PMID: 7334284Jan 1, 1981Paper

Approximate solution of a model of biological immune responses incorporating delay

Journal of Mathematical Biology
A C Fowler

Abstract

A model of the humoral immune response, proposed by Dibrov, Livshits and Volkenstein (1977b), in which the antibody production by a constant target cell population depends on the antigenic stimulation at earlier times, is considered from an analytic standpoint. A method of approximation based on a consideration of the asymptotic limit of "large" delay in the antibody response is shown to be applicable, and to give results similar to those obtained numerically by the above authors. The relevance of this type of approximation to other systems exhibiting "outbreak" phenomena is discussed.

References

Jul 15, 1977·Science·M C Mackey, L Glass
Mar 28, 1978·Journal of Mathematical Biology·A S PerelsonG F Oster
Apr 21, 1977·Journal of Theoretical Biology·B F DibrovM V Volkenstein
Nov 7, 1977·Journal of Theoretical Biology·B F DibrovM V Volkenstein
Apr 7, 1977·Journal of Theoretical Biology·P Waltman, E Butz
Nov 25, 1976·Journal of Mathematical Biology·A S PerelsonG F Oster
Nov 1, 1971·Journal of Theoretical Biology·G I Bell
Apr 1, 1974·Proceedings of the National Academy of Sciences of the United States of America·S H FrancisH N Eisen
Sep 17, 1974·British Dental Journal·J J Murray
Dec 1, 1973·The Journal of Experimental Medicine·C G Romball, W O Weigle
Nov 1, 1970·Journal of Theoretical Biology·G I Bell

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Citations

Jan 1, 1993·Bulletin of Mathematical Biology·R J De BoerI G Kevrekidis
Jan 5, 2014·Journal of Mathematical Biology·Tanvi P Gujarati, G Ambika
Sep 29, 2011·Mathematical Biosciences·Jerry J Batzel, Franz Kappel
Apr 7, 1991·Journal of Theoretical Biology·R J de Boer, A S Perelson
Dec 1, 1995·AORN Journal·A Eisenman, B Cohen
Sep 1, 2021·Bulletin of Mathematical Biology·A C Fowler

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