Abstract
A nonlinear age-structured tumor cell population model is presented and analyzed. The population is divided into proliferating and quiescent cell compartments. The nonlinearity of the birth rate is designed to halt population’s exponential growth and force the system to converge to stable equilibria or stable cycles. The existence and uniqueness of solutions are studied. The local and global stabilities of the trivial steady state are investigated. Moreover, the existence and local stability of the positive steady state are analyzed. Numerical examples are performed to verify the validity of the results and to discuss the impacts of parameters on the nonlinear dynamics of the model.
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