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。     

前馈型神经网络在SARS疫情分析中的应用

前馈神经网络在非线性系统的建模及控制中有着广阔的应用前景,其中用差商近似代替导数的Powell法是一种高效、快速的学习方法本文采用三层前馈神经网络结构对SARS在中国的传播与流行趋势及控制策略建立了网络模型.并利用Powell学习方法,针对北京、山西的疫情进行了计算仿真.结果表明,该网络模型算法收敛速度较快,预测精度很高.     

前馈型神经网络在SARS疫情分析中的应用

前馈神经网络在非线性系统的建模及控制中有着广阔的应用前景,其中用差商近似代替导数的Powell法是一种高效、快速的学习方法本文采用三层前馈神经网络结构对SARS在中国的传播与流行趋势及控制策略建立了网络模型.并利用Powell学习方法,针对北京、山西的疫情进行了计算仿真.结果表明,该网络模型算法收敛速度较快,预测精度很高.     

基于Logistic模型的企业竞争互动分析

基于生态学理论,构建了企业竞争互动的Logistic模型,解释模型平衡点及稳定条件在企业竞争中的现实意义,并通过数值仿真来模拟企业竞争互动的动态演化过程。仿真结果表明:企业竞争互动的动态演化与企业的竞争力、固有增长率、初值大小以及市场容量等密切相关。给出在不同稳定条件下企业竞争互动策略的建议。     

SARS传播预测的数学模型

SARS的传播是2003年全国大学生数学建模竞赛的赛题之一，这是一个完全开放、国内外一直在探索的问题。同学们提交的论文中建立了许多模型，对SARS的传播和预测进行研究。本文对竞赛情况和需要探讨的问题进行了简单的总结。     

基于Logistic回归的移动通信业客户细分模型

在移动通信业务运营中,目前所采用的传统细分方法通过ARPU值来为客户分类,这种方法存在一些问题和不足。本文引入Logistic回归方法,结合移动通信客户的实际特点与需求,构建具有创新性的客户细分模型,为运营商的客户方案提供客观准确的参考依据。本文所构建的移动通信客户细分方法,能够在把握客户的具体特征的前提下对其进行清晰地分类,有利于运营商实施保持客户的策略。     

考虑自愈的SARS的传播模型

本文根据对SARS传播的分析,把人群分为5类:易感类、潜伏期类、患病未被发现类、患病已被发现类和治愈及死亡组成的免疫类,并考虑自愈因素,提出了两个模型:微分方程模型和基于Small-World Network的模拟模型。对微分方程模型,以香港为例讨论了自愈的影响,在一定意义下说明白愈现象在SARS传播中是普遍存在的。模拟模型利用Small-World Network模拟现实中人们之间的接触;借鉴Sznajd模型观念传播的基本思想“考察区域内每个成员如何影响与其有联系的其他成员”,用影响类比传染,从患病者去传染与其有接触的健康人的角度,模拟SARS的传播过程;然后吸收元胞自动机模型同步更新的思想,最终建立了一个患病者传染邻居,且一个成员同时受所有邻居影响的基于Small-WorldNetwork的模拟模型。对此模型,我们讨论了一些主要参数及接种疫苗的影响,最后拟合北京数据,讨论了提前或推迟5天采取措施的影响。     

考虑自愈的SARS的传播模型

本文根据对SARS传播的分析,把人群分为5类:易感类、潜伏期类、患病未被发现类、患病已被发现类和治愈及死亡组成的免疫类,并考虑自愈因素,提出了两个模型:微分方程模型和基于SmallWorld Network的模拟模型.对微分方程模型,以香港为例讨论了自愈的影响,在一定意义下说明自愈现象在SARS传播中是普遍存在的.模拟模型利用Small-World Network[1]模拟现实中人们之间的接触;借鉴Sznajd模型[2]观念传播的基本思想"考察区域内每个成员如何影响与其有联系的其他成员",用影响类比传染,从患病者去传染与其有接触的健康人的角度,模拟SARS的传播过程;然后吸收元胞自动机模型[3]同步更新的思想,最终建立了一个患病者传染邻居,且一个成员同时受所有邻居影响的基于Small-WorldNetwork的模拟模型.对此模型,我们讨论了一些主要参数及接种疫苗的影响,最后拟合北京数据,讨论了提前或推迟5天采取措施的影响.     

