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. 2024 Jan 12;14:1196. doi: 10.1038/s41598-024-51669-5
N: Total number of subsystems in one organism
F(t): The number of failed subsystems at time t, F(t)=N·F0F0+(N-F0)e-rNt
M(t): The number of subsystems which are functioning correctly at time t, M(t)=N-F(t)
τ: inflection point τ=1/(rN)·ln(N/F0-1), such that F(τ)=N/2
μ(t):

mortality rate, μ(t)F0F0+(N-F0)e-rNt

In the limit of small fractions of failed subsystems (small F(t)/N): μ(t)R0ebt

where b=rN