The Application of Linear Piecewise Regression to Basal Body Temperature Data

In many situations one wishes to fit a piecewige regression which enables one to obtain estimates of the join points as well as the slopes and intercepts of the fitted submodels. This study developes a technique for fitting piecewise models to data which contain measurement error in an independent variable. The technique developed here combines the HUDSON (1966) procedure for estimating parameters in piecewise regression and the WALD (1940) Grouping Technique which obviates the problem of measurement error. If one assumes some knowledge of the position of the join point in relation to the data, methodology has been developed to estimate the parameters and study the asymptotic properties of the means and variances of the parameter estimates. However, in the more realistic case, when additional knowledge is limited, it is only possible to obtain the parameter estimates using an iterative technique (TEETER, 1982). The general technique for obtaining the join point estimate in the presence of measurement error is presented here and an example is given using data on women's basal body temperature during menstrual cycles.     

时滞传染病模型的指数稳定性

利用分析技巧研究了一类SEIRS传染病模型的动力学行为.结论表明如果再生数小于1,则带变时滞的传染病模型的无病平衡点是全局指数渐近稳定的,如果再生数大于1,得到传染病平衡点局部指数稳定的充分条件,同时给出了例子说明结论的有效性.     

Fitting Survival Data to a Piecewise Linear Hazard Rate in the Presence of Covariates

This paper extends the work of KODLIN (1967), who proposed a method for analyzing patient survival data wherein the hazard rate was linearly related to the survival time. The present paper extends Kodlin's model to permit maximum likelihood estimation of the parameters so that covariate effects are included and the slope and intercept parameters are allowed to change over fixed intervals of the time domain of study. An illustration of the method using multiple myeloma data is given and the results are compared with those of Kodlin's model, the Feigl-Zelen, Zippin-Armitage model, the exponential model, and Cox's proportional hazards model.     

一类具有饱和发生率的SEIS模型的全局稳定性

建立并分析了一类具有饱和发生率、在潜伏期具有传染性的SEIS模型.得到了模型的基本再生数R_0和无病平衡点与地方病平衡点全局渐近稳定的充分条件.     

一类具有非单调发生率SIS流行病模型的分析

该文讨论了具有非单调发生率SIS流行病模型,分别建立了带有分布时滞和离散时滞形式的感染个体的恢复时滞模型,同时分析了系统平衡态的稳定性．     

Logical Gaps in the Approximate Solutions of the Social Learning Game and an Exact Solution

After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

一类具有垂直传染和预防接种的传染病模型的稳定性

考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行.     

一类具有标准发生率的SIS型传染病模型的全局稳定性

研究一类具有标准发生率的SIS传染病模型,讨论了各类平衡点存在的条件;运用微分方程的定性理论,得到了无病平衡点E_1和地方病平衡点E_2的全局渐近稳定的充分条件.     

Intent to Receive Pandemic Influenza A (H1N1) Vaccine,Compliance with Social Distancing and Sources of Information in NC, 2009

Background

Public adherence to influenza vaccination recommendations has been low, particularly among younger adults and children under 2, despite the availability of safe and effective seasonal vaccine. Intention to receive 2009 pandemic influenza A (H1N1) vaccine has been estimated to be 50% in select populations. This report measures knowledge of and intention to receive pandemic vaccine in a population-based setting, including target groups for seasonal and H1N1 influenza.

Methodology and Principal Findings

On August 28–29, 2009, we conducted a population-based survey in 2 counties in North Carolina. The survey used the 30×7 two-stage cluster sampling methodology to identify 210 target households. Prevalence ratios (PR) and 95% confidence intervals (CI) were estimated. Knowledge of pandemic influenza A (H1N1) vaccine was high, with 165 (80%) aware that a vaccine was being prepared. A total of 133 (64%) respondents intended to receive pandemic vaccine, 134 (64%) intended to receive seasonal vaccine, and 109 (53%) intended to receive both. Reporting great concern about H1N1 infection (PR 1.55; 95%CI: 1.30, 1.85), receiving seasonal influenza vaccine in 2008–09 (PR 1.47; 95%CI: 1.18, 1.82), and intending to receive seasonal influenza vaccine in 2009–10 (PR 1.27; 95%CI: 1.14, 1.42) were associated with intention to receive pandemic vaccine. Not associated were knowledge of vaccine, employment, having children under age 18, gender, race/ethnicity and age. Reasons cited for not intending to get vaccinated include not being at risk for infection, concerns about vaccine side effects and belief that illness caused by pandemic H1N1 would be mild. Forty-five percent of households with children under 18 and 65% of working adults reported ability to comply with self-isolation at home for 7–10 days if recommended by authorities.

Conclusions and Significance

This is the first report of a population based rapid assessment used to assess knowledge and intent to receive pandemic vaccine in a community sample. Intention to receive pandemic and seasonal vaccines was higher than previously published reports. To reach persons not intending to receive pandemic vaccine, public health communications should focus on the perceived risk of infection and concerns about vaccine safety.     

一类疫苗预防接种具有效期性的SIRS模型稳定性分析

研究了一类预防接种下疫苗具有有效期的SIRS传染病模型,得到了决定疾病绝灭与否的闽值,给出了无病平衡点和地方病平衡点的全局稳定性的充分条件,最后借助Matlab软件进行了数值模拟．     

一类具有隔离干预的非线性传染率的传染病模型的全局稳定性分析(英文)

研究一类具有隔离干预的非线性传染率的SIQR传染病模型的全局稳定性,得到了阈值R及无病平衡点和地方病平衡点的存在的条件,并利用构造李雅普诺夫函数证明无病平衡点和地方病平衡点的全局稳定性.     

Equilibria in an epistatic viability model under arbitrary strength of selection

A class of viability models that generalize the standard additive model for the case of pairwise additive by additive epistatic interactions is considered. Conditions for existence and stability of steady states in the corresponding two-locus model are analyzed. Using regular perturbation techniques, the case when selection is weaker than recombination and the case when selection is stronger than recombination are investigated. The results derived are used to make conclusions on the dependence of population characteristics on the relation between the strength of selection and the recombination rate.