期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 16, 期 5, 页码 4818-4845出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2019243
关键词
adaptive cell population dynamics; hematopoietic stem cells; stromal cells; leukemic stem cells; Dirac concentrations; asymptotic methods
资金
- European Research Council (ERC) under the European Union [740623]
- Plan Cancer HTE programm EcoAML
- European Research Council (ERC) [740623] Funding Source: European Research Council (ERC)
We propose a mathematical model to describe the evolution of hematopoietic stem cells (HSCs) and stromal cells in considering the bi-directional interaction between them. Cancerous cells are also taken into account in our model. HSCs are structured by a continuous phenotype characterising the population heterogeneity in a way relevant to the question at stake while stromal cells are structured by another continuous phenotype representing their capacity of support to HSCs. We then analyse the model in the framework of adaptive dynamics. More precisely, we study single Dirac mass steady states, their linear stability and we investigate the role of parameters in the model on the nature of the evolutionary stable distributions (ESDs) such as monomorphism, dimorphism and the uniqueness properties. We also study the dominant phenotypes by an asymptotic approach and we obtain the equation for dominant phenotypes. Numerical simulations are employed to illustrate our analytical results. In particular, we represent the case of the invasion of malignant cells as well as the case of co-existence of cancerous cells and healthy HSCs.
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