基于三次样条插值的艾滋病治疗模型

基于数学建模提供的艾滋病治疗方案中的实验数据,依据病人的初始CD4状态,将实验数据分类筛选,采用一维三次样条插值法描绘各类病人服药时间与病情的关系图形,进而由图形确定最佳治疗终止时间;并建立了CD4与时间的函数关系模型,借助于性价比函数进行疗效、价格的综合比较分析,此模型解法对最佳治疗方案的选择提供了有力依据.     

抗艾滋病药物的评价与预测模型

第一问中对CD4数量和HIV浓度随周期变化分别建立线性模型和二次模型,由数据确立中度患者CD4随时间变化模型为:C(T)=0.0496T+3.0659,HIV随时间变化为:H(T)=0.0044T2-0.2317T+4.2899.确定最佳治疗终止时间为:轻度患者28.90周,中度患者31.97周,重度患者为40.86周,平均最佳终止治疗时间33.91周.第二问中得出疗法4效果最好,疗法3次之,疗法1最差.然后通过建立了回归分析模型,对最优疗法进行预测,得到最佳终止治疗时间为25.53周.第三问在第二问的基础上增加了治疗费用对治疗效果的影响,计算得出:疗法3为最优,疗法1次之,疗法2最差.用疗法3的数据进行作图分析得到疗法3的最佳治疗终止时间为40周.     

线性混合模型用于艾滋病疗效预测和疗法选优

为探究线性混合效应模型在艾滋病疗效预测和疗法选优中的应用。利用美国艾滋病医疗试验机构ACTG的193A研究中的一组非平衡重复测量数据,以logcd4为体现疗效的因变量,年龄、性别为固定效应,建立截距和治疗时间的斜率随受试者随机变化且其期望值因疗法不同的线性混合效应模型,用SAS软件中mixed过程求解并预测。通过疗法对截距和治疗时间斜率期望值的影响选择最优疗法。结果表明模型有非常好的拟合和预测效果,疗法4为最优疗法。本研究为专业医生进行艾滋病疗效的预测和疗法选优提供了科学依据和方法。     

基于线性混合模型的艾滋病最佳治疗时机选择

本文利用美国艾滋病医疗试验机构ACTG的193A研究中的一组非平衡重复测量数据。以log(cd4+1)为体现疗效的因变量,年龄、性别为固定效应,治疗时间和滞后治疗时间为随机效应,同时考虑疗法对疗效的影响引入其与治疗时间的交互效应,建立线性混合效应模型。用SAS软件求解。再通过建立以治疗时间斜率随机效应为因变量初始logcd4为解释变量的回归模型判断艾滋病最佳治疗时机。结果表明,当初始cd4为185个/mm~3时治疗时机最佳,即为无症状感染的晚期.与美国DHHS推荐的小于200个/mm~3一致,却更为科学和精确。本研究对艾滋病治疗的临床实践具有重要的指导意义。     

HIV患者外周血CD4+/CD25hi/CD127low调节性T细胞的表达及临床意义

目的探讨感染人类自身免疫缺陷病毒（HIV）患者抗病毒治疗前后外周血CD4+/CD25hi/CD127low调节性T细胞的表达情况及临床意义。方法选择符合HIV诊断标准、接受抗病毒治疗超过3个月的64例患者,采用高效抗逆转录病毒治疗（HARRT）,分别于治疗前、治疗3个月后采用流式细胞术检测外周血CD4+/CD25hi/CD127low调节性T细胞和CD4+T细胞的表达情况,并与80例健康体检者（对照组）比较。结果与对照组比较,HIV患者CD4+/CD25hi/CD127low调节性T细胞绝对计数及百分比显著降低,差异有统计学意义（P＜0.01）。HIV患者的CD4+/CD25hi/CD127low调节性T细胞绝对计数和CD4+T细胞呈正相关（P＜0.01）;HIV患者治疗3个月后CD4+/CD25hi/CD127low调节性T细胞均有升高,与治疗前的差异均有统计学意义（均P＜0.01）。根据年龄将患者分为18~30岁、31~45岁、＞45岁,各年龄段患者治疗后CD4+/CD25hi/CD127low调节性T细胞绝对计数分别是治疗前的4.28倍、3.00倍、2.00倍。结论 HIV患者外周血CD4+/CD25hi/CD127low调节性T细胞的表达与病毒的感染、清除有关;外源性药物可升高调节性T细胞的表达。     

