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Modelling and analysis of time-lags in some basic patterns of cell proliferation. (English) Zbl 0908.92026
Summary: We present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their nonlinear biases and standard deviations, for sets of experimental data.
We demonstrate our method for solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.

92D25 Population dynamics (general)
92C99 Physiological, cellular and medical topics
34K40 Neutral functional-differential equations
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