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At least 1,693 records · Page 94Linked to original sources
PubMed2000

A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in china.

BACKGROUND: Before universal infant immunization against hepatitis B virus (HBV) in 1986 China was a region endemic for HBV infection. The prevalence of HBV infection in the population was about 60% and the proportion of chronic HBV carriers around 10%. These HBV carriers could progress to chronic hepatitis B, cirrhosis, and primary hepatocellular carcinoma. Since 1976, large-scale sero-surveys of HBV infection have been carried out and a lot of data have been collected. METHOD: This paper describes a mathematical model developed to predict the dynamics of HBV transmission and to evaluate the long-term effectiveness of the vaccination programme. We used a compartment model expressed by a set of partial differential equations based on the characteristics of HBV infection. RESULTS: All parameters, expressed in the model as a non-linear function of age and time since vaccination, were estimated using sero-survey data. The model fits well with both pre-vaccination and post-vaccination sero-surveys. The observed and estimated age-specific prevalence rates of HBV infection and HBV carriage agree with each other. According to our model, if all newborns are vaccinated according to schedule, the rate of HBV carriage will decline sharply over time to 0.2% in 70 years. By then, the ratio of acute hepatitis B will be less than 0.5% and the ratio of chronic hepatitis B will be around 5%. CONCLUSIONS: The results suggest that HBV infection in China can be controlled in just one generation, and eventually eliminated. Our model shows that vaccination coverage is the most important indicator for the elimination of HBV transmission. The higher the vaccination coverage, the better the long-term effectiveness of immunization. Thus, the key to controlling and eliminating HBV transmission in China is to find ways to immunize all infants throughout the country, especially in poor, rural areas.

Adolescent↗
PubMed1984

A mathematical model of exoprotein production in bacteria.

We present a simple mathematical model for the synthesis of extracellular proteins by a class of bacteria which secrete significant quantities of this exoprotein in late-exponential and stationary phases. This model is the simplest generalization of Michaelis-Menten kinetics (the Monod model) and agrees well with laboratory experiments in batch culture. The model may serve as a simple prototype for the analysis of certain virulent bacterial infections in vivo, particularly that of Pseudomonas aeruginosa in burn wounds.

Bacteria↗
PubMed1984

A mathematical model for a thermal clearance probe.

We introduce a new mathematical model for a thermal clearance probe for the measurement of skin blood flow. It is concluded that the technique is more sensitive to differences in the thermal conductivity of the skin than to differences in blood flow. The depth of measurement is also considered.

Body Temperature Regulation↗
PubMedDate not supplied

Setting up waiting-time targets to satisfy patients: an application of mathematical programming.

An out-patient-waiting-time standard has been set up by the government in the Patient's Charter and the standard is supposed to be effective nationwide indiscriminately. This standard is static and does not take into account local variations in patient expectations, patient unpunctualities in keeping their appointments, changing demand, and resource (or budget) constraints. Therefore, it is not surprising that many acute hospitals or Trusts (including the best-known teaching hospitals) have failed to achieve a satisfactory performance against this standard. In this paper, we argue that, while regarding this standard as the government's expectation, local out-patient-waiting-time targets could be set up more comprehensively each year on the basis of prevailing patient expectations, so that the most cost-effective (or optimal) quality is achieved instead of the ideal (or best) quality. We have also developed a mathematical-programming model which can be used to help determine the out-patient waiting-time targets in a systematic way, once the expected degrees of patient satisfaction are specified. A numerical example is provided to illustrate how the model works.

Ambulatory Care↗
PubMed1990

Some problems in the mathematical modelling of erythrocyte sedimentation.

The rate at which red blood cells fall in vitro is used as a common clinical test, amongst others, for a number of pathological conditions. The use of this test is cast into doubt when one finds flaws in the underlying models and confusion over fundamental issues such as the aggregation of the red blood cells. Both of these deficiencies are evident in an otherwise innovative publication by Huang et al. (1971). In examining the mathematics of this relatively unknown study, it is found that the Huang model resembles certain moving-boundary problems. The consequences of this observation are discussed.

Blood Sedimentation↗
PubMed1991

A mathematical model for the rate of oxygenation of blood in pulmonary capillaries using nth-order one-step kinetics of oxygen uptake by haemoglobin.

