Abstract
Interest in mathematical immunology has been growing. This is reflected in the several monographs that have been published and the conferences that have been held lately. Examples of recent work are available in Bell, Perelson and Pimbley (1978), Merrill (1980), Mohler, Bruni and Gandolfi (1980), DeLisi (1983), Marchuk (1983), Marchuk and Belykh (1983), Marchuk, Belykh and Zuev (1985), and Mohler (1987). The mathematical study of events that are involved at the cellular level in transmission of information seems to be generally missing in the literature, the reference here being to the study of recirculation of lymphocytes. These events functionally interconnect many of the parts of the immune response by physically and biochemically conveying information and providing defense. This paper is concerned with a particular approximation for the distribution of recirculating lymphocytes. Besides the healthy state of an organism such distribution is also of significance for disease states. Any maldistribution could be a symptom of a disease, for example, in humans, Hodgkin’s disease, hepatitis B, psoriasis, and chronic lymphocytic leukemia. Thus quantification of the norm of distribution pattern, statistical analysis of the deviation from the norm and/or maldistribution, and modeling and identification of the models can be useful in diagnosis and estimation of disease severity, and in the classification and differential diagnosis of abnormalities in migratory patterns of lymphocytes.
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References
Bell, G.I., A.S. Perelson, and G.H. Pimbley ,Jr. (1978), “Theoretical Immunology,” Immunology Series (New York: Marcel Dekker, Vol. 8
DeLisi, C. (1983), “Mathematical Modeling in Immunology,” Ann. Rev. Biophys. Bioeng., 12, 117–138.
DeBoer, R.J., P. Hogeweg, et al. (1985), “Macrophage T Lymphocyte Interactions in the Anti-Tumor Immune Response,” J. Immunology, 134, 1–11.
DeSousa, M. (1981), Lymphocyte Circulation: Experimental & Clinical Aspects, (New York: John Wiley & Sons).
Feigin, P.D., and R.L. Tweedie (1985), “Random Coefficient Autoregressive Processes: A Markov Chain Analysis of Stationarity and Finiteness of Moments,” J. Time Series Anal., 6(1), 1–14.
Fung, Y.C. (1984), Biodynamics: Circulation, (New York: Springer-Verlag).
Lancaster, P. (1969), Theory of Matrices, (New York: Academic Press).
Lipster, R.S., and A.N. Shiryayev (1977), Statistics Processes I — General Theory (New York: Springer-Verlag).
Lipster, R.S., and A.N. Shiryayev (1978), Statistics Processes II — Applications (New York: Springer-Verlag).
Marchuk, G.I. (1983), Mathematical Models in Immunology Translation, Series in Mathematics and Engineering (New York: Optimization Software).
Marchuk, G.I., and L.N. Belykh (eds.) (1983), “Mathematical Modeling in Immunology and Medicine,” Proceedings of the IFIP-TC 7 Working Conference on Mathematical Modeling in Immunology & Medicine, Moscow, USSR, 5–11 July, 1982 (Amsterdam: North-Holland Publishing Co.).
Marchuk, G.I., L.N. Belykh, and S.M. Zuev (1985), “Mathematical Modelling of Infectious Diseases,” Problems of Computational Mathematics and Mathematical Modelling, Advances in Science and Technology in U.S.S.R. (Mathematics and Mechanics Series), Eds. G.I. Marchuk and V.P. Dymnikov (Moscow: Mir Publishers, 223–240.
Merrill, S.J. (1980), “Mathematical Models of Humoral Immune Response,” Modeling and Differential Equations in Biology, (Lecture Notes in Pure & Applied Mathematics), Ed. T.A. Burton (New York: Marcel Dekker), 13–50.
Mohler, R.R. (1973), Bilinear Control Processes (New York: Academic Press).
Mohler, R.R. (1987), “Foundations of Immune Control and Cancer,” Recent Advances in System Science, Ed. A.V. Balakrishnan (New York: Optimization Software, Inc.), (to appear).
Mohler, R.R., C. Bruni, and A. Gandolfi (1980), “A Systems Approach to Immunology,” Proc. IEEE 68(8), 964–990.
Nicholls, D.F., and B.G. Quinn (1982), “Random Coefficient Autoregressive Models: An Introduction,” Lecture Notes in Statistics (New York: Springer-Verlag), Vol. 11.
Roitt, I. (1974), Essential Immunology (Oxford and London: Blackwell Scientific), 162.
Rubinow, S.I. (1975), Introduction to Mathematical Biology (New York: John Wiley and Sons).
Smith, M.E., and W.L. Ford (1983), “The Recirculating Lymphocyte Pool of the Rat: A Systematic Description of the Migratory Behavior of Circulating Lymphocytes,” Immunol. 49, 83–94.
Subba Rao, T., and M.M. Gabr (1984), “An Introduction to Bispectral Analysis and Bilinear Time Series Models,” Lecture Notes in Statistics (New York: Springer-Verlag), Vol. 24.
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© 1989 Kluwer Academic Publishers, Dordrecht, Holland
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Mohler, R.R., Farooqi, Z.H. (1989). Distribution of Recirculating Lymphocytes: A Stochastic Model Foundation. In: Kurzhanski, A.B., Sigmund, K. (eds) Evolution and Control in Biological Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2358-4_14
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DOI: https://doi.org/10.1007/978-94-009-2358-4_14
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