Abstract
The structure of various immune processes are studied. While the overall feedback systems are seen to be highly nonlinear, distributed and stochastic, the basic open-loop processes in many cases are bilinear. This opens the door for the application of numerous new theories and methodologies which are being derived or have been developed for bilinear systems BLS and so-called affine systems which are a subclass of BLS.
Research reported here is supported by US National Science Foundation Grant No. ENG-74-15530-AO1
On leave from Oregon State Uni., Corvallis, OR97331, USA, until June 1979.
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References
Bell, G.I., “Mathematical Model of Clonal Selection and Antibody Production”, J. Theor. Biol. 29, 191–232, (1970).
Bell, G.I., “Mathematical Model of Clonal Selection and Antibody Production, II”, J. Theor. Biol. 33, 339–378, (1971).
Bell, G.I., “Model for the Binding of Multivalent Antigen to Cell”, Nature 248, 430–431, (1974).
Bell, G.I., and DeLisi, C.P., “Antigen Binding to Receptors on Immunocompetent Cells. I. Simple Models and Interpretation of Experiments”, Cell Immunol. 10, 415–431, (1974).
Bell, G.I., Perelson, A.S., and Pimbley, G.H., Jnr., Eds. Theoretical Immunology, Marcel Dekker, New York, (1978).
Brockett, R.W., “On the Reachable Set for Bilinear Systems”, in Variuable Structure Systems (Ruberti and Mohler, Eds.), Springer-Verlag, New York, 54–63, (1975).
Bruni, C., Giovenco, M., Koch, G., and Strom, R., “The Immune Response as a Variable Structure System”, in Variable Structure Systems with Application to Economics and Biology, (A. Ruberti and R.R. Mohler, Eds.), Springer-Verlag, New York, (1975).
Bruni, C., Giovenco, M., Koch, G. and Strom, R., “Modeling of the Immune Response: A System Approach”, in Bell, G.I., et al, Eds., 379–414, (1978).
DeLisi, C., Antigen-Antibody Interactions, Springer-Verlag, New York, (1976).
Gatica, S.A. and Waltman, P., “A threshold Model of Antigen — Antibody Dynamics”, Proc. IEEE Decision and Control Conf., San Diego, (1979).
Gear, C.W., “DIFSUB for Solution of Ordinary Differential Equations”, Comm. ACM 14, 185–190, (1971).
Hege, J.S., and Cole, L. J., “Mathematical Model Relating Circulating Antibody and Antibody Forming Cells”, J. Immunol., 94, 34–40, (1966).
Hoffmann, G.W., “A Theory of Regulation and Self-Nonself Discrimination in an Immune Network”, Eur. J. Immunol. 5, 50–75, (1975).
Hoffmann, G.W., “A Theory of Regulation and Self-Nonself Discrimination in an Immune Network”, Proc. IEEE Decision and Control Conf., San Diego, (1979).
Jerne, N.K., “Clonal Selection in a Lymphocyte Network”, in Cellular Selection and Regulation in the Immune Response (Edelman, Ed.), Raven, New York, (1974).
Jilek, M. and Sterzl, J., “Modeling of Immune Response”, in Morphological and Functional Aspects of Immunity, Plenum, New York, 333–349, (1971).
Jilek, M., “Immune Response and Its Stochastic Theory”, Proc. IFAC Sympos. Sys. Identif., the Hague, 209–212, (1973).
Merril, S.J., “A Geometric Study of B-Cell Stimulation and Humoral Response”, Proc. Int'l Conf. Nonlin. Sys. and Applic., Academic Press, (1977).
Marchuk, G.F., “An Immunological Model of Virus and Bacterial Diseases”, Proc. 8th IFIP Conf., Optimization Techniques, Würzburg, Springer-Verlag, New York, (1977).
Mohler, R.R., “Bilinear Control Processes, Academic Press, New York, (1973).
Mohler, R.R., “Biological Modeling with Variable Compartmental Structure”, IEEE Trans.Auto. Control AC19, 922–926, (1974).
Mohler, R.R., Barton, C.F. and Hsu, C.S., “System Theoretic Models in Immunology”, Proc. 1975 IFIP Optimization Conf., Nice, Springer-Verlag, New York, (1976).
Mohler, R.R., Barton, C.F., “Compartmental Control Model of the Immune Process”, Proc. 8th IFIP Conf. Optimization Tech., Würzburg, Springer-Verlag, New York, (1977).
Mohler, R.R., Barton, C.F., and Hsu, C.S., “T and B-Cell Models in the Immune System”, in Bell, G.I., et al., Eds., 415–436, (1978).
Mohler, R.R., and Hsu, C.S., “T-B Cell Control Processes in Immunology”, IEEE Decision and Control Conf., San Diego, (1979).
Mohler, R.R., and Rao, V.K., “BLS Identification by Orthogonal Functions with Application to Immunology”, Proc. IEEE Decision and Control Conf., Clearwater Beach, Elorida, (1976).
Richter, P.H., “A Network Theory of the Immune Response”, Eur. J. Immunol. 5, 350–354, (1975).
Smith, W.D., and Mohler, R.R., “Necessary and Sufficient Conditions in the Tracer Determination Compartmental System Order”, J. Theoret. Biol. 57, 1–21, (1976).
Waltman, P., “A Threshold Model of Antigen-Stimulated Antibody Production”, in G.I. Bell, et al, Eds., 437–454, (1978).
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Mohler, R.R. (1979). Bilinear control structures in immunology. In: Marchuk, G.I. (eds) Modelling and Optimization of Complex System. Lecture Notes in Control and Information Sciences, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004151
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DOI: https://doi.org/10.1007/BFb0004151
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