A mathematical model is described for the process of gas exchange in pulmonary capillaries by taking into account the transport mechanisms of molecular diffusion, convection, and the facilitated diffusion due to haemoglobin. The nth-order one-step kinetics of oxygen uptake by haemoglobin has been incorporated. The rate k at which blood becomes oxygenated is determined by setting up an appropriate eigenvalue problem. This method eventually leads to a transcendental equation in k. A multiprecision technique due to Verma and Sharan (1980) is employed to obtain a physically acceptable solution. It is shown that, at equilibrium, the saturation of haemoglobin with oxygen computed from the analysis is fairly close to the data of Severinghaus (1966). It was found that 97.15% of the total haemoglobin combined with oxygen. The blood is oxygenated well before it leaves the pulmonary capillary. The dissolved oxygen takes longer to achieve equilibration whereas the carbon dioxide traverses a comparatively smaller distance in the capillary.

Biological Transport↗
PubMed1991

A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue.

Unless they are furnished with an adequate blood supply and a means of disposing of their waste products by a mechanism other than diffusion, solid tumours cannot grow beyond a few millimetres in diameter. It is now a well-established fact that, in order to accomplish this neovascularization, solid tumours secrete a diffusable chemical compound known as tumour angiogenesis factor (TAF) into the surrounding tissue. This stimulates nearby blood vessels to migrate towards and finally penetrate the tumour. Once provided with the new supply of nutrient, rapid growth takes place. In this paper, a mathematical model is presented for the diffusion of TAF into the surrounding tissue. The complete process of angiogenesis is made up of a sequence of several distinct events and the model is an attempt to take into account as many of these as possible. In the diffusion equation for the TAF, a decay term is included which models the loss of the chemical into the surrounding tissue itself. A threshold distance for the TAF is incorporated in an attempt to reflect the results from experiments on corneal implants in test animals. By formulating the problems in terms of a free boundary problem, the extent of the diffusion of TAF into the surrounding tissue can be monitored. Finally, by introducing a sink term representing the action of proliferating endothelial cells, the boundary of the TAF is seen to recede, and hence the position and movement of the capillaries can be indirectly followed. The changing concentration gradient observed as the boundary recedes may offer a possible explanation for the initiation of anastomosis. Several functions are considered as possible sink terms and numerical results are presented. The situation where the tumour (i.e. the source of TAF) is removed is also considered.

Angiogenesis Inducing Agents↗
PubMed1992

Mathematical models of wound healing in embryonic and adult epidermis.

Epidermal wound healing occurs by quite different mechanisms in embryos and adults. In the latter case, it has long been known that cells crawl inwards via lamellipodia to close the defect. In the embryonic system, recent evidence suggests that healing may be caused by a quite different mechanism, namely the contraction of a cable of filamentous actin at the wound edge. The authors use mathematical modelling to investigate both systems. A mechanical model for the initial formation of the actin cable in embryonic epidermal wounds is presented, which incorporates the important phenomenon of stress-induced microfilament alignment. Also discussed is a reaction-diffusion model for the healing of adult wounds subject to autoregulation of cell division. In both cases, the results suggest possible biological mechanisms for key aspects of the healing process.

Actins↗
PubMed2005

Automating phase singularity localization in mathematical models of cardiac tissue dynamics.

Electrical wave-fronts are responsible for contraction in heart tissue. Rotary wave-fronts break up into daughter waves and it is this break up that is believed to underlie ventricular fibrillation. Mathematical methods abound for simulation of fibrillation, and localizing the core of rotary wave-fronts (the phase singularities) is key to characterizing the state of fibrillation and effectiveness of defibrillation in these models. We present a formal method for automating this process in these various models. Automation will allow for side-by-side comparisons of suggested mechanisms of fibrillation, comparison of various models of these mechanisms and faster evaluation of defibrillation strategies making use of these models.

Action Potentials↗
PubMed1996

Mathematical model of beta-lactam penetration into a biofilm of Pseudomonas aeruginosa while undergoing simultaneous inactivation by released beta-lactamases.

