International audienceA reaction–diffusion system of equations describing the distribution of population density is considered. The existence of pulse solutions is proved by the Leray–Schauder method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions. Numerical simulations show that such solutions become stable in the case of global consumption of resources while they are unstable without the integral terms. This model is used to describe human height distribution
The paper is devoted to modelling of cell differentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell differentiation is initiated locally in space in the population of undifferentiated cells, it can propagate as a travelling wave converting undifferentiated cells into differentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular regulation and different cell types. They include undifferentiated cells and two types of differentiated cells. When a cell differentiates, its choice between two types of differentiated cells is determined by the concentrations of intracellular proteins. Differentiated cells can either stimulate differentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of differentiated cells will finally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave.
In this work, we propose a mathematical model based on reaction-diffusion equations to describe the development of normal and leukemic hematopoiesis. Specifically, we introduce a parameter that characterizes the strength of mutation. According to its value, leukemia will or will not develop. On the other hand, we show the existence of a traveling wave providing a transition from an equilibrium to other.
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