the COVID-19 outbreak, we divided the 2016–2021 period into two phases. Based on the time of the COVID-19 outbreak, we divided the new stage of economic development into pre-epidemic and post-epidemic stages and employed the DCC-GARCH model to investigate the dynamic correlation coefficients among the financial sub-markets in China. Furthermore, we employed complex network theory and the minimum tree model to describe the risk contagion path between two-stage Chinese financial submarkets. Finally, we provided pertinent recommendations for investors and policymakers and conducted a brief discussion based on the findings of the research.     

新型冠状病毒肺炎早期时空传播特征分析

通过最新公布的流行病学数据估计了易感者-感染者模型参数,结合百度迁徙数据和公开新闻报道,刻画了疫情前期武汉市人口流动特征,并代入提出的支持人口流动特征的时域差分方程模型进行动力学模拟,得到一些推论:1)未受干预时传染率在一般环境下以95%的置信度位于区间[0.2068,0.2073],拟合优度达到0.999;对应地,基本传染数R0位于区间[2.5510,2.6555];极限环境个案推演的传染率极值为0.2862,相应的R0极值为3.1465;2)百度迁徙规模指数与铁路发送旅客人数的Pearson相关系数达到0.9108,有理由作为人口流动的有效估计;3)提出的模型可有效推演疫情蔓延至外省乃至全国的日期,其中41.38%的预测误差≤1 d,79.31%的预测误差≤3 d,96.55%预测误差≤5 d,总体平均误差约为2.14 d.     

Complexity of COVID-19 Dynamics

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.     

Comparative Analysis of Different Univariate Forecasting Methods in Modelling and Predicting the Romanian Unemployment Rate for the Period 2021–2022

Unemployment has risen as the economy has shrunk. The coronavirus crisis has affected many sectors in Romania, some companies diminishing or even ceasing their activity. Making forecasts of the unemployment rate has a fundamental impact and importance on future social policy strategies. The aim of the paper is to comparatively analyze the forecast performances of different univariate time series methods with the purpose of providing future predictions of unemployment rate. In order to do that, several forecasting models (seasonal model autoregressive integrated moving average (SARIMA), self-exciting threshold autoregressive (SETAR), Holt–Winters, ETS (error, trend, seasonal), and NNAR (neural network autoregression)) have been applied, and their forecast performances have been evaluated on both the in-sample data covering the period January 2000–December 2017 used for the model identification and estimation and the out-of-sample data covering the last three years, 2018–2020. The forecast of unemployment rate relies on the next two years, 2021–2022. Based on the in-sample forecast assessment of different methods, the forecast measures root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) suggested that the multiplicative Holt–Winters model outperforms the other models. For the out-of-sample forecasting performance of models, RMSE and MAE values revealed that the NNAR model has better forecasting performance, while according to MAPE, the SARIMA model registers higher forecast accuracy. The empirical results of the Diebold–Mariano test at one forecast horizon for out-of-sample methods revealed differences in the forecasting performance between SARIMA and NNAR, of which the best model of modeling and forecasting unemployment rate was considered to be the NNAR model.     

Ordinal Time Series Forecasting of the Air Quality Index

This research models and forecasts daily AQI (air quality index) levels in 16 cities/counties of Taiwan, examines their AQI level forecast performance via a rolling window approach over a one-year validation period, including multi-level forecast classification, and measures the forecast accuracy rates. We employ statistical modeling and machine learning with three weather covariates of daily accumulated precipitation, temperature, and wind direction and also include seasonal dummy variables. The study utilizes four models to forecast air quality levels: (1) an autoregressive model with exogenous variables and GARCH (generalized autoregressive conditional heteroskedasticity) errors; (2) an autoregressive multinomial logistic regression; (3) multi-class classification by support vector machine (SVM); (4) neural network autoregression with exogenous variable (NNARX). These models relate to lag-1 AQI values and the previous day’s weather covariates (precipitation and temperature), while wind direction serves as an hour-lag effect based on the idea of nowcasting. The results demonstrate that autoregressive multinomial logistic regression and the SVM method are the best choices for AQI-level predictions regarding the high average and low variation accuracy rates.     

新型冠状病毒肺炎的流行病学参数与模型

一种新型冠状病毒感染导致的肺炎自2019年12月至今在我国以及200多个国家和地区传播.本文旨在介绍近期关于新型冠状病毒肺炎的几个重要流行病学参数的研究进展和估计方法,包括基本再生数、潜伏期和代间隔,同时还介绍两个动力学模型及其结果.这些参数刻画了新型冠状病毒肺炎的传播特点,影响控制策略的制定和有效性.简要来说,新型冠状病毒肺炎的基本再生数R0的中位数为2.6,潜伏期均值约为5.0 d,代间隔均值约为5.5 d.这表明新型冠状病毒肺炎传播速度快.诸如对确诊病人的隔离治疗、对疑似病例的隔离、对密切接触者的追踪、对疾病信息的宣传和采取自我防护等防控措施能有效降低疾病暴发的风险和规模.     

