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 Press for Viet Nam 1999-2003 Male and Female Morality Rate Charts. Press for American Death Rate Chart from Social Security Data. Press for USA Life Expectancy Chart. μ(t) = μ(midlife)*exp[(t/8)In(2)] for 38 < t < 80. The actual death rate law is probably better described by The infant death rate approaches the nearly constant maturity death rate after a couple of years. A more complicated dual exponential form of the Gompertz function has been given. Note that the growth rate c of a simple exponential process y(t) = A*exp(ct) is obtained from dy/dt = c*y(t). According to James R. Carey, Population Study of Longevity and Mortality with Gompertzian Analysis, in Methods in Aging Research edited by Byung Pal Yu, Let N(t) be the number of a population initially N(0) surviving at age t, and let μ(t) be the age-specific mortality rate at age t, such that N(t) = N(0)exp(-∫0t[μ(T)dT]), where ∫0t[μ(T)dT] is the integral of μ(T)dT from 0 to t. Then dN/dt = -μ(t)N(t) displays μ(t) as the mortality rate at time t. Then the Gompertz mortality rate has the form μ(t) = a*exp(bt), and the Makeham mortality rate has the form μ(t) = a*exp(bt) + c. Our graph resembles a plot of the number of Childhood's End grey hairs on a man's head, and may reflect the population level of senescent stem cells arising from telomere DNA damage. On the average, 50% of persons have 50% grey hair by age 50 [Hisama, Chromosomal Instability and Aging, p.565].  |
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