In this work we study a nonlocal reaction-diffusion equation arising in population
dynamics. The integral term in the nonlinearity describes nonlocal stimulation of
reproduction. We prove existence of travelling wave solutions by the Leray-Schauder method
using topological degree for Fredholm and proper operators and special a priori estimates
of solutions in weighted Hölder spaces.
The paper is devoted to mathematical modelling of erythropoiesis,
production of red blood cells in the bone marrow.
We discuss intra-cellular regulatory networks which determine
self-renewal and differentiation of erythroid progenitors.
In the case of excessive self-renewal, immature cells can fill
the bone marrow resulting in the development of leukemia.
We introduce a parameter characterizing the strength of mutation.
Depending on its value, leukemia will or will not develop.
The simplest...
Download Results (CSV)