  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. We firstly derive a delay
differential equation which allows us to prove several inequalities and
equalities on the growth rates. We also discuss about the necessity to take
into account the structure of the cell division cycle for chronotherapy
modeling. Numerical simulations illustrate the results.
