针对新型冠状病毒肺炎隔离措施的动力学评估

针对2019年底暴发的新型冠状病毒肺炎,中国政府采取了一系列严格的防控措施,其中起关键作用的是普通民众的居家隔离与密切接触者的追踪隔离.建立新型冠状病毒传播与控制动力学模型,定量评估这两项措施的有效性.利用下一代矩阵法计算了基本再生数和有效再生数,给出了有效再生数的极限范围,分析了模型的动力学特征.以安徽省为例,利用MCMC(Markov chain Monte Carlo)参数估计方法进行数值拟合,得到安徽省新型冠状病毒传播模型的基本再生数为0.402 1(95%CI:0.397 3～-0.407 0),有效再生数的极限范围为[0,0.048 745].随着隔离措施的有效实施,安徽省的有效再生数迅速下降到0.05以下并趋于0.048 735,疫情及时得到了控制.如果没有采取这些隔离措施,基本再生数为2.103 0(95%CI:2.080 4～2.125 5),疾病将会在人群中持续传播.通过参数敏感性分析,发现加强密切跟踪隔离力度,即增加染病者的隔离速率系数,能够有效降低基本再生数;加强居家隔离力度,即增加易感者的隔离速率系数与减少易感者的隔离解除速率系数,有助于降低有效再生数极限范围...     

广东省新型冠状病毒肺炎疫情流行趋势的初步预测

目的:通过计算和预测广东省新型冠状病毒肺炎的基本再生数,研究广东省疫情的流行趋势为其防控和相关政策支持提供依据.方法:依据广东省卫健委截至2020年2月8日的官方数据,构建传染病动力学SIR模型,计算现阶段新型冠状病毒肺炎基本再生数,并结合指数平滑法对未来基本再生数的变化加以预测.结果:疫情初期,广东省新冠肺炎基本再生数为2.48,并呈现波动下降的趋势.疫情将在2月下旬迎来拐点,3月下旬疫情将走向消亡.结论:新型冠状病毒肺炎在广东省的传播致病能力逐渐降低,目前阶段疫情正在逐步得到控制,采用及时有效的防控措施能够加快疫情的扑灭.     

具有垂直传播及感染期的乙肝传播模型

研究具有垂直传播和感染期的乙肝病毒感染模型,考虑了发生率函数为非线性时模型的性质,以乙肝的平均感染期作为时滞,利用Routh-Hurwite判别法得到了系统的疾病消失的平衡点局部渐近稳定的条件,找到了基本再生数R0,通过构造Lyapunov函数,证明了地方病平衡点的全局渐近稳定性.     

数据驱动下新冠肺炎基本再生数的计算方法

2019年突如其来的新冠肺炎疫情给我国经济社会发展和人民生活带来严重影响.如何科学合理计算新冠肺炎传播的基本再生数对疫情的控制尤为重要.目前,已有的计算新冠肺炎基本再生数方法大都基于数据辨识模型参数进而算出其值.给出一种利用数据结合模型直接计算新冠肺炎传播基本再生数的新方法.利用该方法及峰值数据可以计算基于SIR模型、SEIR模型及SEIAR模型全国、湖北及广东新冠肺炎传播的基本再生数.该方法能反映基本再生数和新冠肺炎传播相关数据的直接关系.     

基于早期监测病例的埃博拉病毒传播风险评估

基本再生数是传染病动力学中反映传染病传播潜力最重要的参数,对基本再生数的估算是传染病传播风险评估工作的核心内容。该文针对2013年末发生于西非的埃博拉疫情的风险评估问题,提出了改进的最小二乘法作为疫情参数拟合方法,并对该次埃博拉疫情中3个重灾区国家(几内亚、塞拉利昂、利比里亚)境内的早期疫情数据进行了拟合,估算出了疫情的基本再生数,拟合结果与实际数据吻合得较好;通过分析几内亚境内疫情的早期数据,改进前人研究中所采用的基于均匀混合假设的易感者S(susceptible)、携带者E(exposed)、传染者I(infectious)以及移出者R(removed)(SEIR)模型,提出了多次疫情假说模型,较好地解释了几内亚境内疫情数据波动现象。该文提出的拟合标准和传染病动力学建模思路对于确定病毒传播性质、评估防疫措施效果、预测传播趋势以及遏制未来可能出现的疫情有着重要意义。     