艾滋病治疗综效的评价和预测

本文利用美国艾滋病医疗试验机构ACTG的临床试验小组193A研究中的一组数据为样本,以10g(cd4+1)和治疗费用作为艾滋病治疗综效评价的指标,对疗法一的不同患者相同治疗时间的综合评价值平均得到平均治疗综效周时间序列,在此基础上建立ARIMA(3,1,1)模型,并做15周的外延预测。结果表明,模型有非常好的拟合和预测效果,治疗费用使欠发达地区的治疗综效有明显的下降趋势,约在第45周后直线下降,说明患者的病情此时得以很好的控制。     

第四讲 均值、方差和相关矩阵的计算(续)

(一)功能 估计多元样本的均值、标准差和方差──协方差、相关系数矩阵.其中样本数据可以分组提供。 (二)算法概述 设M个变量的N次观测数据矩阵为(xki)N×M.定义前n次观测数据的均值与差积和为并令可证有如下递推公式*: *证明见本刊1983年第4期杨自强的文章。该文通过大量数据对比计算后认为这是一个较好的一轮算法,特别在数 据服从正态分布。且均值比方差小时。于是对于N次观测数据有均值标准差方差──协方差相关系数递推算法对于数据的调用是一次性的,即在一轮循环计算中同时完成均值与差积和的计算。本程序允许把数据矩阵分割为k个子…     

基于CD4细胞计数的HIV仓室模型与数据分析

迄今我国每年统计艾滋病的新增人数与死亡人数仍呈上升趋势,由于潜伏期长和初期无明显症状等原因,还存在大量未发现的HIV携带者,这给HIV的防控带来巨大挑战.旨在利用中国疾控中心网报数据和深圳市患者随访数据,结合传染病动力学和统计分析方法与临床知识,建立依微观CD4细胞计数划分的宏观HIV仓室数学模型,通过数值计算方法与MCMC参数估计方法实现稳健的参数拟合,进而利用不确定性和敏感性以及随机森林方法进行灵敏度分析.研究结果表明:2013年广东省未确诊HIV携带者约为13.1061万人,且该地区HIV疫情传播的基本再生数为2.8133.敏感性分析揭示艾滋病疫情防控最优方法是控制患者有效接触人数与沉默系数,由此建议制定针对控制艾滋病传播中一些现象的法律法规,在艾滋病高发地区实施清洁针具交换工作等,对疫情防控提出指导性建议.     

卵巢癌患者外周血调节性T细胞的变化及其临床意义

目的探讨卵巢癌患者外周血调节性T细胞（Treg）水平变化的意义及其临床意义。方法采用流式细胞术测定130例卵巢癌患者和50例体检健康女性的外周血中CD4+、CD8+、NK以及Treg等不同淋巴细胞亚群的比例,比较两组间的差异,分析卵巢癌不同临床病理因素患者Treg水平的差异,并比较手术和化疗患者手术前后或化疗前后Treg水平的变化。结果卵巢癌组外周血CD4+、NK细胞比例以及CD4+/CD8+比值均明显低于正常对照组,而Treg细胞比例明显高于正常对照组;淋巴结转移卵巢癌患者其Treg水平高于淋巴结未转移,且在不同的FIGO分期中III、IV期患者的Treg细胞比例要高于I、II期,差异均有统计学意义（均P＜0.05）;手术后Treg细胞比例较手术前明显下降,差异有统计学意义（P＜0.05）;化疗后Treg细胞比例与化疗前的差异无统计学意义（P＞0.05）。结论卵巢癌患者外周血Treg水平与卵巢癌的分期和进展有关,在卵巢癌预后判断以及疗效监测中有重要意义。     

两类多元GARCH模型的预测绩效和组合VaR的研究

运用V aR模型对股票组合进行风险测度的关键之一是得到组合条件协方差矩阵.而经典的多元GARCH模型来求解波动率面临着估计参数过多,计算量庞大的问题.因此,使用正交GARCH模型和CCC模型来估算波动率,并以沪深两市A股市场上四个行业的65只股票为样本,使用RM SE和M AD指标比较这些模型的预测能力,求得股票组合的V aR,得出前者效率高和后者预测能力略高的结论.     

