Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

Halanay, A.

doi:10.1051/mmnp/20127110

Cited by 6 publications

(6 citation statements)

References 16 publications

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“…Periodic oscillations were studied depending on five haematopoietic stem cell parameters: the mitotic rate sensitivity, the maximal rate of cell entry into proliferation from the resting G 0 phase, the differentiation and apoptosis rate and the time to entry into mitosis. Extensions of this work [37], have proven that, under periodic treatment, there is a periodic solution with the same period. This could be related to the observed oscillatory behaviour of blood cells' counts under treatment in CML.…”

Section: Cell-cycle-based Mathematical Models Of Myeloid Leukaemiasmentioning

confidence: 60%

Mathematical models of leukaemia and its treatment: a review

Chulián

Rubio

Rosa

et al. 2022

SeMA

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Leukaemia accounts for around 3% of all cancer types diagnosed in adults, and is the most common type of cancer in children of paediatric age (typically ranging from 0 to 14 years). There is increasing interest in the use of mathematical models in oncology to draw inferences and make predictions, providing a complementary picture to experimental biomedical models. In this paper we recapitulate the state of the art of mathematical modelling of leukaemia growth dynamics, in time and response to treatment. We intend to describe the mathematical methodologies, the biological aspects taken into account in the modelling, and the conclusions of each study. This review is intended to provide researchers in the field with solid background material, in order to achieve further breakthroughs in the promising field of mathematical biology.

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Section: Cell-cycle-based Mathematical Models Of Myeloid Leukaemiasmentioning

confidence: 60%

Mathematical models of leukaemia and its treatment: a review

Chulián

Rubio

Rosa

et al. 2022

SeMA

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“…The delays in system (2.1) are τ 1 , τ 2 , τ 3 , τ 4 , τ 5 , τ 6 and n 1 τ 4 . The first two equations, for the density of stem-like leukemia cells and of the leukemia neutrophil cells, are similar to those in [25] (see also [10], [15]).…”

Section: Description Of the Modelmentioning

confidence: 66%

“…For the description of biological processes implied in hematopoiesis, a mathematical model that includes time delays will be used. It is based on the mass action principle, in the spirit of [4], [5], [6], [9], [15], [19] and [25]. The aim is the study of the dynamics of Chronic Myelogenous Leukemia (CML) when the action of different cell lines of the immune system is considered.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia

Balea

Halanay

Jardan

et al. 2014

Math. Model. Nat. Phenom.

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A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of seven delay differential equations with seven delays. Three equilibrium points E0, E1, E2 are highlighted. The stability and the existence of the Hopf bifurcation for the equilibrium points are investigated. In the analysis of the model, the rate of asymmetric division and the rate of symmetric division are very important.

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“…Interaction of different cell lineages was studied in [12], [13]. There are numerous works devoted to modelling of leukemia development and treatment [6], [23], [24], [37], [41].…”

Section: Introduction 1cell Fate and Multi-scale Modellingmentioning

confidence: 99%

Modelling of cell choice between differentiation and apoptosis on the basis of intracellular and extracellular regulations and stochasticity

Banerjee¹,

Volpert²

2016

Preprint

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The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the number of differentiated cells. Initial intracellular protein concentrations are considered for each cell as random variables with a given area of variation. Intracellular regulation, extracellular regulation and random initial conditions work together to produce differentiated cells and to control their number. The role of intracellular regulation is to provide a possible choice between differentiation and apoptosis, extracellular regulation controls the number of differentiated cells, stochastic initial conditions can suppress oscillations and provide stability of the system.

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Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

Cited by 6 publications

References 16 publications

Mathematical models of leukaemia and its treatment: a review

Mathematical models of leukaemia and its treatment: a review

Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia

Modelling of cell choice between differentiation and apoptosis on the basis of intracellular and extracellular regulations and stochasticity

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