基于SEIR模型的大面积航班延误传播

为研究大面积航班延误在机场间传播的规律,通过构建空中交通网络,并基于SEIR(susceptible-explored-infected-recovered)模型的基本思想,分析大面积航班延误发生时节点状态的变化规律,建立大面积航班延误传播模型,并进一步讨论模型中各个参数变化对航班延误传播的影响。算例分析表明,建立的模型可以用来描述大面积航班延误传播特性。     

基于改进SEIR模型的新冠肺炎疫情分析与预测

针对新型冠状病毒的潜伏期较长，基于每日发布的新冠疫情数据集，在经典SEIR (Susceptible-Exposed-Infected-Recovered)模型的基础上，考虑了隐性传播人群，并且将确诊人群分为两类(一类感染者具有传染能力；一类感染者由于处于隔离期间，其感染能力可忽略不计),构建了基于改进SEIR的新冠肺炎传播动力学模型。以2021年12月15日到2022年1月13日的西安市疫情数据为依据，拟合得到了改进SEIR模型的动力学参数，对西安市COVID-19疫情进行预测和评估。结果表明，基于改进SEIR传染病动力学模型对疫情的理论估计与西安市疫情的实际情况较为符合，数据可视化和医学隔离等措施对抑制疫情大面积传播有重要作用。     

基于广义SEIR模型的新冠肺炎传播机制及干预效果仿真

 新型冠状病毒肺炎（新冠肺炎）已在全球多个国家和地区蔓延,且不同国家和地区新冠肺炎的传播扩散过程和传染预测模式不尽相同。以美国和中国新冠肺炎公开数据为样本,首先应用广义SEIR模型,对疾病传播参数进行估计。其次,确定基本传染数R₀中各参数对疾病的影响,进而基于Anylogic仿真,利用系统动力学模型进行参数敏感性分析,定量表征关键参数对疾病传播的影响。最后,根据分析结果提出针对性的防控干预措施,以中美为例模拟不同防控级别的干预效果。研究发现,广义SEIR模型对中国与美国新冠肺炎传播机制的拟合性较好,保护率、感染率和平均检疫时间对防控疫情影响显著,并可以通过针对性的措施来提高保护率、降低感染率、缩短平均检疫时间。     

基于广义SEIR模型的新冠肺炎传播机制及干预效果仿真

 新型冠状病毒肺炎（新冠肺炎）已在全球多个国家和地区蔓延，且不同国家和地区新冠肺炎的传播扩散过程和传染预测模式不尽相同。以美国和中国新冠肺炎公开数据为样本，首先应用广义SEIR模型，对疾病传播参数进行估计。其次，确定基本传染数R₀中各参数对疾病的影响，进而基于Anylogic仿真，利用系统动力学模型进行参数敏感性分析，定量表征关键参数对疾病传播的影响。最后，根据分析结果提出针对性的防控干预措施，以中美为例模拟不同防控级别的干预效果。研究发现，广义SEIR模型对中国与美国新冠肺炎传播机制的拟合性较好，保护率、感染率和平均检疫时间对防控疫情影响显著，并可以通过针对性的措施来提高保护率、降低感染率、缩短平均检疫时间。     

北京市SARS传播的预测模型研究

本文根据卫生部公布的2003年4月20日到5月15日的数据,对此后疫情的发展进行分析和预测,在SQIR模型的基础上,利用微分方程理论建立相应的更加复杂的房室模型,然后采取了整体拟合的方式,成功预测了北京地区累积的SARS感染者人数和疫情的结束时间,从此后真实的数据来看,预测值与实际情况吻合的较好。同时,根据历史数据,建立了北京市接待海外游客人数的灰色模型,针对SARS期间北京的海外游客人数进行了定量预测和分析。应用瑞利分布拟合SARS对北京旅游业的干扰函数,预测了SARS对北京旅游行业的影响时间,对类似结果的预测与控制具有实际意义。     

SARS流行预测分析

表面上突如其来的SARS本质上却有极规律的内在发展演化机制，遵从初始缓慢增长、加速、减速和稳定终止四个阶段总体道路，自然和社会生活领域众多事件演化都符合这一规律，因而可以运用广义的Logistic生长模型进行描述。基于先期流行的广东SARS感染病例数据，以及尚未结束的北京、全国2003年SARS流行统计数据，借助于最优化分析技术，运用广义的Logistic生长模型对该事件演化特征参量进行了辨识；在此基础上，又借助于广义生长模型的特例——Gompertz函数进行了演化过程的预测，并与其他生长模型结果进行了比较。研究表明，生长模型模拟结果均与实际数据有很好的一致性，可以用来预测事件的发生演化过程，此次SARS事件堪称生长模型的经典实例。     