We present a mathematical model that describes penetration of an antibacterial agent into a bacterial biofilm and, in particular, the penetration of a beta-lactam compound into a biofilm of Pseudomonas aeruginosa. As well as dealing with this penetration, and the consequent bacterial lysis, the model considered diffusion of the released beta-lactamases in the extracellular space and the consequent inactivation there of further incoming antibiotic; it also allowed for any chosen fraction of the total beta-lactamase to be permanently accessible to exogenous substrate. The modelling scheme was validated against analytical solutions under appropriately simplified conditions. Using published experimental data we show here that lysis of cells in the surface layers of a film could have an important protective effect on the viability of underlying bacteria, especially in thick biofilms.

Anti-Bacterial Agents↗
PubMed2005

Mathematical model--tell us the future!

Studying bacterial resistance has direct importance for the antimicrobial treatment of individual patients. In addition, surveillance data pooled from individual diagnostic reports help physicians to choose the most effective drug for empirical therapy. However, this is not the limit of what can be done with the resistance data. There is an increasing need to synthesize the available strands of data in order to construct mathematical models that can be used as tools to predict the likely outcomes of various antibiotic policy options.

Anti-Bacterial Agents↗
PubMed1990

Autogenous and anautogenous mosquitoes: a mathematical analysis of reproductive strategies.

A mathematical model is presented to compare the relative advantage of an anautogenous mosquito population (in which females blood feed throughout life) with an obligate autogenous population (in which females do not feed on blood for the first oviposition). The advantage is measured by the intrinsic rate of natural increase. Autogeny was more advantageous than anautogeny when host searching time (ts), the ratio of the fecundity of the first autogenous to anautogenous oviposition (p), the fecundity in one anautogenous oviposition (n), or the instantaneous death rate of the adult population (D) was large, or when the preimaginal period (xo), the instantaneous death rate during the preimaginal period (D'), or survival during blood feeding (s) was low. The parameters most sensitive to the advantage of autogeny were ts, p, and s. The value of n was insensitive, and xo, D, and D' were intermediately sensitive to autogeny. Conditions when autogeny was advantageous were equivalent to conditions conducive to high autogeny rates in facultatively autogenous species, which alter the expression of autogeny depending upon environmental stimuli. Data on several facultatively autogenous species are discussed qualitatively and quantitatively to demonstrate the utility of our model in considering the evolution of autogeny and the autogeny rate.

Animals↗
PubMed1993

Dynamics of a mathematical model of Chrysomya megacephala (Diptera: Calliphoridae).

The laboratory population dynamics of Chrysomya megacephala (F.) was explored with a mathematical model of density-dependent growth. Fecundity and survival decreased significantly as a function of larval density. Parameters in the exponential regressions fitted to the fecundity and survival data were incorporated into a finite-difference equation that incorporates the delayed effect of larval density on fecundity and survival of adults. The theoretical population model of C. megacephala showed cyclic behavior with a stable limit cycle of two points for adults and immatures.

Analysis of Variance↗
PubMed2003

Mathematics of quantitative kinetic PCR and the application of standard curves.

Fluorescent monitoring of DNA amplification is the basis of real-time PCR, from which target DNA concentration can be determined from the fractional cycle at which a threshold amount of amplicon DNA is produced. Absolute quantification can be achieved using a standard curve constructed by amplifying known amounts of target DNA. In this study, the mathematics of quantitative PCR are examined in detail, from which several fundamental aspects of the threshold method and the application of standard curves are illustrated. The construction of five replicate standard curves for two pairs of nested primers was used to examine the reproducibility and degree of quantitative variation using SYBER Green I fluorescence. Based upon this analysis the application of a single, well- constructed standard curve could provide an estimated precision of +/-6-21%, depending on the number of cycles required to reach threshold. A simplified method for absolute quantification is also proposed, in which quantitative scale is determined by DNA mass at threshold.

DNA↗
PubMed1983

Mathematical modelling of malignant melanoma trends in Norway, 1953-1978.

