A model with competition between the cell lines in leukemia under treatment

The evolution of leukemia is modeled with a delay differential equation model of four cell populations: two populations (healthy and leukemic) ) of stem-like cells involving a larger category consisting of proliferating stem and progenitor cells with self-renew capacity and two populations (healthy...

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Bibliographic Details
Main Authors: Halanay, A, Cândea, D, Rădulescu, R
Format: Conference Proceeding
Language:English
Subjects:
APOPTOSIS
ASYMMETRY
ASYMPTOTIC SOLUTIONS
CAPACITY
Cells (biology)
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Competition
DIFFERENTIAL EQUATIONS
EQUILIBRIUM
FUNCTIONALS
LEUKEMIA
LYAPUNOV METHOD
Populations
STABILITY
STEM CELLS
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Summary:The evolution of leukemia is modeled with a delay differential equation model of four cell populations: two populations (healthy and leukemic) ) of stem-like cells involving a larger category consisting of proliferating stem and progenitor cells with self-renew capacity and two populations (healthy and leukemic) of mature cells, considering the competition of healthy vs. leukemic cell populations and three types of division that a stem-like cell can exhibit: self-renew, asymmetric division and differentiation. In the model it is assumed that the treatment acts on the proliferation rate of the leukemic stem cells and on the apoptosis of stem and mature cells. The emphasis in this model is on establishing relevant parameters for chronic and acute manifestations of leukemia. Stability of equilibria is investigated and sufficient conditions for local asymptotic stability will be given using a Lyapunov-Krasovskii functional.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4907298