疫苗与隔离措施对流感暴发影响的动力学研究

2018年1月爆发了规模空前的流感,以乙型流感为主,本次流感几乎席卷了中国大部分的地区,导致多人死亡,在社会引起了较大的恐慌.为了更好的应对流感的爆发,减少累计染病量和染病峰值,实现对流感的有效预防控制,在流感病例数据的基础上,建立动力学模型来描述乙型流感爆发的传播过程,计算了基本再生数与有效再生数,并利用遗传算法拟合数据估计出了模型中的参数;通过数值模拟,探究采取疫苗和隔离措施对累计染病数和峰值的影响,得到:隔离与免疫可降低染病峰值,减小染病规模;越早采取免疫措施,越快地减少总染病人数;与采用隔离措施相比,注射疫苗能更快得降低有效再生数.为预防和控制乙型流感爆发提供可以借鉴的理论依据与可行的控制措施.     

SARS流行病传染动力学模型

建立了 SARS流行病的数学模型 ,根据部分国家和地区的 SARS疫情数据 ,计算出其模型参数 ,给出了各地 SARS疫情与模拟结果的比较图 ,模拟结果与实际疫情十分吻合 .分析了 SARS流行特征 ,并对疫情发展进行了预测 .     

北京市SARS疫情统计分析

本文对严重急性呼吸道综合症 SA RS疾病进行了统计分析 .文章首先以北京市海淀区 SARS确诊病例和疑似病例为研究对象 ,分别按照地区、人口进行了统计分析 ,得出海淀区不同小区疫情发展的显著程度 .然后利用正交试验设计 ,分别就年龄、性别、职业等因素对海淀区 SARS确诊病人和疑似病人影响程度进行了统计分析 ,得出 2 1岁到 50岁的学生和干部得病率最高的统计结果 ,这完全符合海淀区的疫情事实 .这个统计结果已经被海淀区政府“海淀区政府应急管理信息系统 ( H EMIS)”[6]采用 . H EMIS系统作为中国第一个政府应急系统在海淀区 SARS防治中起到了一定作用 [1 ] .文章最后研究了北京市每天新增的确诊病例和每天疑似病例转为确诊病例之间的相关系数 ,从它们的相关性分析可以反映出防治 SARS疫情措施的有效性 .     

传染病模型的研究及应用

分析了传染病的传播扩散特点,建立了传染病传播扩散的微分方程模型.利用最大似然估计法对模型中的参数进行了估计.并以SARS传染扩散为例,利用网上的公开数据对模型进行了检验,所得结果与实际情况一致.此模型为传染病的预防和控制提供了理论依据.     

具有连续接种与剔除的SIQR流行病模型全局稳定性

本文研究一类考虑接种、剔除和隔离等策略的SIQR流行病模型,得到疾病流行与否的阈值-基本再生数R0;证明无病平衡点E0和地方病平衡点E*的存在性及全局稳定性;指出接种、隔离和剔除等预防和控制措施均可使疾病的流行得以控制;最后,进行计算机数值模拟来进一步验证理论结果的正确性.     

染病者有常数输入的传染病模型

讨论在隔离措施下易感者和染病者都有常数移民的传染病模型.给出了模型的地方病平衡点,证明了地方病平衡点的稳定性.     

基于公开数据的SARS流行规律的建模及预报

基于全球与我国公开发表的有关SARS确诊病例、疑似病例和死亡病例的实际数据,建立有关流行病学的模型是本研究的目的。我们探讨了SARS的简单流行病学微分方程模型,建立了北京医院尚有确诊病例的时间序列的ARMA模型,得出6月底左右北京医院SARS病人数将会降到60人以下。同时,通过经验模型和贝叶斯方法对病死率进行了初步估计。     

具有跟踪隔离措施的新冠肺炎传播模型分析及应用

报道于2019年12月底的新型冠状病毒肺炎(COVID-19)疫情, 由于2020年春运期间人口的大规模流动, 使得其迅速蔓延.自2020年1月23日起, 我国采取了各种措施使得疫情得到了有效的控制, 例如武汉封城、确诊病例的密切接触者跟踪隔离、湖北人员的居家隔离等.该文基于COVID-19在山西省的实际传播情况, 建立了具有输入病例和确诊病例密切接触者跟踪隔离的动力学模型.在不考虑输入病例的情况下, 分析了模型的动力学行为.利用山西省COVID-19病例数据, 计算了实时再生数, 发现山西省2020 年1月25日全省封村封街道有效控制了COVID-19疫情的传播, 即实时再生数小于1, 从宏观角度验证了防控措施的有效性.进一步通过模型的数值拟合得到: 早期染病者隔离14天的防控策略是合理有效的; 武汉封城时间越早, 染病者的规模越小; 跟踪隔离到大量确诊病例的接触者时, 染病者的规模越小.     

