Vitality heterogeneity in the Strehler-Mildvan theory of mortality

In this paper the Strehler-Mildvan theory of mortality and aging is generalised to cover heterogeneity effects in the population. The theory is based on the concept of environmental shocks that cause death of an individual when exceeding its vitality. Heterogeneity is introduced via the value of the vitality of an individual at birth. The main result of the paper is an expression for the observed mortality rate of the heterogeneous population. This mortality rate grows according to Gompertz's Law at midlife-ages, then its growth declines, levelling off at high ages. This behaviour is qualitatively consistent with real mortality rates, which is illustrated for period data of Japanese females in the years 1947, 1967, 1987 and 2007. Finally, the duality between a continuous SM-version and the ρ - γ - Gompertz model is discussed.