Abstract：
Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.
摘要：
细胞增殖对于人体的发育和稳态至关重要。对于这种情况的发生，细胞经历细胞周期，在此期间它们复制遗传物质并最终完成细胞分裂，当一个细胞分裂成两个具有相同遗传物质的新细胞时。然而,如果细胞周期中有一些错误或异常破坏细胞死亡和增殖之间的平衡，可能会出现严重的问题，比如肿瘤的发展，这是目前世界上主要的死亡原因之一。如今,数学和计算模型用于理解和研究几种生物机制和过程，即细胞增殖。在过去的45年里，几种模型试图描述细胞增殖及其调节。由于工艺的复杂性,已经考虑了许多假设和简化。这项工作对其中一些模型进行了回顾，主要关注哺乳动物或通用真核生物模型。以前出版的连续体，提出并比较了离散方法和混合方法，为了理解和强调这些模型的相关性和功能，他们的缺点和未来的挑战。
