A Single Compartment Quantal Response Model with a Renewal Type Input Process and IID Releases

We deal with a single compartment quantal response model, where unlike the previous models, which do not have any input after the administration of a single dose Z(0)=z at time t=0, we allow inputs of doses after time t=0. More precisely, the system uses the (s, S) input policy as in inventory models, and has IID releases. Also when the amount of dose in the subject reaches 0, there is a probability p to stop having input thereafter. Among other results, the probability that the subject never responds and the expressions for some quantities of interest are obtained.     

A Generalized Logistic Model for Quantal Response Bioassay

In bioassay, where different levels of the stimulus may represent different doses of a drug, the binary response is the death or survival of an individual receiving a specified dose. In such applications, it is common to model the probability of a positive response P at the stimulus level x by P = F(x′β), where F is a cumulative distribution function and β is a vector of unknown parameters which characterize the response function. The two most popular models used for modelling binary response bioassay involve the probit model [BLISS (1935), FINNEY (1978)], and the logistic model [BERKSON (1944), BROWN (1982)]. However, these models have some limitations. The use of the probit model involves the inverse of the standard normal distribution function, making it rather intractable. The logistic model has a simple form and a closed expression for the inverse distribution function, however, neither the logistic nor the probit can provide a good fit to response functions which are not symmetric or are symmetric but have a steeper or gentler incline in the central probability region. In this paper we introduce a more realistic model for the analysis of quantal response bioassay. The proposed model, which we refer to it as the generalized logistic model, is a family of response curves indexed by shape parameters m₁ and m₂. This family is rich enough to include the probit and logistic models as well as many others as special cases or limiting distributions. In particular, we consider the generalized logistic three parameter model where we assume that m₁ = m, m is a positive real number, and m₂ = 1. We apply this model to various sets of data, comparing the fit results to those obtained previously by other dose-response curves such as the logistic and probit, and showing that the fit can be improved by using the generalized logistic.     

A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

多重二元响应Probit模型的渐近有效估计

针对多重二元响应Probit模型提出了两步估计方法,第一步由边际似然得到参数√n相合的估计,第二步通过一步迭代得到渐近有效估计,由于只需一步迭代,因此在利用模拟方法计算信息阵时,可以增加模拟的次数,从而减少模拟所产生的扰动对估计的影响．     

A Model with Three Compartments and Nonnegative Transfers

We consider a periodic model with three compartments, which can be considered as a simplified model for the dynamics of follicles. We give necessary and sufficient conditions for the solvability in nonnegative inputs, transfers and outputs, and we determine the minimal solution. If the problem is not solvable according to measurement errors of the given data, we recover suitable values by the method of least-squares, solving a quadratic optimization problem.     

Microbial Metabolism as an Evolutionary Response: The Cybernetic Approach to Modeling

ABSTRACT:?

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions.

The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.

IMTECH communication no.001/2001     

A Bayesian Estimator of the Optimum for a Single Factor Quadratic Response Model

Estimation of the location and magnitude of the optimum has long been considered an important problem in response surface methodology. In the industrial context, prior information accumulated by the subject matter specialist bears special significance. In this paper we use the Bayesian approach to estimating the optimum in a single factor quadratic regression model. Following the Bayesian general linear model development by Broemeling the normal/gamma conjugate prior is used. Explicit formulas for the generalized maximum likehood estimates of the characteristic parameters are obtained from the joint posterior distribution.     

A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors

Biophysics - The course of an infection was modeled as a controlled nonlinear process. Understanding the substantial differences observed in the trajectory of the disease caused by the new...     

一类具有Crowley-Martin型的恒化器模型的定性分析

研究了恒化器中一类具有Crowley—Martin型功能反应函数的单种微生物培养系统,应用微分方程定性理论,得到微生物培养失败和成功的充分条件．最后给出本文的一个应用．     

具免疫时滞的HIV感染模型动力学性质分析

讨论了一类具免疫时滞的HIV感染模型.分析了未感染平衡点的全局渐近稳定性,给出了感染无免疫平衡点及感染免疫平衡点局部渐近稳定的充分条件.数值模拟结果表明,当易感细胞生成率的取值使得基本再生数满足平衡存在的条件且低于某一临界值时,时滞对平衡点的稳定性没有影响;若大于该临界值,随着时滞增大,稳定性开关发生,平衡点不稳定,出现一系列Hopf分支,最终表现为周期波动模式.     