一类SARS流行病模型的改进及分析

为进一步研究政府行为在SARS流行病控制中的作用,对我们建立的SARS流行病模型进行了改进.利用常微分方程动力系统的理论,研究了改进的模型,给出了奇点及奇点的类型,并作出了相图.得到的结论进一步表明:在SARS的控制中,政府行为是最重要的因素.     

关于全期望和全概公式及其应用的教学研究——以新型冠状病毒为例

本文利用全期望公式和全概公式对采取隔离措施来应对新冠肺炎疫情进行了分析,以实际问题引入较难的知识点,最终达到既解决实际问题又剖析了理论知识的目的.     

The geometry of solutions to a segregation problem for nondivergence systems

Segregation systems and their singular perturbations arise in different areas: particle anihilation, population dynamics, material sciences. In this article we study the elliptic and parabolic limits of a nonvariational singularly perturbed problem. Existence and regularity properties of solutions and their limits are obtained.     

The checkerboard model of social interaction

The checkerboard model is a computer simulation of social interaction among members of two groups. The checkerboard represents a social field on which two groups of checkers move on the board on the basis of positive, neutral or negative attitudes toward one another assigned to them. The resulting pattern of positions of the pieces represents the social structure. The theoretical basis for the checkerboard model is explained and the rules for operating the model are outlined. This is followed by illustrative runs named Crossroads, Mutual Suspicion, Segregation, Social Climber, Social Worker, Boy‐Girl, Couples and Husband‐Wives, showing intermediate and final positions on the board for each. It is concluded that the checkerboard model is capable of demonstrating the intimate connection between attitudes of group members toward their own group and toward others to a continuous social interactional process and to the resulting social structure.     

Segregation of Carbon Paste in a Smelting Electrode

Requests for reprints to A. C. Fowler An industrial problem concerning segregation in carbon pasteis described. Billets of paste, which are a mixture of cokeand pitch, are fed into a steel tube in a furnace, and the tubeis lowered at a rate of about 0.75 m day^–1. In the tube,the pitch is defonnable, and the paste is essentially a veryviscous two-phase participate medium. The grain size distributionis essentially bimodal, consisting of coarse ({small tilde}10mm) particles in a distribution of finer (100 µm) particles.Segregation occurs near the walls of the tube, leading to alower content of coarse particles; such segregation is unwanted,and so the length of this segregated region is required to beminimized. It is suggested that segregation is due to the stiffnessof the coarse particulate mixture, which is less able to deformthan the pitch/fines mixture. Consequently, the length of thesegregated region is controlled by the coarse mixture viscosity,and an expression is derived for the segregation length.     

关于多个子空间的交空间与维数公式的推广

通过讨论,得到了关于多个子空间的交空间的进一步的结果.并利用这些结果,给出了维数公式的一个新的推广形式,从而完善了维数公式的理论.     

A short proof of the inclusion of the core in the Weber set

For a transferable utility game the convex hull of the Weber allocations contains the core as a subset. A proof of this result normally involves an induction hypothesis to the number of players. We will give here a short proof based on a well known result in convex analysis.     

Acceleration property for the columns of the E-algorithm

A convergence acceleration result for the E-algorithm is proved for sequences such that the error has an asymptotic expansion on a scale of comparison for which a determinantal relation holds. This result is also generalized to the vector case.     

On the Hardness of Approximating the Chromatic Number

k -colorable for some fixed . Our main result is that it is NP-hard to find a 4-coloring of a 3-chromatic graph. As an immediate corollary we obtain that it is NP-hard to color a k-chromatic graph with at most colors. We also give simple proofs of two results of Lund and Yannakakis [20]. The first result shows that it is NP-hard to approximate the chromatic number to within for some fixed ε > 0. We point here that this hardness result applies only to graphs with large chromatic numbers. The second result shows that for any positive constant h, there exists an integer , such that it is NP-hard to decide whether a given graph G is -chromatic or any coloring of G requires colors. Received April 11, 1997/Revised June 10, 1999     

取油管振动方程解的整体不存在性

讨论推广的海底取油管振动方程的初边值问题和初值问题解的整体不存在性,对初边值问题推广了Gmira和Guedda得到的结果,对初值问题的结果是新的.     

Asymptotic normality of the size of the giant component via a random walk

In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of G(n,p) above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp?s exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work.     

广义Minkowski不等式的进一步改进

针对"亚正定阵理论(Ⅱ)"一文的广义Minkowski不等式不成立问题,在已有的修正结果基础上,给出一种完整的修正结果;并更正了"亚正定阵的几个开问题及一些不等式"一文中有关的错误结论;用反例说明"广义正定矩阵的进一步研究"一文中的有关结论是错误的,给出完整的修正结果.