A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells

Abstract

In this paper, we investigate a linear population model of cells that are capable of simultaneous proliferation and maturation. We consider the case when the time required for a cell to divide depends on its maturity. This model is described by first order partial differential system with a retardation of the maturation variable and a time delay depending on this maturity. Both delays are due to cell replication.

Keywords

• Structured population
• cell cycle
• stem cells
• first order partial differential equation with delays
• non constant delay.