Mathematical model of histamine bronchospasm]

A mathematical model of changes in histamine concentration in the wall of human bronchiole was constructed. The parameters of the model adequately characterize the state of patients with bronchial asthma.     

Mathematical model of the immune response]

A model of immune reaction is suggested, ahich takes into account the delay in the development of an immune response. The model depending on parameters values describes: an asymptotic decrease of antigene quantity, approach of its quantity towards constant value, periodic course of the illness, unlimited growth of the antigene quantity. It is shown that the course of the reaction essentially depends on the duration of delay. Parameters regions corresponding to different regimes are determined.     

Mathematical model for the control and standardization of discs]

Analysis of tetracycline and erythromycin diagnostic discs manufactured in the USSR showed their conformity with the requirements of the USA Federal Register. Comparison of the antibiotic amounts extracting and diffusing from the discs showed that as an average 92 and 90 per cent of the extracted amounts of erythromycin and tetracycline respectively diffused into the agar. Subsequently, it is desirable that on control testing of the disc quality both the similarity of the antibiotic content in the discs and the real amount of the antibiotic diffusing into the agar should be considered. A statistically reliable correlation between the values of the growth inhibition zones around the discs with definite and constant amounts of erythromycin, tetracycline or oxacillin and different resistance levels for every staphylococcal strain was found. On the basis of such a control system it is possible to divide the staphyloccal strains into the groups with high, low and intermediate resistance levels to the above antibiotics. However, it is not possible to use such data for accurate calculation of the value of the minimum inhibitory concentration of unknown strains because of a high value of the main error.     

Short-term dynamics of intertidal microphytobenthos biomass. Mathematical model]

We formulate a deterministic mathematical model to describe the dynamics of the microphytobenthos of intertidal mudflats. It is 'minimal' because it only takes into account the essential processes governing the functioning of the system: the autotrophic production, the active upward and downward migrations of epipelic microalgae, the saturation of the mud surface by a biofilm of diatoms and the global net loss rates of biomass. According to the photic environment of the benthic diatoms inhabiting intertidal mudflats, and to their migration rhythm, the model is composed of two sub-systems of ordinary differential equations; they describe the simultaneous evolution of the biomass 'S' concentrated in the mud surface biofilm--the photic layer--and of the biomass 'F' diluted in the topmost centimetre of the mud--the aphotic layer. Qualitatively, the model solutions agree fairly well with the in situ observed dynamics of the S + F biomass. The study of the mathematical properties of the model, under some simplifying assumptions, shows the convergence of solutions to a stable cyclic equilibrium, whatever the frequencies of the physical synchronizers of the production. The sensitivity analysis reveals the necessity of a better knowledge of the processes of biomass losses, which so far are uncertain, and may further vary in space and time.     

A mathematical model of postradiation autoimmunity

A mathematical model of cellular autoimmune process in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases.     

Hypothesis: a model for generalised autoimmunity

A detailed mechanism for the development of generalised autoimmunity is suggested, and the significance of the association between autoimmunity and leukemia is discussed.     

Mathematical model of the cytokinetics of erythropoiesis in mouse bone marrow and spleen]

The described model approximates the function of the erythropoietic system of the mouse to the function of a self-renewed cellular system, describable in the terms of cell population kinetics. The model is based on a number of experimentally proved ideas of contemporary haematology and arises from the assumption that there exists mutual negative influence between the cellular populations of the bone marrow and spleen. Considering the erythropoietic system in the mouse to be composed of two relatively independent parts - the bone marrow and spleen - the described model differs from the attempts so far made on the mathematical modelling of erythropoiesis.     

Mathematical model of children mortality

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.     

Mathematical model of visual perception

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.     

Mathematical model of self-cycling fermentation

This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation. (c) 1995 John Wiley & Sons, Inc.     

Mathematical model of immune processes

In the model the time lags of the antibody production and immune memory formation are taken into account explicitly. The antibody-antigen reaction is supposed to be very fast. The cases of a reproducing antigen as well as that of a non-reproducting antigen are considered. The conditions of the infinite increase of the antigen quantity and of the antigen elimination are obtained. For the rapidly reproducing antigen the latter condition includes the requirement for the time lag of the immune response to be not too short or not too long. In the case of the poorly catabolized non-reproducing antigen the cyclic appearance of the antibody producing cells due to the immune memory is described in the frame-work of the model.The mathematical structure of the model is similar to that of the Volterra-Lotka jequations. The only difference is the presence of the time lags in the non-linear terms. The time lags lead to the instability of the stationary state. In the prolonged reaction the antigen quantity may perform several oscillations before the elimination of the antigen.     

Mathematical model of honeycomb construction

We developed a mathematical model and an algorithm for numerical treatment of a model of honeycomb construction in a beehive. The model contains essential features of the bee-bee and bee-wax interactions, and in a qualitative way captures the dynamics of parallel comb construction. The construction is represented by a set of dynamical coupled partial differential equations for the density of bees situated on the hive ceiling, and the quantity of wax distributed by the bees. A spectral algorithm is invented for treatment of these equations, based on a modified thin-sheet gain scheme and a fast Fourier transform technique.Work at City College supported in part by the Army Research Office and the Department of Energy     

Mathematical model of retinal mosaic formation

The retina is one of the best examples of modular organisation in neural circuitry. This modular structure enables it to perform parallel processing. A mathematical model of the retina has been set up, focusing on mechanical features of retinal neurons and on the interaction and dendritic overlapping among retinal cells. The model focuses on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton is regarded as a structure in which elastic and rigid elements are combined according to the tensegrity concept. We have assumed that dendritic overlap takes place in such a way as to favour uniform retinal neurons' distribution and that dendritic overlap is the only cause of neuron's motion on the retinal surface. This overlap depends on the growth of the dendrites due to the cytoskeletic deformation. The results obtained are in agreement with experimental results that support the notion that local mechanical interaction and dendritic overlapping are capable to transform random cell distributions into regular mosaics.