Fig. 6.

Comparison of the dynamical responses to a transient increase in cell influx by three different frameworks that are capable of modeling cells with fixed lifespan and furthermore allow continuous random loss: ODE with age classes (ODE; ); DDE (DDE; and DDE corr; ); and discrete recursive equation (DRE; ) with age classes. All models were set up with as much equivalence as possible (see Text). Panel A shows the simulation results for the total numbers of cells for the four frameworks. Panels B and C show the numbers of cells in each age class of the ODE and DRE frameworks, respectively. These are shown with a color gradient from black (first age class) to light gray (sixth age class). The addition of a first-order term for cell removal to the DDE (DDE; ) does not accurately represent the system (Eq. 7.1), but a correction (Eq. 7.3) remedies the performance to some degree (DDE corr; ). Once corrected, the DDE framework (DDE Corr) performs similarly to the DRE, although it takes a very long time for the system to reach the steady-state, whereas the other two frameworks reach their steady states more quickly. Similar to the previous study without a random process of cell removal (Fig. 5), the ODE framework with age classes does not retain the extra number of cells that enter the pool between 5 < t ≤ 7 for the expected 6 time units. Overall, the DRE system emerges as the preferred option for modeling a cell population with a fixed lifespan that is furthermore subject to random, age-independent, losses.