A Stochastic Model for Estimating Adolescent Sterility Among Married Women

In this paper a stochastic model is presented for the time to the first conception of a cohort of married women. By identifying three states “adolescent sterility”, “ovulation” and “conceived”, into which the women can be placed, the model incorporates individual differences for the women in the “adolescent sterility” state which allow for the individual characteristics to affect the conversion of these women into the “ovulation” state. Using straightforward probabilistic arguments it is shown that the model provides a close fit to recently published data, compares favorably with previously published models on the same subject and it is useful for planning purposes in predicting future developments.     

A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

远缘杂交中不育基因的位置和效应的最大似然估计

提出了一种统计方法,利用标记位点的异常分离,来估计远缘杂交中不育基因位点的位置和效应,在回交群体中,用最大似然法对不育基因与标记位点之间的生组值和配子存活率进行估计。将表现连续分布的育性指标转化为百连续变异的遗传标记的分离,可以避免对育性直接观测所带来的重组值估计结果的不稳定,还可以同时估计雌雄配子的存活率。     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

A Stochastic Model for Oviposition Tactics in the Bean Weevil

In a recent paper, MITCHELL (1975) experimentally investigated the oviposition behavior of weevils on mung beans. In this paper, we develop a stochastic model to study the oviposition tactics of the female weevils on beans.     

Stochastic modeling of nonlinear epidemiology

The objectives of this paper to analyse, model and simulate the spread of an infectious disease by resorting to modern stochastic algorithms. The approach renders it possible to circumvent the simplifying assumption of linearity imposed in the majority of the past works on stochastic analysis of epidemic processes. Infectious diseases are often transmitted through contacts of those infected with those susceptible; hence the processes are inherently nonlinear. According to the classical model of Kermack and McKendrick, or the SIR model, three classes of populations are involved in two types of processes: conversion of susceptibles (S) to infectives (I) and conversion of infectives to removed (R). The master equations of the SIR process have been formulated through the probabilistic population balance around a particular state by considering the mutually exclusive events. The efficacy of the present methodology is mainly attributable to its ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equations. Solving these equations simultaneously along with rates associated influenza epidemic data yields information concerning not only the means of the three populations but also the minimal uncertainties of these populations inherent in the epidemic. The stochastic pathways of the three different classes of populations during an epidemic, i.e. their means and the fluctuations around these means, have also been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. The master equation and Monte Carlo algorithms have given rise to the identical results.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

A Stochastic Model of Oscillatory Blood Testosterone Levels

A continuous-time, discrete-state stochastic model of testosterone secretion in men is considered. Blood levels of testosterone in men fluctuate periodically with a period of 2–3 h. The deterministic model, on which the stochastic model considered here is based, is well studied and has been shown to have a globally stable fixed point. Thus, no sustained oscillations are possible in the deterministic case. However, the stochastic model does observe periodic, pulsatile behavior. This demonstrates how oscillations can occur due to a switching behavior dependent on the random degradation of testosterone molecules in the system. The Gillespie algorithm is used to simulate the hormone secretion model. Important parameters of the model are discussed and results from the model are compared to experimental observations.     

Stochastic von Bertalanffy models, with applications to fish recruitment

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.     

A Stochastic Compartmental Model with Long Lasting Infusion

Most of the compartmental models in current use to model pharmacokinetic systems are deterministic. Stochastic formulations of pharmacokinetic compartmental models introduce stochasticity through either a probabilistic transfer mechanism or the randomization of the transfer rate constants. In this paper we consider a linear stochastic differential equation (LSDE) which represents a stochastic version of a one‐compartment linear model when input function undergoes random fluctuations. The solution of the LSDE, its mean value and covariance structure are derived. An explicit likelihood function is obtained either when the process is observed continuously over a period of time or when sampled data are available, as it is generally feasible. We discuss some asymptotic properties of the maximum likelihood estimators for the model parameters. Furthermore we develop expressions for two random variables of interest in pharmacokinetics: the area under the time‐concentration curve, M₀(T), and the plateau concentration, x_ss. Finally the estimation procedure is illustrated by an application to real data.     