Epidemiologic studies have documented a rapid rise in the mortality and incidence of malignant melanoma of the skin in many countries. This paper presents an analysis of malignant melanoma time trends in data from the Norwegian Cancer Registry, 1953-1978, by subsite and sex. The purpose of this study is to quantify previous qualitative analysis of the same data, mainly to distinguish birth cohort effects from time period effects. This analysis shows that time trends in malignant melanoma in Norway can be explained economically by a common age effect and a separate cohort effect for each subsite in both sexes or alternatively, by a common cohort effect but different age effects for each sex and subsite. In neither case is a time period effect required. Mathematical modelling can never fully explain any situation exactly and it is more than likely that the increases observed have been produced by a measure of both extreme descriptions. The different cohort effects and age effects are discussed in terms of their implications for etiology.

Adolescent↗
PubMed1991

Chromosome analysis in human oocytes unfertilized in vitro: a mathematical model for the estimation of the first meiotic non-disjunction frequency.

The results of cytogenetic analysis of unfertilized human oocytes in an in-vitro fertilization programme are to a large extent influenced by the methodology used. Exact conclusions cannot be drawn due to technical and interpretational errors. A mathematical model was constructed, therefore, to estimate the weight of these errors and to calculate the exact frequency of first meiotic non-disjunction in IVF oocytes. Of 246 prepared oocytes only 105 could be karyotyped exactly. Using the classical method of calculation, an aneuploidy frequency of 39% was obtained. By applying the maximum likelihood method a correlation between the frequency of first meiotic non-disjunction and the interpretational error level was found. Loss of chromosomes by anaphase lagging seemed to be undetectable, but the probability of chromosome loss due to fixation and unhomogeneous spreading was found to be 20%. Accepting an error level of 10-20%, the true non-disjunction frequency expected should range between 20 and 40%. This model yields a standard curve which can offer a basis for comparison of results obtained in different studies.

Anaphase↗
PubMed1977

Mathematical analysis of ligand-induced monomerization and dimerization in the monomer dimer equilibrium of proteins. Application to D-amino acid oxidase.

We have mathematically analyzed ligand-induced monomerization and dimerization in a protein monomer-dimer equilibrium system, in which the monomer has one and the dimer two binding sites. These dimer sites have the same binding constants for the first ligand but may cooperatively interact when one of them is occupied by a ligand molecule. In this system, the apparent dimerization constant and the apparent molecular weight are functions of free ligand concentration, and depend on the intrinsic binding constants of the ligand molecule to the monomer and the dimer. The behavior of these functions is classified into 17 cases according to the values of the three intrinsic binding constants, and some calculated examples are shown graphically for selected parameters. The theory was also applied to D-amino acid oxidase [EC 1.4.3.3], a flavoprotein, and the pH dependence of the apparent dimerization constant and the apparent molecular weight in the presence of ligand, p-aminobenzoate, were studied theoretically using parameters obtained in our previous experiments (5).

4-Aminobenzoic Acid↗
PubMed1987

Experimental evidence supporting a mathematical theory of the physiological mechanism regulating follicle development and ovulation number.

In higher vertebrates, follicular development is regulated so that the number of follicles that periodically mature and ovulate is controlled within a narrow range. Lacker has proposed a simple mathematical model of follicle development that can account for the regulation of ovulation number. To support the assumption of the theory that follicle interactions are mediated by estradiol acting as a chemical messenger to communicate follicular maturity to the pituitary and other follicles, we have presented data to demonstrate that in the rabbit physiological concentrations of circulating estradiol inhibit follicle maturation. Implants containing estradiol were placed subcutaneously after surgical rupture of the existing follicles that were 1 mm in diameter or larger. Serum estradiol concentrations were maintained near physiological concentrations by the implants. Concentrations of circulating estradiol were 74 +/- 5.7 pg/ml in the untreated groups, whereas the concentrations with the implants were increased by approximately 50 pg/ml/implant over this basal concentration with a range of 100-300 pg/ml. In the control groups, the average number of follicles before surgical rupture was 27 +/- 2.9 and there was no significant difference (p greater than 0.05) in the number of follicles, 26 +/- 1.9, three days after follicle rupture. The follicles ranged in size from 1 mm to 4 mm, and only those over 3 mm were considered mature. In the first group of animals with implants, the total number of follicles before surgery was 19 +/- 3; three days after follicle rupture, the number of follicles was only 9 +/- 1.1.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