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Journal of Theoretical Medicine
Volume 1, Issue 2, Pages 117-128

Mathematical Modelling of the Interleukin-2 T-Cell System: A Comparative Study of Approaches Based on Ordinary and Delay Differential Equation

1Mathematics Department, The University, Manchester M13 9PL, UK
2Institute of Numerical Mathematics, Russian Academy of Sciences, Mascow, Russia

Received 27 January 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cell proloferation and differentiation phenomena are key issues in immunology, tumour growth and cell biology. We study the kinetics of cell growth in the immune system using mathematical models formulated in terms of ordinary and delay differential equations. We study how the suitability of the mathematical models depends on the nature of the cell growth data and the types of differential equations by minimizing an objective function to give a best-fit parameterized solution. We show that mathematical models that incorporate a time-lag in the cell division phase are more consistent with certain reported data. They also allow various cell proliferation characteristics to be estimated directly, such as the average cell-boubling time and the rate of commitment of cells to cell division. Specifically, we study the interleukin-2-dependent cell division of phytohemagglutinin stimulated T-cells — the model of whic can be considered to be a general model of cell growth. We also review the numerical techniques available for solving delau differential equations and calculating the least-squares best-fit parameterized solution.