A nonlinear age-structured tumor cell population model with quiescence and bidirectional transition is presented and studied. The division rate of the proliferating cells is assumed to be nonlinear due to the limitation of the nutrient and space. The model includes a proportion of newborn cells that enter directly the quiescent phase with age zero. This proportion can reflect the effect of treatment by drugs such as erlotinib. The bidirectional transition between proliferating cells and quiescent cells is considered. The local and global stabilities of the trivial steady state are investigated. The existence and local stability of the positive steady state are also analyzed. Numerical simulations are performed to verify the results and to examine the impacts of parameters on the nonlinear dynamics of the model.

中文翻译：

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具有静态和双向过渡的非线性年龄结构肿瘤细胞种群模型的稳态分析

提出并研究了具有静态和双向转移的非线性年龄结构肿瘤细胞种群模型。由于营养和空间的限制，假定增殖细胞的分裂速率是非线性的。该模型包括一定比例的零年龄新生细胞直接进入静止期。该比例可以反映出药物如厄洛替尼的治疗效果。考虑了增殖细胞和静止细胞之间的双向转变。研究了微不足道的稳态的局部和全局稳定性。分析了正稳态的存在性和局部稳定性。进行数值模拟以验证结果并检查参数对模型非线性动力学的影响。