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Cell Modelling of Hematopoiesis

N. Bessonov, L. Pujo-Menjouet, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

In this work, we introduce a new software created to study hematopoiesis at the cell population level with the individually based approach. It can be used as an interface between theoretical works on population dynamics and experimental observations. We show that this software can be useful to study some features of normal hematopoiesis as well as some blood diseases such as myelogenous leukemia. It is also possible to simulate cell communication and the formation of cell colonies in the bone marrow. ...

Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models

J. Clairambault, S. Gaubert, Th. Lepoutre (2009)

Mathematical Modelling of Natural Phenomena

We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients....

Competition of Species with Intra-Specific Competition

N. Apreutesei, A. Ducrot, V. Volpert (2008)

Mathematical Modelling of Natural Phenomena

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....

Competitive Exclusion in a Discrete Stage-Structured Two Species Model

A. S. Ackleh, P. Zhang (2009)

Mathematical Modelling of Natural Phenomena

We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...

Conditional differential equations

Celina Rom (2016)

Applicationes Mathematicae

We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.

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