In this work we develop a mathematical model of chronic myeloid leukemia including treatment with instantaneous effects. Our analysis focuses on the values of growth rate γ which give either stability or instability of the disease free equilibrium. If the growth rate γ of sensitive leukemic stem cells is less than some threshold γ * , we obtain the stability of disease free equilibrium which means that the disease is eradicated for any period of treatment τ 0. Otherwise, for γ great than γ * , the period of treatment must be less than some specific value τ * 0. In the critical case when the period of treatment is equal to τ * 0 , we observe a persistence of the tumor, which means that the disease is viable.

Source : oai:HAL:hal-01904650v3

Volume: Volume 30 - 2019 - MADEV health and energy (2017)

Published on: June 8, 2019

Submitted on: November 23, 2018

Keywords: Fixed point theorem,impulsive differential equation,Positive solution,Bifurcation,Bifurcation Volume 30 -2018,pages 1 à 20 -Revue,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]

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