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  • 1
    Digitale Medien
    Digitale Medien
    Complementary variational principles for diffusion problems with Michaelis-Menten kinetics (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 131-135 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462371
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Structural order and partial disorder in biological systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 137-141 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462372
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Primitivity of the product of two Leslie matrices (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 181-189 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464637
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Frequency analysis of time-varying elastance model of the left ventricle (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 173-180 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464636
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    The 9th Annual Northeast Biomedical Engineering Conference (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 901-901 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461068
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Book review (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 195-196 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1006/bulm.1997.0018
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    A mathematical model for fibroblast and collagen orientation (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 101-129 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integrodifferential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum of orientations and a continuous distribution of orientations with several maxima. The effect of altering the parameters in the system is explored, including the angular diffusion coefficient for the fibroblasts, as well as the strength and range of the interaction between fibroblasts and collagen. We find the initial conditions and the range of influence between the collagen and the fibroblasts are the two factors which determine the behavior of the solutions. The implications of this for wound healing and cancer are discussed including the conclusion that the major factor in determining the degree of scarring is the initial deposition of collagen.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1006/bulm.1997.0027
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  • 8
    Digitale Medien
    Digitale Medien
    Extinction times and phase transitions for spatially structured closed epidemics (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 215-230 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N 〉 N c where N c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1006/bulm.1997.0014
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    Book reviews (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 409-415 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1006/bulm.1997.0019
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  • 10
    Digitale Medien
    Digitale Medien
    The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 355-372 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract When directly transmitted infectious diseases are modeled assuming an everlasting induced immunity (and constant contact rate), there are well-established formulas to deal with, which is not true if we include the loss of induced immunity. In general, the immunity induced by the disease is everlasting. We propose a model considering the loss of immunity and present methods for the estimation of two epidemiological parameters: the force of infection and the basic reproduction ratio. We also analyze the effects of the loss of immunity on these parameters. Based on these results, we conclude that reinfection can play an important role in highly vaccinated populations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1006/bulm.1997.0031
    Standort Signatur Erwartet Verfügbarkeit
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