考虑自愈的SARS的传播模型

本文根据对SARS传播的分析，把人群分为5类：易感类、潜伏期类、患病未被发现类、患病已被发现类和治愈及死亡组成的免疫类，并考虑自愈因素，提出了两个模型：微分方程模型和基于Small-world Network的模拟模型。对微分方程模型，以香港为例讨论了自愈的影响，在一定意义下说明自愈现象在SARS传播中是普遍存在的。模拟模型利用Small-World Network模拟现实中人们之间的接触；借鉴Sznajd模型观念传播的基本思想“考察区域内每个成员如何影响与其有联系的其他成员”，用影响类比传染，从患病者去传染与其有接触的健康人的角度，模拟SARS的传播过程；然后吸收元胞自动机模型同步更新的思想，最终建立了一个患病者传染邻居，且一个成员同时受所有邻居影响的基于Small-World Network的模拟模型。对此模型，我们讨论了一些主要参数及接种疫苗的影响，最后拟合北京数据，讨论了提前或推迟5天采取措施的影响。     

上市公司财务困境预测实证研究——基于Logistic模型的概率置信区间

财务危机是导致企业生存危机的重要因素,因此,需要针对可能造成财务危机的因素,采取监测和预防措施,及早防范财务风险,控制财务危机。本文介绍了一种利用Logistic模型度量单个企业发生财务危机概率的方法,提出了通过选择流动比率和资产负责率等确定置信区间,预测公司发生财务危机概率的统计量,试图得出企业发生财务危机前的征兆。     

SARS传播的数学原理及预测与控制

众所周知,SARS对中国社会带来了重大的影响。我们以北京地区4月到6月有关SARS的数据为参考资料,就病毒的实际传播特征引入了电子线路中的负反馈的概念,建立了SARS传播的负反馈系统,并在分析该系统参数实际意义的情况下,建立时间序列的模型。该模型将传染率定义为时间的函数,以拟合数据和实际数据之间的总残差最小为目标,利用matlab中的fminsearch函数模拟得到最优的模型参数。该模型可以较好的预测SARS的发展趋势,且可以就此趋势提出如何控制SARS传播的措施。继而,本文通过模拟出在不同日期提前或滞后5天实施隔离政策所引起SARS发展趋势变化的曲线,分析了卫生部门实施隔离政策的日期对SARS发展趋势的影响。 在SARS对经济影响的这个问题上,本文适当选取医疗业具有代表性的17支股票,构造了医疗板块指数,以此测度医疗业的经济表现。在传统的CAPM模型中,我们引入了虚拟变量,利用OLS技术进行估计分析,检验出SARS这一事件对医药业的经济影响是正影响。该影响反映在医疗版指数的日收益上,但这个影响是由SARS引起的,会随着SARS的结束而结束。     

一种适用于声化学的新型复合超声变幅杆

提出一种新型复合超声变幅杆,该变幅杆总长为一个波长,由五段组成,其中三段为等截面圆柱杆,两段为变截面圆柱杆。给出了该类复合变幅杆的设计方法,并计算了两个实例。结果表明,和普通使用的半波长复合变幅杆相比,该类复合变幅杆具有在不减少甚至增大辐射面积的情况下放大振幅的特点,这对提高整个超声系统的辐射声功率和辐射效率具有积极意义。此类复合变幅杆特别适合在声化学等超声液体处理领域使用。     

Global dynamics of a time delayed SIR model with varying population size

A disease transmission model of susceptible-infective-recovered type with a constant latent period is analysed. The global dynamics of the disease-free equilibrium is investigated. If the basic reproduction number is greater than unity, a unique endemic equilibrium exists. Using Lyapunov functional approach, this endemic equilibrium is globally stable in the feasible region. The disease will persist (and is permanent) at the endemic equilibrium if it is initially present. The effects of loss of immunity on the dynamics of the model are analysed, and the parameters that drive the disease dynamics are obtained. Numerical simulations support our analytical results and illustrate possible behavioural scenarios of the model.     

Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmission

Infection with Mycobacterium tuberculosis leads to tuberculosis (TB) disease by one of the three possible routes: primary progression after a recent infection; re-activation of a latent infection; or exogenous re-infection of a previously infected individual. Recent studies show that optimal TB control strategies may vary depending on the predominant route to disease in a specific population. It is therefore important for public health policy makers to understand the relative frequency of each type of TB within specific epidemiological scenarios. Although molecular epidemiologic tools have been used to estimate the relative contribution of recent transmission and re-activation to the burden of TB disease, it is not possible to use these techniques to distinguish between primary disease and re-infection on a population level. Current estimates of the contribution of re-infection therefore rely on mathematical models which identify the parameters most consistent with epidemiological data; these studies find that exogenous re-infection is important only when TB incidence is high. A basic assumption of these models is that people in a population are all equally likely to come into contact with an infectious case. However, theoretical studies demonstrate that the social and spatial structure can strongly influence the dynamics of infectious disease transmission. Here, we use a network model of TB transmission to evaluate the impact of non-homogeneous mixing on the relative contribution of re-infection over realistic epidemic trajectories. In contrast to the findings of previous models, our results suggest that re-infection may be important in communities where the average disease incidence is moderate or low as the force of infection can be unevenly distributed in the population. These results have important implications for the development of TB control strategies.     

