A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

草场资源综合评价的数学模型

本文在前人评价我国草场资源工作的基础上,对草场资源评定因素进行了筛选与合理组合,编排了各评定因素的多层次评判顺序,组建了综合评价草场资源的模糊数学模型。首次在我国应用数学模型对草场资源进行了综合评价。为验证该数学模型的灵敏程度,作者列举了我国北方四个草场类型,作了具体计算。结果表明,数学模型本身具有较高的灵敏度,可以应用于评价我国北方天然草场资源。     

A Mathematical Model of the Pancreatic Ductal Epithelium

A mathematical model of the HCO⁻ ₃-secreting pancreatic ductal epithelium was developed using network thermodynamics. With a minimal set of assumptions, the model accurately reproduced the experimentally measured membrane potentials, voltage divider ratio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO₂/HCO⁻ ₃-free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO₂/HCO⁻ ₃-buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K⁺ concentration, and the effect of K⁺ channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na⁺-free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl⁻-free extracellular solution and the effect of DIDS on this alkalinization. In addition, the model predicted that the luminal Cl⁻ conductance plays a key role in controlling both the HCO⁻ ₃ secretory rate and intracellular pH during HCO⁻ ₃ secretion. We believe that the model will be helpful in the analysis of experimental data and improve our understanding of HCO⁻ ₃-transporting mechanisms in pancreatic duct cells. Received: 18 October 1995/Revised: 5 July 1996     

A Mathematical Model of the Human Menstrual Cycle

A mathematical model for the hormonal interactions of the human menstrual cycle is presented. The feedback effects of estrogen on the release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) are considered, including a mechanism describing the midcycle LH peak. Computer simulation with this model yields results which are periodic and in good agreement with physiological data.     

A Mathematical Model for Extrachromosomal Heredity

During embryogeny the components of the cytoplasm of a zygote are subject to certain irregularities. This has been investigated with the aid of some probability models and distribution functions. For mitochondria, which are the most important cell components with respect to extra-chromosomal heredity, a four-phase model with computer programs was developed. The complete arithmetical results total 15,000 pages from a fast printer. For the jobs a CPU-time of 500 hours, using a SIEMENS 4004 system, was required.     

A Mathematical Model for Bacterial Chemotaxis

A differential equation describing the chemotactic migration of a bacterial population in a fixed exponential gradient of attractant has been integrated using the appropriate boundary conditions. The solution predicts an initial bacterial accumulation at the concentration “knee” with the final distribution of bacteria approaching a time-independent state. Specific additional experiments to obtain further data for a rigorous test of the theory are suggested.     

一个人体运动的数学模型

本文采用L-E法和铰分解法研究了人体运动的数学模型问题,给出了一种人体运动的规范建模方法。该方法适用于多种拓扑结构形式的人体运动（如空翻、步行、滑行等）,所得方程具有适合于计算机程式求解的特点。     

A Mathematical Model of the Human Respiratory Control System

The respiratory system exhibits the properties of a control system of the regulator type. Equations describing this biological control system have been derived. Transient and steady-state solutions for various CO₂ and O₂ step input disturbances were obtained utilizing a digital computer and are compared with experimental results. The effectiveness of the respiratory system as a regulator is investigated. Further extensions of the model are suggested.     

A Mathematical Model of Idiopathic Pulmonary Fibrosis

Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs.     

A Mathematical Model of Leaf Carbon Metabolism

A dynamic mechanistic mathematical model of C₃ leaf carbon metabolism,incorporating the Calvin cycle with starch and sucrose synthesisand degradation, is proposed. The model consists of a systemof non-linear differential equations based on biochemical andphysiological assumptions. An analytical steady-state solution,with interesting mathematical properties that are interpretedbiologically, is presented and shown to be stable. The systemequations are integrated numerically, and an approximate analyticalsolution to the sucrose sub-system is derived. Some resultsof the model are compared with experimental data. Mathematical model, Calvin cycle, leaf carbon metabolism, photosynthesis, differential equations     

A Mathematical Model of Photorespiration and Photosynthesis

A comprehensive mathematical model of C₃ leaf carbon metabolism,involving the Calvin cycle and the glycolate and glycerate pathwaysof photorespiration, is formulated in terms of a system of non-lineardifferential equations. A steady state, which is found to beeffectively stable, is derived. The model behaves realisticallywhen tested under varying external carbon dioxide and oxygenconcentrations: photosynthesis is inhibited by higher oxygenlevels, while photorespiration is inhibited by higher carbondioxide levels. Calvin cycle, differential equations, glycolate pathway, mathematical model, photorespiration, photosynthesis     