SF网络上的SIR模型

为促进复杂网络和传染病动力学在传染病研究中的应用,分析了SF(无标度)网络的拓扑结构对传染病传播的影响,深入讨论了SIR(易感者一染病者一康复者)模型的传播规律并得到基本再生数Ro.为了进一步控制疾病的传播,采取目标免疫策略,得到了有限的基本再生数Rto.     

具捕杀效应的SEI狂犬病模型的空间动力学分析

为讨论针对性的捕杀对狂犬病传播的影响,研究了一类具捕杀效应的易感者-潜伏期感染者-已经感染者(SEI)狂犬病模型.通过相应的特征值问题,引入基本再生数,并利用上下解方法建立了平衡点的稳定性.结果表明:有针对性的捕杀对狂犬病的控制和预防起着重要的作用.     

年龄结构SIR流行病传播数学模型渐近分析

研究一类具有年龄结构SIR流行病传播数学模型动力学性质，得到疾病绝灭和持续生存的阈值条件——基本再生数．当基本再生数小于或等于l时，仅存在无病平衡点，且在其小于l的情况下，无病平衡点全局渐近稳定，疾病将逐渐消除；当基本再生数大于l时，存在不稳定的无病平衡点和惟一的局部渐近稳定的地方病平衡点，疾病将持续存在．本模型的基本再生数小于H．R．Thieme等人所得到的基本再生数，表明预防接种、宣传教育等积极措施对疾病消除和控制的重要作用。     

一类具有双线性发生率的SEIR流行病传播数学模型

利用Lasalle不变集原理探讨系统的渐近性态,研究了一类具有双线性发生率且染病期传染的SEIR流行病传播数学模型的动力学性质.得到了疾病绝灭与持续的阈值-基本再生数,证明了无病平衡点的全局渐近稳定性和地方病平衡点的全局渐近稳定性,揭示了潜伏期传染的影响.     

一类潜伏期传染且具有病毒变异的传染病模型

针对COVID-19的特点，建立了一类潜伏期与染病期均传染且具有病毒变异的SEI₁I₂QR传染病模型。首先，得到了模型的基本再生数与平衡点，利用Routh-Hurwitz判据、Lyapunov函数及LaSalle不变集原理证明了各类平衡点的全局稳定性。其次，选取印度的COVID-19累计病例数，对模型的参数进行了估计，并对疫情发展趋势进行了数值模拟。最后，对部分参数进行了敏感性分析，结果表明，易感者与潜伏者的有效接触率、易感者与病毒变异前的染病者的有效接触率和基本再生数之间存在强相关性关系，降低易感者与染病者的有效接触率可以有效控制疫情的进一步蔓延。     

The role of evolution in the emergence of infectious diseases

It is unclear when, where and how novel pathogens such as human immunodeficiency virus (HIV), monkeypox and severe acute respiratory syndrome (SARS) will cross the barriers that separate their natural reservoirs from human populations and ignite the epidemic spread of novel infectious diseases. New pathogens are believed to emerge from animal reservoirs when ecological changes increase the pathogen's opportunities to enter the human population and to generate subsequent human-to-human transmission. Effective human-to-human transmission requires that the pathogen's basic reproductive number, R(0), should exceed one, where R(0) is the average number of secondary infections arising from one infected individual in a completely susceptible population. However, an increase in R(0), even when insufficient to generate an epidemic, nonetheless increases the number of subsequently infected individuals. Here we show that, as a consequence of this, the probability of pathogen evolution to R(0) > 1 and subsequent disease emergence can increase markedly.     