A Bayesian Approach to Predict Football Matches with Changed Home Advantage in Spectator-Free Matches after the COVID-19 Break

Since the coronavirus disease 2019 (COVID-19) pandemic, most professional sports events have been held without spectators. It is generally believed that home teams deprived of enthusiastic support from their home fans experience reduced benefits of playing on their home fields, thus becoming less likely to win. This study attempts to confirm if this belief is true in four major European football leagues through statistical analysis. This study proposes a Bayesian hierarchical Poisson model to estimate parameters reflecting the home advantage and the change in such advantage. These parameters are used to improve the performance of machine-learning-based prediction models for football matches played after the COVID-19 break. The study describes the statistical analysis on the impact of the COVID-19 pandemic on football match results in terms of the expected score and goal difference. It also shows that estimated parameters from the proposed model reflect the changed home advantage. Finally, the study verifies that these parameters, when included as additional features, enhance the performance of various football match prediction models. The home advantage in European football matches has changed because of the behind-closed-doors policy implemented due to the COVID-19 pandemic. Using parameters reflecting the pandemic’s impact, it is possible to predict more precise results of spectator-free matches after the COVID-19 break.     

A Multi-Criteria Decision Support and Application to the Evaluation of the Fourth Wave of COVID-19 Pandemic

The COVID-19 pandemic caused important health and societal damage across the world in 2020–2022. Its study represents a tremendous challenge for the scientific community. The correct evaluation and analysis of the situation can lead to the elaboration of the most efficient strategies and policies to control and mitigate its propagation. The paper proposes a Multi-Criteria Decision Support (MCDS) based on the combination of three methods: the Group Analytic Hierarchy Process (GAHP), which is a subjective group weighting method; Extended Entropy Weighting Method (EEWM), which is an objective weighting method; and the COmplex PRoportional ASsessment (COPRAS), which is a multi-criteria method. The COPRAS uses the combined weights calculated by the GAHP and EEWM. The sum normalization (SN) is considered for COPRAS and EEWM. An extended entropy is proposed in EEWM. The MCDS is implemented for the development of a complex COVID-19 indicator called COVIND, which includes several countries’ COVID-19 indicators, over a fourth COVID-19 wave, for a group of European countries. Based on these indicators, a ranking of the countries is obtained. An analysis of the obtained rankings is realized by the variation of two parameters: a parameter that describes the combination of weights obtained with EEWM and GAHP and the parameter of extended entropy function. A correlation analysis between the new indicator and the general country indicators is performed. The MCDS provides policy makers with a decision support able to synthesize the available information on the fourth wave of the COVID-19 pandemic.     

Prediction of epidemics dynamics on networks with partial differential equations: A case study for COVID-19 in China

Since December 2019, the COVID-19 epidemic has repeatedly hit countries around the world due to various factors such as trade, national policies and the natural environment. To closely monitor the emergence of new COVID-19 clusters and ensure high prediction accuracy, we develop a new prediction framework for studying the spread of epidemic on networks based on partial differential equations (PDEs), which captures epidemic diffusion along the edges of a network driven by population flow data. In this paper, we focus on the effect of the population movement on the spread of COVID-19 in several cities from different geographic regions in China for describing the transmission characteristics of COVID-19. Experiment results show that the PDE model obtains relatively good prediction results compared with several typical mathematical models. Furthermore, we study the effectiveness of intervention measures, such as traffic lockdowns and social distancing, which provides a new approach for quantifying the effectiveness of the government policies toward controlling COVID-19 via the adaptive parameters of the model. To our knowledge, this work is the first attempt to apply the PDE model on networks with Baidu Migration Data for COVID-19 prediction.     

