Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.

中文翻译：

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健康细胞和癌细胞在造血系统中竞争的整体动力学。

骨髓中的干细胞通过严格调节的过程（造血）分化为最终成熟的功能性血细胞，包括干细胞的小生境相互作用和免疫系统的反馈。造血干细胞中的突变会产生癌症干细胞，导致造血系统中功能异常细胞的生产受到较少的控制。这是由Andersen等人数学建模的。（2017年）包括动态变量：健康和癌症干细胞和成熟细胞，死细胞以及免疫系统反应。在这里，我们对该模型应用准稳态逼近，以构建一个二维模型，该模型具有由四个简单代币模型表示的代数方程。这两个动态变量是临床可用量JAK2V617F等位基因负担和白细胞数量。简单的Cancanitis模型很好地代表了原始模型。对简单的Cancanitis模型进行完整的相空间分析，包括证明全局吸引稳态的存在和位置。因此，来自干细胞，成熟细胞和免疫细胞区室的参数值与疾病和治疗预后直接相关，显示了早期干预的至关重要。简单的Cancanitis模型可以对轨迹的长期演变进行完整分析。尤其是，发现造血干细胞的自我更新的价值除以癌症干细胞的自我更新的价值是重要的诊断标记，在干预时干扰该参数值可以使模型再现临床数据。低癌细胞数的治疗可使血液恢复健康，而疾病后期的相同干预可消除健康血液的产生。假设在癌症的早期阶段，白细胞的总数是恒定的，而等位基因的负担增加，则建议并明确求解一维模型，包括所有原始区室的参数。该解决方案明确表明，当癌症干细胞比造血干细胞更有效地繁殖时，外源性炎症会促进血液癌症。