Figure 3
Individual trajectories of mortality-risk and biological age. (A) 12 individual trajectories of mortality risk as computed by Monte Carlo simulation. The insert displays trajectories at early ages, for which the stochastic nature of the trajectories is more clear. Black dots indicate death-events. Parameters used for the model are: \(N = 10^{6}\), \(F_0/N = 1 \times 10^{-5}\), \(b = 9.24 \times 10^{-3}\) per year, \(R_0 = 4.2 \times 10^{-5}\) per year, and \(r N = b / 0.977\) is used in order to correct for the fact that the stochastic model lags slightly compared to the mean field model (see main text and Supplemental Appendix C). (B) 220 individual trajectories of mortality risk are displayed together with the median (black line). Black dots indicate death-events. The corresponding distribution of total life-span (age at death) in shown in Fig. 2D. (C) Standard deviation (shown in grey dots) of the 220 individual trajectories shown in panel B. The black line corresponds to the approximate solution for standard deviation given by the square root of equation (11). We see that the approximate solution agrees extremely well with the simulated data. The standard deviation increases almost exponentially (an exponential curve is displayed by the blue dashed line for comparison). (D) Individual trajectories of “Biological age” corresponding to the 220 individual trajectories shown in panel (B). The colored trajectories correspond to the trajectories shown in panel (A). Black dots indicate death-events. Here “Biological Age” is defined as the age obtained by projection of individual values of \(f_i(t)\) onto the average \(\langle f \rangle\). From this plot it is clear that the timing of stochastic events at early age have large impact on the individual trajectory.
