This review aims at presenting a
synoptic, if not exhaustive, point of view on some of the problems
encountered by biologists and physicians who deal with natural
cell proliferation and disruptions of its physiological control in
cancer disease. It also aims at suggesting how mathematicians are
naturally challenged by these questions and how they might help,
not only biologists to deal theoretically with biological
complexity, but also physicians to optimise therapeutics, on which
last point the...
We study the growth rate of a cell population that follows an
age-structured PDE with time-periodic coefficients. Our motivation
comes from the comparison between experimental tumor growth curves
in mice endowed with intact or disrupted circadian clocks,
known to exert their influence on the cell division cycle.
We compare the growth rate of the model controlled by a time-periodic
control on its coefficients with the growth rate of stationary
models of the same nature, but with averaged coefficients....
In order to better understand the dynamics of acute leukemia, and in particular to find
theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia,
we investigate stability of a system modeling its cell dynamics.
The overall system is a cascade connection of sub-systems consisting of distributed
delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are
improved by the analysis of the...
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