Showing papers in "Bulletin of Mathematical Biology in 1991"

TL;DR: In order to apply the theory developed here to the tropical tuna fishery, it will be necessary to compile statistics of catch, abundance and intensity of fishing over a considerable series of years, beginning as early in the history of the fishery as possible.

TL;DR: A mathematical investigation has been made of the progress of an epidemic in a homogeneous population, finding a threshold density of population is found to exist, which depends upon the infectivity, recovery and death rates peculiar to the epidemic.

TL;DR: The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms and the law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats.

TL;DR: Quantitative productivity data provide a basis for enunciating certain trophic principles, which, when applied to a series of successional stages, shed new light on the dynamics of ecological succession.

TL;DR: In this article, the authors examined the economic theory of natural resource utilization as it pertains to the fishing industry and showed that most of the problems associated with the words "conservation" or "depletion" or ''overexploitation" in the fishery are, in reality, manifestations of the fact that the natural resources of the sea yield no economic rent.

TL;DR: In this paper, a mathematical analysis of the prevalence of a disease in a population from which certain individuals are being removed as the result of the disease, whilst fresh individuals were being introduced as a result of birth or immigration.

TL;DR: The mathematical investigation of the progress of an infectious disease in a community of susceptible individuals has been extended to include the case where members of the community are removed as the result of some general cause of death acting according to constant non-specific death rates, as well as by death from the disease itself.

TL;DR: Taxation would be a more economic method than publicly ordained inefficiency in the case of purely commercial activities such as mining and fishing for profit, if not also for sport fishing.

TL;DR: It is shown that the model is equivalent to a dynamical system with stochastic dynamics, the Annealed Random Map Model, and it is possible to solve exactly for the genealogy statistics and for the genetic variability of the population.

TL;DR: In this article, the authors reviewed the work of Kermack and McKendrick on the development of simple mathematical models of the transmission dynamics of viral and bacterial infectious agents within population of hosts.

TL;DR: This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

TL;DR: This concluding survey of the problems considered in the Symposium naturally falls into three sections; a rather detailed analysis of one particular problem is given, and possible directions for future research are discussed.

TL;DR: In this paper, it was shown that with a constant concentration of S 0 a necessary condition for instability at a critical point (steady state) is β 1 β 2 … β n − 1 φ α 1 α 2 … α n ⩾ ( sec ⁡ π / n ) n, where βi is the order of reaction (with respect to the concentration Si of Si) of the formation of Si + 1 from Si; αi is a combined processes of metabolic conversion and all other processes removing Si.

TL;DR: Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance the understanding of this complex phenomenon.

TL;DR: A mathematical model of tumor growth including autocrine and paracrine control has been developed and the mode is being extended to include the description of heterogeneous tumors, within which subpopulations can express differential degrees of growth activity.

TL;DR: The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod's classical chemostat model, which allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates.

TL;DR: It is shown that, under certain assumptions, a critical point is always stable in a single two-step enzymatic process (formation of enzyme-substrate complex, followed by conversion to product, then loss of product) with slow negative feedback by competitive product inhibition.

TL;DR: The distribution of the kinetic rates that produces the stretched exponential probability distribution, exp(−atb) where 0 is the kinetic rate constants, is derived.

TL;DR: A statistical framework is proposed for analysing DNA fingerprint data from experiments aimed at constructing ordered clone physical maps of chromosomes and a solution to the fundamental problem of deciding whether or not two randomly selected clones overlap is developed.

TL;DR: It is shown that the distance geometry approach has some nice geometry not associated with other methods that allows one to prove detailed results with regard to the location of local minima and is exploited to develop some algorithms which are faster and find more minima than the algorithms presently used.

TL;DR: The existence of a malignant tumour in the underlying tissues of epidermis of a human body is considered and the effect of this factor is studied on the temperature profiles of the skin.

TL;DR: A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable, resulting in a Riccati differential equation whose six solutions control the amount and degree of taper found in the equivalent cable model.

TL;DR: Kliemann et al. as discussed by the authors used the Wald statistics for χ2-test to predict branching patterns of dendritic trees and the distribution of the maximal order of the tree.

TL;DR: The construction of a neural network that can learn and identify the quality (direction cosines) of an input vector or extract information from a sequence of correlated input vectors is constructed.

TL;DR: A method for obtaining delay histograms for the time course of neurotransmitter release is presented, derived from the measured psc and the mpsc by means of a simple, quick, mathematical procedure.

TL;DR: This paper synthesizes the theory and examines effects of different immigration/extinction rate-species diversity curves on original predictions from the theory by using the System Dynamics simulation modeling approach, and develops a comprehensive and generic model to incorporate a variety of recent modifications and extensions of the theory.

TL;DR: By calculation of 2341 coding regions of nucleic acid sequences it is demonstrated that about 2/3 of sequences has correlation length ≤2, 10% of sequences—correlation with 3-periodicity and others—long range aperiodic correlations.

TL;DR: In this paper, the imaging of aerial objects by one or two submerged eyes was studied and the aerial binocular image field was determined for pairs of submerged eyes in horizonal and vertical planes.