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.
A model with competition between the cell lines in leukemia under treatment
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway
AIP Conference Proceedings ; 1637 , 1 ; 1325-1334
2014-12-10
10 pages
Conference paper
Electronic Resource
English
A feedback model for leukemia including cell competition and the action of the immune system
American Institute of Physics | 2014
|The analysis and application of competition and cooperation between the bus lines
Springer Verlag | 2015
|The analysis and application of competition and cooperation between the bus lines
Online Contents | 2016
|Branch lines, wayside stations and road competition
Online Contents | 1995
|Legal Lines: Competition - a brave new world
British Library Online Contents | 1999