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Cell proliferation 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-doubling 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 which can be considered to be a general model of cell growth.
We also review the numerical techniques available for solving delay
differential equations and calculating the least-squares best-fit parameterized
solution.
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