In this paper we propose a mathematical model to describe the evolution of leukemia
in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous
medium. We show the existence of two stationary solutions, one of them corresponds to the normal
case and another one to the pathological case. The leukemic state appears as a result of a bifurcation
when the normal state loses its stability. The critical conditions of leukemia development
are determined by the proliferation...
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 propose and analyze a nonlinear mathematical model of hematopoiesis,
describing the dynamics of stem cell population subject to impulsive
perturbations. This is a system of two age-structured partial differential
equations with impulses. By integrating these equations over the
age, we obtain a system of two nonlinear impulsive differential equations with
several discrete delays. This system describes the evolution of the total
hematopoietic stem cell populations with impulses. We first examine...
We study the influence of natural convection on stability of reaction fronts in
porous media. The model consists of the heat equation, of the equation for the depth of
conversion and of the equations of motion under the Darcy law. Linear stability analysis of
the problem is fulfilled, the stability boundary is found. Direct numerical simulations are
performed and compared with the linear stability analysis.
We investigate the structure of
travelling waves for a model of a fungal disease propagating over
a vineyard. This model is based on a set of ODEs of the SIR-type
coupled with two reaction-diffusion equations describing the
dispersal of the spores produced by the fungus inside and over the
vineyard. An estimate of the biological parameters in the model
suggests to use a singular perturbation analysis. It allows us to
compute the speed and the profile of the travelling waves. The
analytical results...
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