Control dynamics of severe acute respiratory syndrome transmission

Severe acute respiratory syndrome (SARS) is a serious disease with many puzzling features. We present a simple, dynamic model to assess the epidemic potential of SARS and the effectiveness of control measures. With this model, we analysed the SARS epidemic data in Beijing.The data fitting gives the basic case reproduction number of 2.16 leading to the outbreak, and the variation of the effective reproduction number reflecting the control effect. Noticeably, our study shows that the response time and the strength of control measures have significant effects on the scale of the outbreak and the lasting time of the epidemic.     

Exploring the epidemic transmission network of SARS in-out flow in mainland China

The changing spatiotemporal patterns of the individual susceptible-infected-symptomatic-treated-recovered epidemic process and the interactions of information/material flows between regions,along with the 2002-2003 Severe Acute Respiratory Syndrome(SARS) epidemiological investigation data in mainland China,including three typical locations of individuals(working unit/home address,onset location and reporting unit),are used to define the in-out flow of the SARS epidemic spread.Moreover,the input/output transmission networks of the SARS epidemic are built according to the definition of in-out flow.The spatiotemporal distribution of the SARS in-out flow,spatial distribution and temporal change of node characteristic parameters,and the structural characteristics of the SARS transmission networks are comprehensively and systematically explored.The results show that(1) Beijing and Guangdong had the highest risk of self-spread and output cases,and prevention/control measures directed toward self-spread cases in Beijing should have focused on the later period of the SARS epidemic;(2) the SARS transmission networks in mainland China had significant clustering characteristics,with two clustering areas of output cases centered in Beijing and Guangdong;(3) Guangdong was the original source of the SARS epidemic,and while the infected cases of most other provinces occurred mainly during the early period,there was no significant spread to the surrounding provinces;in contrast,although the input/output interactions between Beijing and the other provinces countrywide began during the mid-late epidemic period,SARS in Beijing showed a significant capacity for spatial spreading;(4) Guangdong had a significant range of spatial spreading throughout the entire epidemic period,while Beijing and its surrounding provinces formed a separate,significant range of high-risk spreading during the mid-late period;especially in late period,the influence range of Beijing’s neighboring provinces,such as Hebei,was even slightly larger than that of Beijing;and(5) the input network had a low-intensity spread capacity and middle-level influence range,while the output network had an extensive high-intensity spread capacity and influence range that covered almost the entire country,and this spread and influence indicated that significant clustering characteristics increased gradually.This analysis of the epidemic in-out flow and its corresponding transmission network helps reveal the potential spatiotemporal characteristics and evolvement mechanism of the SARS epidemic and provides more effective theoretical support for prevention and control measures.     

SARS epidemical forecast research in mathematical model

The SLJR model, simplified from the SEIJR model, is adopted to analyze the important parameters of the model of SARS epidemic such as the transmission rate, basic reproductive number. And some important parameters are obtained such as the transmission rate by applying this model to analyzing the situation in Hong Kong, Singapore and Canada at the outbreak of SARS. Then forecast of the transmission of SARS is drawn out here by the adjustment of parameters (such as quarantined rate) in the model. It is obvious that inflexion lies on the crunode of the graph, which indicates the big difference in transmission characteristics between the epidemic under control and not under control.This model can also be used in the comparison of the control effectiveness among different regions. The results from this model match well with the actual data in Hong Kong, Singapore and Canada and as a by-product, the index of the effectiveness of control in the later period can be acquired. It offers some quantitative indexes, which may help the further research in epidemic diseases.     

