Necessary and Sufficient Conditions for Asynchronous Exponential Growth in Age Structured Cell Populations with Quiescence

A linear model on age structured cell population is analyzed. The population is divided into proliferating and quiescent compartments. Necessary and sufficient conditions are established for the population to exhibit the asymptotic behavior of asynchronous exponential growth. The model is analyzed as a semigroup of linear operators which is shown to be eventually compact and irreducible.