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.     

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.     

Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19

The main research question concerned the identification of changes in the COVID-19 epidemiological situation using fuzzy clustering methods. This research used cross-sectional time series data obtained from the European Centre for Disease Prevention and Control. The identification of country types in terms of epidemiological risk was carried out using the fuzzy c-means clustering method. We also used the entropy index to measure the degree of fuzziness in the classification and evaluate the uncertainty of epidemiological states. The proposed approach allowed us to identify countries’ epidemic states. Moreover, it also made it possible to determine the time of transition from one state to another, as well as to observe fluctuations during changes of state. Three COVID-19 epidemic states were identified in Europe, i.e., stabilisation, destabilisation, and expansion. The methodology is universal and can also be useful for other countries, as well as the research results being important for governments, politicians and other policy-makers working to mitigate the effects of the COVID-19 pandemic.     

Evolving Network Analysis of S&P500 Components: COVID-19 Influence of Cross-Correlation Network Structure

The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The analysis is performed on a representative set of USA companies—the S&P500 components. Four different network structures are constructed (strong, weak, typically, and significantly connected networks), and the rank entropy, cycle entropy, averaged clustering coefficient, and transitivity evolution are established and discussed. Based on the mentioned structural parameters, four different stages have been distinguished during the COVID-19-induced crisis. The proposed network properties and their applicability to a crisis-distinguishing problem are discussed. Moreover, the optimal time window problem is analysed.     

A simple statistical physics model for the epidemic with incubation period

Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model are directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia.     

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.     

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.     

Immunity in the ABM-DSGE Framework for Preventing and Controlling Epidemics—Validation of Results

The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020.     

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.     

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.     

基于手机大数据的中国人口迁徙模式及疫情影响研究

新型冠状病毒感染的肺炎(COVID-19)可通过人员接触与流动迅速传播,因此研究人类迁徙和出行模式的变化对疫情防控至关重要.本文基于手机运营商2020年春运及疫情暴发前后连续两个月的全国地级市之间的人口流动数据,运用时序网络分析方法构建人口流动网络拓扑结构指标,并通过引入地理衰减因子提出Spatial-Louvain社团检测算法,研究平时、春运、疫情防控隔离和生产复工四阶段的人口迁徙模式的时空演化规律.研究发现:受各地疫情防控措施影响,武汉封城后全国城市间人口流量急剧下降,并持续至2月中旬.疫情期间人口流动网络结构呈现四阶段的时空演化模式;本文提出的空间网络社团检测算法比传统Louvain算法平均模块度值提高了14%;中国城市分布以经济交互和地理位置为基础,形成了以核心城市为中心,向周边辐射的城市群格局;疫情因素仅能在短暂时间内改变部分城市的城市群归属,当该因素消失或减弱后,城市群能迅速恢复原有格局.     

To Freeze or Not to Freeze? Epidemic Prevention and Control in the DSGE Model Using an Agent-Based Epidemic Component

The ongoing COVID-19 pandemic has raised numerous questions concerning the shape and range of state interventions the goals of which are to reduce the number of infections and deaths. The lockdowns, which have become the most popular response worldwide, are assessed as being an outdated and economically inefficient way to fight the disease. However, in the absence of efficient cures and vaccines, there is a lack of viable alternatives. In this paper we assess the economic consequences of the epidemic prevention and control schemes that were introduced in order to respond to the COVID-19 pandemic. The analyses report the results of epidemic simulations that were obtained using the agent-based modelling methods under the different response schemes and their use in order to provide conditional forecasts of the standard economic variables. The forecasts were obtained using the dynamic stochastic general equilibrium model (DSGE) with the labour market component.     

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.     

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading.Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response.Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed.Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.     

Inferring epidemiological parameters from phylogenetic information for the HIV-1 epidemic among MSM

The HIV-1 epidemic in Europe is primarily sustained by a dynamic topology of sexual interactions among MSM who have individual immune systems and behavior. This epidemiological process shapes the phylogeny of the virus population. Both fields of epidemic modeling and phylogenetics have a long history, however it remains difficult to use phylogenetic data to infer epidemiological parameters such as the structure of the sexual network and the per-act infectiousness. This is because phylogenetic data is necessarily incomplete and ambiguous. Here we show that the cluster-size distribution indeed contains information about epidemiological parameters using detailed numberical experiments. We simulate the HIV epidemic among MSM many times using the Monte Carlo method with all parameter values and their ranges taken from literature. For each simulation and the corresponding set of parameter values we calculate the likelihood of reproducing an observed cluster-size distribution. The result is an estimated likelihood distribution of all parameters from the phylogenetic data, in particular the structure of the sexual network, the per-act infectiousness, and the risk behavior reduction upon diagnosis. These likelihood distributions encode the knowledge provided by the observed cluster-size distrbution, which we quantify using information theory. Our work suggests that the growing body of genetic data of patients can be exploited to understand the underlying epidemiological process.     

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.     

Breakpoint Analysis for the COVID-19 Pandemic and Its Effect on the Stock Markets

In this research, statistical models are formulated to study the effect of the health crisis arising from COVID-19 in global markets. Breakpoints in the price series of stock indexes are considered. Such indexes are used as an approximation of the stock markets in different countries, taking into account that they are indicative of these markets because of their composition. The main results obtained in this investigation highlight that countries with better institutional and economic conditions are less affected by the pandemic. In addition, the effect of the health index in the models is associated with their non-significant parameters. This is due to that the health index used in the modeling would not determine the different capacities of the countries analyzed to respond efficiently to the pandemic effect. Therefore, the contagion is the preponderant factor when analyzing the structural breakdown that occurred in the world economy.     

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.     

Fluctuations in mean-field self-organized criticality

We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.     

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.