SARS传播模型的探讨

首先以传统的Logistic模型和SEIR模型分析了SARS传播的一般规律,并以北京地区2003年4月20日到6月23日有关SARS数据为参考资料,对北京地区SARS疫情高峰期和最终感染人数作出估计,由此得到SARS传播服从Logistic模型和SEIR模型,其次,在此基础上分析了两物种间的疾病传播规律,建立了两物种间疾病传播的SEIR模型。     

传染病模型中的马尔萨斯常数(英文)

建立了一个随机传染病模型,此模型中传染个体可能具有多样化的疾病传播模式.利用最近一个关于算子谱半径连续性的结果,证明了汉基本再生数R0>1时,在一个疾病大爆发的初期,染病人口的数量呈指数增长,而染病人数的本质增长率就是基本再生核的马尔萨斯常数.     

The outbreak pattern of the SARS cases in Asia

The severe acute respiratory syndrome (SARS) caused tremendous damage to many Asia countries, especially China. The transmission process and outbreak pattern of SARS is still not well understood. This study aims to find a simple model to describe the outbreak pattern of SARS cases by using SARS case data commonly released by governments. The outbreak pattern of cumulative SARS cases is expected to be a logistic type because the infection will be slowed down due to the increasing control effort by people and/or due to depletion of susceptible individuals. The increase rate of SARS cases is expected to decrease with the cumulative SARS cases, as described by the traditional logistical model, which is widely used in population dynamic studies. The instantaneous rate of increases were significantly and negatively correlated with the cumulative SARS cases in mainland of China (including Beijing, Hebei, Tianjin, Shanxi,the Autonomous Region of Inner Mongolia) and Singapore. The basic reproduction number R0 in Asia ranged from 2.0 to 5.6 (except for Taiwan, China). The R0 of Hebei and Tianjin were much higher than that of Singapore, Hongkong, Beijing, Shanxi, Inner Mongolia, indicating SARS virus might have originated differently or new mutations occurred during transmission. We demonstrated that the outbreaks of SARS in many regions of Asia were wall described by the logistic model, and the control measures implemented by governments are effective. The maximum instantaneous rate of increase, basic reproductive number, and maximum cumulative SARS cases were also calculated by using the logistic model.     

Spatial epidemiology of networked metapopulation: an overview

An emerging disease is one infectious epidemic caused by a newly transmissible pathogen, which has either appeared for the first time or already existed in human populations, having the capacity to increase rapidly in incidence as well as geographic range. Adapting to human immune system, emerging diseases may trigger large-scale pandemic spreading, such as the transnational spreading of SARS, the global outbreak of A（H1N1）, and the recent potential invasion of avian influenza A（H7N9）. To study the dynamics mediating the transmission of emerging dis- eases, spatial epidemiology of networked metapopulation provides a valuable modeling framework, which takes spatially distributed factors into consideration. This review elaborates the latest progresses on the spatial metapopula- tion dynamics, discusses empirical and theoretical findings that verify the validity of networked metapopulations, and the sketches application in evaluating the effectiveness of disease intervention strategies as well.     

受疾病意识影响的SIR传染病模型分析

为控制传染病的传播, 该文建立了一个受疾病意识影响的传染病模型. 利用下一代矩阵法计算了基本再生数R0. 求解了两类平衡点, 并用Lyapunov函数的代数方法证明了当R0〈1时, 无病平衡点全局渐近稳定; 当R0〉1时, 地方病平衡点全局渐近稳定, 无病平衡点不稳定. 此外, 对R0进行灵敏度分析, 并考虑意识的增强对R0相关参数灵敏度的影响. 结果表明提高个体意识率可以降低疾病基本再生数, 从而有效控制疾病传播. 最后通过数值模拟验证了理论结果, 为分析传染病传播提供了一定的理论依据.     

SARS预测模型及分析

充分考虑对SARS流行有较大影响的多个因素,建立了改进的微分方程模型.特别在模型中加入了反映政府控制措施的多个参数,并在SARS流行的控制前后等不同阶段发挥控制作用,使得模型的计算结果和实际数据吻合较好,有效地预测了SARS的流行趋势,并给出了控制措施及建议.