Approximating posterior probabilities in a linear model with possibly noninvertible moving average errors

The method of Laplace is used to approximate posterior probabilities for a collection of polynomial regression models when the errors follow a process with a noninvertible moving average component. These results are useful in the problem of period-change analysis of variable stars and in assessing the posterior probability that a time series with trend has been overdifferenced. The nonstandard covariance structure induced by a noninvertible moving average process can invalidate the standard Laplace method. A number of analytical tools is used to produce corrected Laplace approximations. These tools include viewing the covariance matrix of the observations as tending to a differential operator. The use of such an operator and its Green's function provides a convenient and systematic method of asymptotically inverting the covariance matrix.In certain cases there are two different Laplace approximations, and the appropriate one to use depends upon unknown parameters. This problem is dealt with by using a weighted geometric mean of the candidate approximations, where the weights are completely data-based and such that, asymptotically, the correct approximation is used. The new methodology is applied to an analysis of the prototypical long-period variable star known as Mira.     

The conditioning of least‐squares problems in variational data assimilation

In variational data assimilation a least‐squares objective function is minimised to obtain the most likely state of a dynamical system. This objective function combines observation and prior (or background) data weighted by their respective error statistics. In numerical weather prediction, data assimilation is used to estimate the current atmospheric state, which then serves as an initial condition for a forecast. New developments in the treatment of observation uncertainties have recently been shown to cause convergence problems for this least‐squares minimisation. This is important for operational numerical weather prediction centres due to the time constraints of producing regular forecasts. The condition number of the Hessian of the objective function can be used as a proxy to investigate the speed of convergence of the least‐squares minimisation. In this paper we develop novel theoretical bounds on the condition number of the Hessian. These new bounds depend on the minimum eigenvalue of the observation error covariance matrix and the ratio of background error variance to observation error variance. Numerical tests in a linear setting show that the location of observation measurements has an important effect on the condition number of the Hessian. We identify that the conditioning of the problem is related to the complex interactions between observation error covariance and background error covariance matrices. Increased understanding of the role of each constituent matrix in the conditioning of the Hessian will prove useful for informing the choice of correlated observation error covariance matrix and observation location, particularly for practical applications.     

The Analysis of a General Input Queue with N Policy and Exponential Vacations

This paper studies a single removable server in a G/M/1 queueing system with finite capacity where the server applies an N policy and takes multiple vacations when the system is empty. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distributions of the number of customers in the system. The method is illustrated analytically for exponential and deterministic interarrival time distributions. We establish the distributions of the number of customers in the queue at pre-arrival epochs and at arbitrary epochs, as well as the distributions of the waiting time and the busy period.     

同步N—策略多重休假M／M／c排队

研究了具有同步N-策略多重休假的M／M／c排队系统．在休假时间服从相型（PH）分布的假设下，给出了系统的稳态指标．证明在已知服务台全忙并且系统中顾客数大于或等于N的条件下，条件随机变量可分解成独立随机变量之和，其中一个是无休假经典M／M／c系统中的对应条件变量，另一个是休假引起的附加随机变量     

On strategies on a mathematical model for leukemia therapy

A mathematical model for leukemia therapy based on the Gompertzian law of cell growth is studied. It is assumed that the chemotherapeutic agents kill leukemic as well as normal cells.Effectiveness of the medicine is described in terms of a therapy function. Two types of therapy functions are considered: monotonic and non-monotonic. In the former case the level of the effect of the chemotherapy directly depends on the quantity of the chemotherapeutic agent. In the latter case the therapy function achieves its peak at a threshold value and then the effect of the therapy decreases. At any given moment the amount of the applied chemotherapeutic is regulated by a control function with a bounded maximum. Additionally, the total quantity of chemotherapeutic agent which can be used during the treatment process is bounded too.The problem is to find an optimal strategy of treatment to minimize the number of leukemic cells while at the same time retaining as many normal cells as possible.With the help of Pontryagin’s Maximum Principle it was proved that the optimal control function has at most one switch point in both monotonic and non-monotonic cases for most relevant parameter values.A control strategy called alternative is suggested. This strategy involves increasing the amount of the chemotherapeutical medicine up to a certain value within the shortest possible period of time, and holding this level until the end of the treatment.The comparison of the results from the numerical calculation using the Pontryagin’s Maximum Principle with the alternative control strategy shows that the difference between the values of cost functions is negligibly small.