A discrete mathematical model based on ordinary differential equations and the associated
continuous model formed by a partial differential equation, which simulate the generational
and temporal evolution of a stem cell population, are proposed. The model parameters are the
maximum proliferation potential and the rates of mitosis, death events and telomerase activity.
The mean proliferation potential at each point in time is suggested as an indicator of population
ageing. The model is applied on hematopoietic stem cells (HSCs), with different telomerase
activity rates, in a range of variation of maximum proliferation potential in healthy individuals,
to study the temporal evolution of ageing. HSCs express telomerase, however not at levels that are
sufficient for maintaining constant telomere length with aging (Zimmermann and Martens, 2008;
Flores et al., 2008). Women with primary ovarian insufficiency (POI) are known to have low
telomerase activity in granulosa cells and peripheral blood mononuclear cells (Xu et al., 2017).
Extrapolating this to haematopoietic stem cells, the mathematical model shows the differences
in proliferation potential of the cell populations when telomerase expression is activated using
sexual steroids, though the endogenous promoter or with gene therapy using exogenous, stronger
promoters within the adeno-associated virus. In the first case, proliferation potential of cells from
POI condition increases, but when adeno-associated viruses are used, the proliferation potential
reaches the levels of healthy cell populations.
