2020/04/28 by Mostafa Adimy, Pablo Amster, Adimy, Mostafa +3
Immunology and Microbiology · Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Reproductive System and Pregnancy
paper · pdf · doi:10.48550/arxiv.2004.13766
openalex publication_date 2020/04/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The main purpose of this paper is to study the existence of periodic\nsolutions for a nonautonomous differential-difference system describing the\ndynamics of hematopoietic stem cell (HSC) population under some external\nperiodic regulatory factors at the cellular cycle level. The starting model is\na nonautonomous system of two age-structured partial differential equations\ndescribing the HSC population in quiescent (G0) and proliferating (G1,\nS, G2 and M) phase. We are interested on the effects of a periodically\ntime varying coefficients due for example to circadian rhythms or to the\nperiodic use of certain drugs, on the dynamics of HSC population. The method of\ncharacteristics reduces the age-structured model to a nonautonomous\ndifferential-difference system. We prove under appropriate conditions on the\nparameters of the system, using topological degree techniques and fixed point\nmethods, the existence of periodic solutions of our model.\n