Abstract:
This paper introduces a new complex mathematical model for the evolution of
chronic myeloid leukemia considering the influence of the immune system and the
Imatinib treatment. The model consists of eleven delay differential
equations: the first four describe hematopoietic cells evolution,
the next five describe the influence of the immune cells and the last two
represent the pharmacokinetics of Imatinib. The stability properties for two
important equilibrium points are investigated through analytical and
numerical approaches. Mathematical findings attest that the action of the
immune system is visible especially when Imatinib treatment is not present.
This result is in good consensus with medical evidences, as it is believed
that Imatinib has an inhibitory effect on some of the most important
components involved in the immune defense against leukemia. As several types
of immunotherapy are currently being explored for the treatment of leukemia,
this complex model may be used as a proving ground for treatment protocols
involving the stimulation of the immune system through specific
immunotherapy.
Key Words: delay differential equations, leukemia,
equilibrium points, stability, Imatinib tratment, immunotherapy.
2010 Mathematics Subject Classification: Primary 34K20, Secondary 37N25, 92C50.