加替沙星注射液无菌检查方法的验证

目的:建立加替沙星注射液无菌检查方法。方法:根据《中国药典》2010年版二部附录XIH无菌检查法验证试验指导原则,采用薄膜过滤法和添加硫酸锰中和剂去除加替沙星抑菌活性的实验方法和条件进行了验证,建立了加替沙星注射液无菌检查的方法。结果:采用薄膜过滤法用pH7.0无菌氯化钠-蛋白胨缓冲液进行冲洗,每桶5×100mL的冲洗量,每桶(100mL)培养基中加入硫酸锰溶液可去除加替沙星对各菌株的抑菌作用。结论:加替沙星注射液的无菌检查可采用上述方法。     

A Stochastic Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

Evaluation of the Sterility Test for Detection of Microbial Contaminants of Allografts

Tissue banks routinely use a sterility test to determine the suitability of processed tissue prior to release. However, many tissue banks also accompany the sterility test with additional types of media to ensure detection of slower-growing or more fastidious organisms that may not be detected in the standard two media/two incubation temperature sterility test. This study was designed to determine if a standard sterility test is capable of detecting the wide variety of organisms that may be isolated from human tissue thereby making the additional plated media unnecessary. More than 100 isolates, representing more than 90 different species were tested. All isolates exhibited growth in at least one of the two standard sterility test media within the 14-day incubation period.     

A Leap-frog Algorithm for Stochastic Dynamics

Abstract

A third-order algorithm for stochastic dynamics (SD) simulations is proposed, identical to the powerful molecular dynamics leap-frog algorithm in the limit of infinitely small friction coefficient γ. It belongs to the class of SD algorithms, in which the integration time step Δt is not limited by the condition Δt ≤ γ^?1, but only by the properties of the systematic force. It is shown how constraints, such as bond length or bond angle constraints, can be incorporated in the computational scheme. It is argued that the third-order Verlet-type SD algorithm proposed earlier may be simplified without loosing its third-order accuracy. The leap-frog SD algorithm is proven to be equivalent to the verlet-type SD algorithm. Both these SD algorithms are slightly more economical on computer storage than the Beeman-type SD algorithm.     

单位点孢子体-配子体互作模型中不育基因的位置和效应的估计方法

水稻籼粳亚种间杂交F1通常表现为高度不育,这种不育性的一种遗传学解释称为单位点孢子体-配子体互作模型.为了研究这种不育性,提出了一种统计方法,可以估计单位点孢子体-配子体互作模型中不育基因位点的位置和效应.该方法利用回交群体中呈现异常分离的标记位点,用最大似然法对不育基因与标记位点之间的重组率和雌配子存活率进行估计.由于所依据的是非连续变异的遗传标记的分离,而不是连续分布的配子育性指标,因此可以避免由育性直接估计所带来的重组率结果的不稳定.     

A Stochastic Model for Surname Evolution

Surnames are inherited in much the same way as biological traits like alleles of one locus. Assuming the heritability of surnames, a simple stochastic model for X, the total number of occurrences of a surname, the Consul distribution defined by the probability mass function: for x = 1, 2, 3,… and zero otherwise and where either (i) m is a positive integer when 0 ≤ θ ≤ 1 such that θ ≦ mθ ≦ 1, or (ii) m≤0, θ ≤0 such that mθ 1, can be arrived at by considering the branching process mechanism. Some applications of the model to real data are also considered.     

Proliferation and Death in a Binary Environment: A Stochastic Model of Cellular Ecosystems

The activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic limit, and of normal fluctuations is provided.     

一个带白噪声的可变时滞Lotka-Volterra人口模型(英文)

因为人口模型经常遭遇环境噪音的影响,本文将如下Lotka-Volterra模型(t)=diag(x(t))[b+Ax(t)+Bx(t-δ(t))]随机扰动为It型随机微分方程dx(t)=diag(x(t))[(b+Ax(t)+Bx(t-δ(t)))dt+(Qx(t)+Rx(t-δ(t))dw(t)].在这个随机模型中对系数b,A,B不需任何限制,我们证明了环境噪音不仅会压制人口的爆炸还会使得方程的解随机一致有界.