Periodic solutions for a nonautonomous mathematical model of hematopoietic stem cell dynamics

The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential–difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a n...

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Bibliographic Details
Published in:Nonlinear analysis 2021-10, Vol.211, p.112397, Article 112397
Main Authors: Adimy, Mostafa, Amster, Pablo, Epstein, Julián
Format: Article
Language:English
Subjects:
Delay differential–difference nonautonomous equations
Dynamical Systems
Hematopoietic stem cells
Mathematics
Periodic solutions
Topological degree and fixed point methods
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Summary:The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential–difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a nonautonomous system of two age-structured partial differential equations describing the HSC population in quiescent (G0) and proliferating (G1, S, G2 and M) phase. We are interested in the effects of periodically time varying coefficients due for example to circadian rhythms or to the periodic use of certain drugs, on the dynamics of HSC population. The method of characteristics reduces the age-structured model to a nonautonomous differential–difference system. We prove under appropriate conditions on the parameters of the system, using topological degree techniques and fixed point methods, the existence of periodic solutions of our model.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112397