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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.
...
A class of degree four differential systems that have an invariant conic , , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
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....
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....
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...
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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