On the basis of recent studies, understanding the intimate relationship between normal and leukaemic stem cells is very important in leukaemia treatment. The authors' aim in this work is to clarify and assess the effect of coexistence and interconnection phenomenon on the healthy and cancerous stem cell dynamics. To this end, they perform the analysis of two time-delayed stem cell models in acute myeloid leukaemia. The first model is based on decoupled healthy and cancerous stem cell populations (i.e. there is no interaction between cell dynamics) and the second model includes interconnection between both population's dynamics. By using the positivity of both systems, they build new linear functions that permit to derive global stability conditions for each model. Moreover, knowing that most common types of haematological diseases are characterised by the existence of oscillations, they give conditions for the existence of a limit cycle (oscillations) in a particularly interesting healthy situation based on Poincare-Bendixson theorem. The obtained results are simulated and interpreted to be significant in understanding the effect of interconnection and would lead to an improvement in leukaemia treatment.

中文翻译：

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急性髓性白血病中正常和白血病干细胞动态的共居和互连效应研究。

根据最近的研究，了解正常干细胞和白血病干细胞之间的密切关系对于白血病治疗非常重要。作者在这项工作中的目的是澄清和评估共存和互连现象对健康和癌性干细胞动力学的影响。为此，他们对急性髓系白血病的两种延时干细胞模型进行了分析。第一个模型基于分离的健康干细胞群和癌性干细胞群（即细胞动力学之间没有相互作用），第二个模型包括两个群动态之间的互连。通过利用两个系统的积极性，他们构建了新的线性函数，可以为每个模型导出全局稳定性条件。此外，知道最常见类型的血液疾病的特征是存在振荡，因此根据庞加莱-本迪克森定理，它们为在特别有趣的健康情况下存在极限环（振荡）提供了条件。所获得的结果经过模拟和解释对于理解互连的效果具有重要意义，并将导致白血病治疗的改进。