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  • 1
    Electronic Resource
    Electronic Resource
    Complex behaviours of AB model describing idiotypic network (1994)
    Springer
    Bulletin of mathematical biology 56 (1994), S. 323-336 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simple chemical model of the idiotypic network of immune systems, namely the AB model, has been developed by De Boeret al. The complexity of the system, such as the steady states, periodic oscillations and chaotic motions, has been examined by the authors mentioned above. In the present paper, the periodic motions and chaotic behaviours exhibited by the system are intuitively described. To clarify in which parameter domains concerned the system exhibits periodic oscillations and in which parameter domains the system demonstrates chaotic behaviours the Lyapounov exponent is explored. To characterize the strangeness of the attractors, the fractal dimension problem is worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460645
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Contributions of memory B cells to secondary immune response (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 713-731 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461848
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Multiple solutions of a model describing cancerous growth (1988)
    Springer
    Bulletin of mathematical biology 50 (1988), S. 1-17 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Multiple solutions of a model describing immune surveillance against cancer are studied. The model was proposed by R. Lefever and co-workers. A limit cycle solution and two kinds of wave front solutions are worked out by means of a perturbation method. The problem of nucleation concerning this model is studied by a singular-perturbation technique. In addition, the pulse wave solution is also found by numerical simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459974
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  • 4
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    A Cellular Automaton Model of Cancerous Growth (1993)
    Elsevier
    Details
    Publication Date: 1993-03-01
    Print ISSN: 0022-5193
    Electronic ISSN: 1095-8541
    Topics: Biology
    Published by Elsevier
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