Threshold parameters for a model of epidemic spread among households and workplaces

The basic reproduction number R ₀ is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number R _H for it. We show how R _H overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.     

煤矿三元复合胶体防灭火材料的制备与性能研究

用快硬硫铝酸盐水泥、大掺量粉煤灰、水玻璃,外加悬浮剂,一步混合法制备了三元复合胶体防灭火材料,研究了该材料的凝结时间、抗压强度和阻化性能,观察了微观形貌,探讨了胶凝机理。结果表明,材料胶结体的初凝时间在1~30 min范围内可控,并具有良好的早期抗压强度;60℃阻化率达90%,70℃达80%,80℃不低于75%;胶结体内部存在大量絮凝状的C-S-H凝胶,且与粉煤灰胶连,结构密实。工业实验表明该防灭火材料具有良好的防灭火效果。     

The price of anarchy in mobility-driven contagion dynamics

Public policy and individual incentives determine the patterns of human mobility through transportation networks. In the event of a health emergency, the pursuit of maximum social or individual utility may lead to conflicting objectives in the routing strategies of network users. Individuals tend to avoid exposure so as to minimize the risk of contagion, whereas policymakers aim at coordinated behaviour that maximizes the social welfare. Here, we study agent-driven contagion dynamics through transportation networks, coupled to the adoption of either selfish- or policy-driven rerouting strategies. In analogy with the concept of price of anarchy in transportation networks subject to congestion, we show that maximizing individual utility leads to a loss of welfare for the social group, measured here by the total population infected after an epidemic outbreak.     

A modified drag model for power-law fluid-particle flow used in computational fluid dynamics simulation

A modified drag model for the power-law fluid-particle flow considering effects of rheological properties was proposed. At high particle concentrations (ε_s ≥ 0.2), based on the Ergun equation, the cross-sectional shape and the tortuosity of the pore channel are considered, and the apparent flow behavior index and consistency coefficient of the power-law fluid at the surface of the particles are corrected. At low particle concentrations (ε_s < 0.2), based on the Wen-Yu drag model, the modified Reynolds number for power-law fluid and the relational expression between drag coefficient for single particle and Reynolds number that considers the effect of the flow behavior index are adopted. Numerical simulations for the power-law fluid-particle flow in the fluidized bed were carried out using the non-Newtonian drag model. The effects of rheological parameters on the drag coefficient were analyzed. The comparisons of simulation and experiment show that the modified drag model predicts reasonable void fraction under different rheological parameters, particle diameters, and liquid velocities in both low particle concentrations and high particle concentrations. The increase in flow behavior index and consistency coefficient increases the drag coefficient between the two phases and decreases the average particle concentration within the bed.     

Logistic regression analysis of pedestrian casualty risk in passenger vehicle collisions in China

A large number of pedestrian fatalities were reported in China since the 1990s, however the exposure of pedestrians in public traffic has never been measured quantitatively using in-depth accident data. This study aimed to investigate the association between the impact speed and risk of pedestrian casualties in passenger vehicle collisions based on real-world accident cases in China. The cases were selected from a database of in-depth investigation of vehicle accidents in Changsha-IVAC. The sampling criteria were defined as (1) the accident was a frontal impact that occurred between 2003 and 2009; (2) the pedestrian age was above 14; (3) the injury according to the Abbreviated Injury Scale (AIS) was 1+; (4) the accident involved passenger cars, SUVs, or MPVs; and (5) the vehicle impact speed can be determined. The selected IVAC data set, which included 104 pedestrian accident cases, was weighted based on the national traffic accident data. The logistical regression models of the risks for pedestrian fatalities and AIS 3+ injuries were developed in terms of vehicle impact speed using the unweighted and weighted data sets. A multiple logistic regression model on the risk of pedestrian AIS 3+ injury was developed considering the age and impact speed as two variables. It was found that the risk of pedestrian fatality is 26% at 50 km/h, 50% at 58 km/h, and 82% at 70 km/h. At an impact speed of 80 km/h, the pedestrian rarely survives. The weighted risk curves indicated that the risks of pedestrian fatality and injury in China were higher than that in other high-income countries, whereas the risks of pedestrian casualty was lower than in these countries 30 years ago. The findings could have a contribution to better understanding of the exposures of pedestrians in urban traffic in China, and provide background knowledge for the development of strategies for pedestrian protection.