Optimal control strategy for COVID-19 concerning both life and economy based on deep reinforcement learning

At present, the global COVID-19 is still severe. More and more countries have experienced second or even third outbreaks. The epidemic is far from over until the vaccine is successfully developed and put on the market on a large scale. Inappropriate epidemic control strategies may bring catastrophic consequences. It is essential to maximize the epidemic restraining and to mitigate economic damage. However, the study on the optimal control strategy concerning both sides is rare, and no optimal model has been built. In this paper, the Susceptible-Infectious-Hospitalized-Recovered (SIHR) compartment model is expanded to simulate the epidemic's spread concerning isolation rate. An economic model affected by epidemic isolation measures is established. The effective reproduction number and the eigenvalues at the equilibrium point are introduced as the indicators of controllability and stability of the model and verified the effectiveness of the SIHR model. Based on the Deep Q Network (DQN), one of the deep reinforcement learning (RL) methods, the blocking policy is studied to maximize the economic output under the premise of controlling the number of infections in different stages. The epidemic control strategies given by deep RL under different learning strategies are compared for different reward coefficients. The study demonstrates that optimal policies may differ in various countries depending on disease spread and anti-economic risk ability. The results show that the more economical strategy, the less economic loss in the short term, which can save economically fragile countries from economic crises. In the second or third outbreak stage, the earlier the government adopts the control strategy, the smaller the economic loss. We recommend the method of deep RL to specify a policy which can control the epidemic while making quarantine economically viable.     

An Interpretation Architecture for Deep Learning Models with the Application of COVID-19 Diagnosis

The Coronavirus disease 2019 (COVID-19) has become one of the threats to the world. Computed tomography (CT) is an informative tool for the diagnosis of COVID-19 patients. Many deep learning approaches on CT images have been proposed and brought promising performance. However, due to the high complexity and non-transparency of deep models, the explanation of the diagnosis process is challenging, making it hard to evaluate whether such approaches are reliable. In this paper, we propose a visual interpretation architecture for the explanation of the deep learning models and apply the architecture in COVID-19 diagnosis. Our architecture designs a comprehensive interpretation about the deep model from different perspectives, including the training trends, diagnostic performance, learned features, feature extractors, the hidden layers, the support regions for diagnostic decision, and etc. With the interpretation architecture, researchers can make a comparison and explanation about the classification performance, gain insight into what the deep model learned from images, and obtain the supports for diagnostic decisions. Our deep model achieves the diagnostic result of 94.75%, 93.22%, 96.69%, 97.27%, and 91.88% in the criteria of accuracy, sensitivity, specificity, positive predictive value, and negative predictive value, which are 8.30%, 4.32%, 13.33%, 10.25%, and 6.19% higher than that of the compared traditional methods. The visualized features in 2-D and 3-D spaces provide the reasons for the superiority of our deep model. Our interpretation architecture would allow researchers to understand more about how and why deep models work, and can be used as interpretation solutions for any deep learning models based on convolutional neural network. It can also help deep learning methods to take a step forward in the clinical COVID-19 diagnosis field.     

Boosting COVID-19 Image Classification Using MobileNetV3 and Aquila Optimizer Algorithm

Currently, the world is still facing a COVID-19 (coronavirus disease 2019) classified as a highly infectious disease due to its rapid spreading. The shortage of X-ray machines may lead to critical situations and delay the diagnosis results, increasing the number of deaths. Therefore, the exploitation of deep learning (DL) and optimization algorithms can be advantageous in early diagnosis and COVID-19 detection. In this paper, we propose a framework for COVID-19 images classification using hybridization of DL and swarm-based algorithms. The MobileNetV3 is used as a backbone feature extraction to learn and extract relevant image representations as a DL model. As a swarm-based algorithm, the Aquila Optimizer (Aqu) is used as a feature selector to reduce the dimensionality of the image representations and improve the classification accuracy using only the most essential selected features. To validate the proposed framework, two datasets with X-ray and CT COVID-19 images are used. The obtained results from the experiments show a good performance of the proposed framework in terms of classification accuracy and dimensionality reduction during the feature extraction and selection phases. The Aqu feature selection algorithm achieves accuracy better than other methods in terms of performance metrics.     

Modeling the COVID-19 epidemic and awareness diffusion on multiplex networks

The coronavirus disease 2019(COVID-19)has been widely spread around the world,and the control and behavior dynamics are still one of the important research directions in the world.Based on the characteristics of COVID-19’s spread,a coupled disease-awareness model on multiplex networks is proposed in this paper to study and simulate the interaction between the spreading behavior of COVID-19 and related information.In the layer of epidemic spreading,the nodes can be divided into five categories,where the topology of the network represents the physical contact relationship of the population.The topological structure of the upper network shows the information interaction among the nodes,which can be divided into aware and unaware states.Awareness will make people play a positive role in preventing the epidemic diffusion,influencing the spread of the disease.Based on the above model,we have established the state transition equation,through the microscopic Markov chain approach(MMCA),and proposed the propagation threshold calculation method under the epidemic model.Furthermore,MMCA iteration and the Monte Carlo method are simulated on the static network and dynamic network,respectively.The current results will be beneficial to the study of COVID-19,and propose a more rational and effective model for future research on epidemics.     

Data-Driven Model Reduction for Stochastic Burgers Equations

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model.