@Article{ArinoSanchezWebb1997b,
  author     = {Arino, Ovide and S{\'a}nchez, E. and Webb, G. F.},
  title      = {Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence},
  journal    = {J. Math. Anal. Appl.},
  year       = {1997},
  volume     = {215},
  number     = {2},
  pages      = {499--513},
  issn       = {0022-247X},
  abstract   = {The authors analyze a linear model of cell
                  population dynamics structured by age (denoted a)
                  with two interacting compartments: proliferating
                  cells (with densities $p(a,t))$ and quiescent cells
                  (with densities $q(a,t))$; $t$ is time. The
                  equations of the model are: $$\partial p/ \partial
                  t+\partial p/ \partial a= -\mu(a)p -\sigma(a)p +\tau
                  (a)q, \quad 0<a <a\sb 1,\ t>0,$$ $$\partial q/
                  \partial t+\partial q/ \partial a= \sigma(a)p -\tau
                  (a)q, \quad 0<a< a\sb 1,\ t>0,$$ $$p(0,t)= 2\int\sp
                  q\sb 0 \mu(a) p(a,t)da, \quad t>0,\quad q(0,t)=0,\
                  t>0,$$ $$p(a,0)= \varphi (a),\quad 0<a<a\sb 1,\quad
                  q(a,0) =\psi(a),\quad 0<a<a\sb 1,$$ where $\mu$ is
                  the division rate, $\sigma$ is the transition rate
                  from the proliferating stage to the quiescent stage,
                  $\tau$ is the transition rate from the quiescent
                  stage to the proliferating stage, and $a\sb 1$ is
                  maximal age of division.\par Necessary and
                  sufficient conditions are established for the
                  population to exhibit asymptotic behavior of
                  asynchronous exponential growth. The model is
                  analyzed as a semigroup of linear operators.},
  classmath  = {*92D25 Population dynamics 47N60 Appl. of operator theory in biology and other sciences 47D03 (Semi)groups of linear operators },
  coden      = {JMANAK},
  fjournal   = {Journal of Mathematical Analysis and Applications},
  keywords   = {age-structured model; linear model; cell population dynamics; proliferating cells; quiescent cells; asymptotic behavior; asynchronous exponential growth},
  mrclass    = {92D25 (35Q80 47D06 47N20)},
  mrnumber   = {99c:92033},
  mrreviewer = {Hassan Emamirad},
  pdf        = {ArinoSanchezWebb-1997-JMAA215.pdf},
  reviewer   = {I.Onciulescu (Iasi)},
}