一类带有非线性传染率的SEIR传染病模型的全局分析

本文建立一类带有非线性传染率的SEIR模型，求出该模型疾病传播的基本再生数和平衡点，并进一步分析它们的关系。     

SARS传染病数学建模及预测预防控制机理研究

首先，利用疾病传播的一般规律及人口守恒统计法则建立了四类人的SARS传染病数学模型，然后运用数学方法对四类人的SARS传染病数学模型进行分析，得出了其生理意义和预防、控制机理。其次，利用人工神经网络理论建立了SARS的预测模型，以北京市的SARS数据为例进行了预测和分析，预测结果显示该模型简单易行，预测精度高。     

考虑防护和隔离的传染病传播建模与分析

基于SEIR模型，引入自我防护和隔离两个仓室，提出一个更加通用的传染病传播模型.通过对模型进行定性分析，计算模型的基本再生数，通过特征值理论和Routh-Hurwitz判据，分析模型的无病平衡点和地方病平衡点的局部渐近稳定性.数值模拟和COVID-19病毒真实数据拟合结果表明，所提出的SEIQRP模型能够有效地描述传染病的动态传播过程.模型中防护率、潜伏期隔离率和感染者隔离率这三个参数对疾病的传播起着非常关键的作用.提高人们加强自我防护意识、重点排查潜伏期患者和对感染者进行隔离治疗可以有效降低传染病的传播.     

SARS传播模型及其对经济的影响

建立了两个关于SARS传播模型并阐述分析了其对经济的影响．通过此模型可获得比较合理的参数。     

两种群相互竞争的具有脉冲接种的SEIR传染病模型

研究了一类两种群相互竞争的具有脉冲接种的SEIR传染病模型,讨论了系统周期解的存在性,并利用Floquet定理证明,在满足一定条件下,周期解是局部渐近稳定的。     

具有潜伏期和双线性发生率的SEIR传染病模型的全局稳定性

建立了一类具有潜伏期和双线性发生率的SEIR传染病模型,得到疾病绝灭与否的阈值R0.证明了当R01时,模型惟一的无病平衡是全局渐近稳定的,疾病最终绝灭;当R01时,模型的地方病平衡点是全局渐近稳定,疾病将持续.     

SEIR-SW,Simulation Model of Influenza Spread Based on the Small World Network

This study modeled the spread of an influenza epidemic in the population of Oran, Algeria. We investigated the mathematical epidemic model, SEIR(Susceptible-Exposed-Infected-Removed), through extensive simulations of the effects of social network on epidemic spread in a Small World(SW) network, to understand how an influenza epidemic spreads through a human population. A combined SEIR-SW model was built, to help understand the dynamics of infectious disease in a community, and to identify the main characteristics of epidemic transmission and its evolution over time. The model was also used to examine social network effects to better understand the topological structure of social contact and the impact of its properties. Experiments were conducted to evaluate the combined SEIR-SW model. Simulation results were analyzed to explore how network evolution influences the spread of desease, and statistical tests were applied to validate the model. The model accurately replicated the dynamic behavior of the real influenza epidemic data, confirming that the susceptible size and topological structure of social networks in a human population significantly influence the spread of infectious diseases. Our model can provide health policy decision makers with a better understanding of epidemic spread,allowing them to implement control measures. It also provides an early warning of the emergence of influenza epidemics.     

一类具有年龄和病程的SEIR传染病模型平衡解的存在性

研究了一类具有年龄和病程的SEIR传染病模型,利用特征线法、零点定理,证明了无病平衡解和地方病平衡解的存在性。     

一类具有垂直传染的SEIR传染病模型的全局稳定性

讨论了一类含潜伏期,染病者有病死且有标准传染率的SEIR传染病模型,给出了修正再生数θ的表达式.当θ≤1则无病平衡点是全局稳定的;当α=0,θ>1则存在唯一的地方病平衡点,且是全局渐近稳定的.     

团体行为对航站楼内流感传播扩散的影响分析

针对团体行为对航站楼内流感传播扩散的影响,运用社会力模型建立基于个体接触的易感者-潜伏者-感染者-移出者(suspicious expoced infected removed,SEIR)改进模型。以某航站楼为例,模拟航站楼内流感的传播扩散过程,定量分析团体行为对楼内流感扩散的影响。实验结果表明,团体行为对进港流程中流感扩散的影响较离港流程大,造成的二者感染者数量增幅分别为47.7%和14.2%。     

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.