A Continuum Mathematical Model of the Developing Murine Retinal Vasculature

Angiogenesis, the process of new vessel growth from pre-existing vasculature, is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis is also a key regulator of pathogenesis in many clinically important disease processes, for instance, solid tumour progression and ocular diseases. Over the past 10–20 years, tumour-induced angiogenesis has received a lot of attention in the mathematical modelling community and there have also been some attempts to model angiogenesis during wound healing. However, there has been little modelling work of vascular growth during normal development. In this paper, we describe an in silico representation of the developing retinal vasculature in the mouse, using continuum mathematical models consisting of systems of partial differential equations. The equations describe the migratory response of cells to growth factor gradients, the evolution of the capillary blood vessel density, and of the growth factor concentration. Our approach is closely coupled to an associated experimental programme to parameterise our model effectively and the simulations provide an excellent correlation with in vivo experimental data. Future work and development of this model will enable us to elucidate the impact of molecular cues upon vasculature development and the implications for eye diseases such as diabetic retinopathy and neonatal retinopathy of prematurity.     

A Mathematical Model of the Inflammatory Response to Pathogen Challenge

The human body’s immune response to bacterial challenge, even when successful in controlling the infection, can result in negative consequences for the host, including reduced functionality of associated tissues. We present and analyze a low-dimensional mathematical model of this immune response to pathogen invasion, incorporating the coordinated actions of active immune cells, and both pro- and anti-inflammatory cytokines. The model simulates both the positive (pathogen reduction) and negative (local tissue dysfunction) effects of the immune response and includes the important role of immunologic memory in the process of a return to stasis. This differential equation-based model is sufficiently general to be applicable to a wide range of human tissues and organs.     

一个新的养分效应数学模型

在养分效应研究中,多采用二次抛物线模型,从容（1991）在米氏方程的基础上提出一个改进抛物线模型,这两种模型都是对称性模型,也即是把养分正负效应的速率视为相同,而大多数实际情形并非如此．本文建立了一个反映养分效应普遍现象的非对称性模型,两个应用实例表明新模型较之原来的模型无论在拟合度（残差平方和）还是在生物学意义方面都具有明显的优越性．     

Anastral Spindle Assembly: A Mathematical Model

Assembly of an anastral spindle was modeled as a two-stage process: first, the aggregation of microtubule foci or asters around the chromosomes, and second, the elongation of cross-linked microtubules and onset of bipolarity. Several possibilities involving diffusion and transport were investigated for the first stage, and the most feasible was found to be binding of the asters to cytoskeletal filaments and directed transport toward the chromosomes. For the second stage, a differential-equation model was formulated and solved numerically; it involves cross-linking of microtubules with those aligned with the spindle axis and between microtubules bound to different chromosomes, and sliding of microtubules along the spindle axis to elongate the spindle. Ncd was postulated to perform both functions. The model shows that spindle formation begins with rapid cross-linking of microtubules, followed by elongation, which continues until the population of microtubules aligned with the spindle axis is depleted and microtubules cross-linking different chromosomes dominate. It also shows that when sliding is inhibited, short bipolar spindles still form, and if clustering is enhanced, normal-length spindles can form, although requiring longer assembly time. These findings are consistent with spindle assembly in live wild-type and ncd mutant Drosophila oocytes.     

A Mathematical Model for Evolution and SETI

Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f_l in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f_l is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually “an infinity”) of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.     

品种综合评价的数学方法

品种的好坏、优劣直接影响农业生产,因此,选育的新品种在投入生产前需要进行品比实验、生产试验和品种鉴定。这些工作实际上就是对选育的新品种进行综合的客观评价。基于这种需要,本文给出了一种建立在主成分分析基础上的综合评价数学方法。应用这种方法对家蚕３０个品种进行综合评价,获得了与实际情况相当吻合的评价结果。根据评价值Ａκ,将这３０个家蚕品种分为４大类,Ａκ〉７．００的为优秀品种,７．００〉Ａκ〉－７．００的为低劣品种,而Ａκ〈－７．００则为极低劣品种。