Figure 2

Gompertzian mortality emerges from logistic growth of subsystem failures. (A) Risk of death—equal to mortality rate on population scale—as a function of age. The blue line shows classical Gompertzian mortality (exponential increase of mortality rate with age). The three black lines show the mortality rate as predicted by the MICC model for three different choices of \(F_0/N\) (full line: \(F_0/N = 1 \times 10^{-6}\), dashed-dotted line: \(F_0/N = 1 \times 10^{-5}\), dashed line: \(F_0/N = 2 \times 10^{-5}\)). The inset marked with a red boarder corresponds to the age range which is relevant for human life-span. Within this age range the mortality rate increases approximately exponentially with age. The age range for which the exponential approximation is valid increases with decreasing values of \(F_0/N\). Parameters used for the mean field model are: \(b = 9.24 \times 10^{-3}\) per year, \(R_0 = 4.2 \times 10^{-5}\) per year, \(N = 10^{6}\), and \(rN = b\). (B) Zoom of the relevant age-range, shown in both linear and logarithmic scale. (C,D) The survival function (C) and life-span distribution (D) corresponding to an approximately exponential mortality rate is displayed overlayed with empirical data from the Danish population—the data consists of all deaths occurring in the Danish population in the time period 1990–2019. The theoretical survival function and life-span distribution correspond to the parameter choice of \(F_0/N = 1 \times 10^{-5}\).