# A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia

Mostafa Adimy, Fabien Crauste, Shigui Ruan

Research output: Contribution to journalArticle

92 Citations (Scopus)

### Abstract

This paper is devoted to the analysis of a mathematical model of blood cell production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the age, we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell cycle duration. This system describes the evolution of the total cell populations. By constructing a Lyapunov functional, it is shown that the trivial equilibrium is globally asymptotically stable if it is the only equilibrium. It is also shown that the nontrivial equilibrium, the most biologically meaningful one, can become unstable via a Hopf bifurcation. Numerical simulations are carried out to illustrate the analytical results. The study may be helpful in understanding the connection between the relatively short cell cycle durations and the relatively long periods of peripheral cell oscillations in some periodic hematological diseases.

Original language English (US) 1328-1352 25 SIAM Journal on Applied Mathematics 65 4 https://doi.org/10.1137/040604698 Published - 2005

### Fingerprint

Hematopoiesis
Leukemia
Cells
Cell Cycle
Distributed Time Delay
Cell Population
Globally Asymptotically Stable
Cell
Lyapunov Functional
Bone
Hopf Bifurcation
Nonlinear Differential Equations
Blood
Hopf bifurcation
Trivial
Partial differential equation
Unstable
Mathematical Model
Oscillation
Partial differential equations

### Keywords

• Asymptotic stability
• Blood cells
• Differential equations
• Distributed delay
• Hematopoiesis
• Hopf bifurcation
• Lyapunov functional

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. / Adimy, Mostafa; Crauste, Fabien; Ruan, Shigui.

In: SIAM Journal on Applied Mathematics, Vol. 65, No. 4, 2005, p. 1328-1352.

Research output: Contribution to journalArticle

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