Summary
The mathematical model of the immune response, that the authors already deduced in a previous work, is here interpreted from the stand point of variable structure systems. In particular it is shown to correspond to an infinite dimensional bilinear system in a nonlinear instantaneous feedback loop. This might help in investigating some basic system theoretic properties of the model which on their own would cast more light on the behaviour of the physical process.
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References
P. Abramoff, M. Lavia, Biology of the Immune Response. Mc Graw-Hill, 1970.
B.Davis, R.Dulbecco, H.N.Eisen, H.S.Ginsberg, W.B.Wood jr., Microbiology. New York, Harper and Row, 1967.
Cold Spring Harbor, Symp. Quant. Biol. 32, 1967.
F.M. Burnet, The Clonal Selection Theory of Immunity. Nashville: Vanderbilt University Press and Cambridge: Cambridge University Press, 1959.
R.N. Pinckard and D.M. Weir, Equilibrium Dialysis and Preparation of Hapten Conjugates, in Handbook of Experimental Immunology. D.M. Weir (edt.). Blackwell Scientif. Publ.,Oxford, 1967, 493 - 526.
C.Bruni, M.A.Giovenco, G.Koch, R.Strom, A Dynamical model of the immune response. Rep. n.74-22, July 1974, Istituto di Automatica, University of Rome. To appear on Math. Biosciences.
R.J. Goldberg, A Theory of Antibody. Antigen reaction. I. Theory for reaction of multivalent antigen with bivalent and univalent antibody, J. Am. Chem. Soc. 74, 1952, 5715 - 5725.
G.J.Bell, Mathematical model of clonal selection and antibody production,J. Theor. Biol., 29, 1970, 191-232.
G.J.Bell, Mathematical model of clonal selection and antibody production II,J. Theor. Biol., 33, 1971, 339-378.
G.J.Bell, Mathematical model of clonal selection and antibody production III. The cellular basis of immunological paralysis,J. Theor. Biol., 33, 1971, 379-398.
G.W. Siskind and B. Benacerraf,Cell selection by antigen in the immune response, Adv. Immunol., 10, 1969, 1 - 50.
T.P. Werblin and G.W. Siskind, Distribution of Antibody affinities. Technique of measurement, Immunochemistry, 9, 1972, 987 - 1011.
F.Karush, Immunologic specificity and molecular structure Adv. Immunol., 2, 1962, 1-40.
C.Larralde, S.Farder, Confidence intervals for affinity constant heterogeneity indices and concentration of reactive sites estimated by the 50% ammonium sulphate method on rat’s antiDNP sera Immunochemistry 1972, v. 9, 699 - 707.
G.Koch, A Realizability Theorem for Infinite Dimensional Bilinear Systems Ricerche di Automatica, v. 3, n.3, Dicembre 1973.
G.E. Laws, V.lausmiikantham, Differential Equations in Abstract Spaces. Acadenic Press, 1972.
K. Yosida, Functional Analysis. Springer Verlag, 1968.
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Bruni, C., Giovenco, M.A., Koch, G., Strom, R. (1975). The Immune Response as a Variable Structure System. In: Ruberti, A., Mohler, R.R. (eds) Variable Structure Systems with Application to Economics and Biology. Lecture Notes in Economics and Mathematical Systems, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-47457-6_14
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DOI: https://doi.org/10.1007/978-3-642-47457-6_14
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