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.


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    Title :

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


    Contributors:

    Conference:

    10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway


    Published in:

    AIP Conference Proceedings ; 1637 , 1 ; 1325-1334


    Publication date :

    2014-12-10


    Size :

    10 pages





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



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