模拟青霉素分批补料发酵过程的细胞自动机模型

根据青霉素产生菌的生长机理和青霉素分批补料发酵过程的动力学特性,在Paull等建立的形态学结构动力学模型的基础上,建立了模拟青霉素分批补料发酵过程的细胞自动机模型。模型采用三维细胞自动机作为菌体生长空间,采用Moore型邻域作为细胞邻域,其演化规则根据青霉素分批补料发酵过程中菌体生长机理和简化动力学结构模型设计。模型中的每一个细胞既可代表单个产黄青霉菌体细胞,又可代表特定数量的这种菌体细胞,它具有不同的状态。对模型进行的仿真实验结果表明：模型不但能一致地复现形态学结构动力学模型所描述的青霉素分批补料发酵过程的演化特性,而且较形态学结构动力学模型更加直观地刻画了青霉素分批补料发酵过程的演化行为。最后,对所建模型在实际生产过程中的应用问题进行了分析,指出了需要进一步研究的问题。     

一类功能性反应模型在常数收获下的动态特性

具有功能性反应的捕食与被捕食模型具有非常复杂的动态性质．特别是在常数收获下,该模型呈现了各种各样、纷杂多变的动态特性。其中包括正平衡点及其稳定性的变化、各种分叉的产生以及周期解和极限环的出现．本文重点研究了常数收获项对一类功能性反应模型的动态性能的影响,得到了该收获模型存在稳定正平衡点、产生分叉以及在Hopf分叉附近产生周期解和极限环的若干充分条件．     

具免疫应答和细胞内部时滞的HIV-1感染模型的稳定性分析

考虑了CTLs免疫应答和细胞内部时滞建立HIV-1感染的数学模型.对模型的无感染平衡点全局稳定性进行了分析,对CTLs未激活和CTLs已激活的感染平衡点给出了局部稳定的充分条件.数值模拟支持了得到的理论结果.     

具有阶段结构和功能反应混合模型的持久性和周期解

讨论了一类具有阶段结构和第Ⅱ类功能反应的三种群混合模型,其中捕食种群具有阶段结构．得到在适当的条件下系统的持续生存,对应周期系统正周期解的存在性、唯一性以及全局稳定性．     

Evaluation of Sampling-Based Methods for Sensitivity Analysis: Case Study for the E. coli Food Safety Process Risk Model

This article evaluates selected sensitivity analysis methods applicable to risk assessment models with two-dimensional probabilistic frameworks, using a microbial food safety process risk model as a test-bed. Six sampling-based sensitivity analysis methods were evaluated including Pearson and Spearman correlation, sample and rank linear regression, and sample and rank stepwise regression. In a two-dimensional risk model, the identification of key controllable inputs that can be priorities for risk management can be confounded by uncertainty. However, despite uncertainty, results show that key inputs can be distinguished from those that are unimportant, and inputs can be grouped into categories of similar levels of importance. All selected methods are capable of identifying unimportant inputs, which is helpful in that efforts to collect data to improve the assessment or to focus risk management strategies can be prioritized elsewhere. Rank-based methods provided more robust insights with respect to the key sources of variability in that they produced narrower ranges of uncertainty for sensitivity results and more clear distinctions when comparing the importance of inputs or groups of inputs. Regression-based methods have advantages over correlation approaches because they can be configured to provide insight regarding interactions and nonlinearities in the model.     

对"功能反应函数为x的食饵——捕食系统的定性分析"一文的注记

重新分析了文[1]所讨论过的功能反应函数为x的捕食系统(1),分析了此系统在第一象限内轨线的拓朴结构,证明了系统(1)的唯一正平衡点如果不稳定,则存在唯一(稳定)极限环;如果稳定,则全局稳定于此正平衡点,纠正了文[1]中关于系统(1)极限环的存在性、稳定性等方面的一些结论.     

具脉冲收获与脉冲单边扩散的单种群动力学模型研究

建立了一类具脉冲收获与脉冲单边扩散在不同固定脉冲时刻的单种群动力学模型利用离散动力系统频闪映射理论,得到了脉冲收获的阈值.该结论说明只要收获量不超过其阈值通过扩散则种群可以保持持续生存.