Modelling mortality dynamics in heterogeneous human populations

The mortality patterns of human populations reflect several inherent biological attributes and other external factors including social, medical and environmental conditions. Mathematical modelling, in addition to experiments and simulations, is an important tool for the analysis of those patterns. One of the main observed characteristics of mortality patterns in human populations is the age-specific increase in mortality rate after sexual maturity. This increase is predominantly exponential and satisfies the well-known Gompertz law of mortality. Although the exponential growth in mortality rate is observed over a wide range of ages, it excludes early- and late-life intervals. The heterogeneity of human populations is a common consideration in describing and validating their various age-related features. In this study we develop a mathematical model that combines (i) the assumption of heterogeneity within each human population, where different subpopulations are distinguished for their certain mortality dynamics and (ii) the assumption that the mortality of each constituent subpopulation increases exponentially with age (in the same way as described by the Gompertz law). The proposed model is used to fit available observational data in order to analyse the dynamics of mortality across the lifespan and the evolution of mortality patterns over time. We first explore the effects of the variation of the model parameters to the dynamics of mortality and use the model to fit actual age-specific mortality data. We show that the model successfully reproduces the entire age-dependent mortality patterns explaining the peculiarities of mortality at young and very old ages. In particular, we show that the mortality data on Swedish populations can be reproduced fairly well by a model comprising of four subpopulations. Besides the confirmation that heterogeneity can explain the irregularities of mortality patterns at young ages and the deceleration of mortality at extremely old ages, we analyse the influence of stochastic effects on mortality and we conclude that evident effects due to stochasticity are manifested at the age intervals (early and late life ages) where only few individuals contribute to mortality. We then analyse the evolution of mortality patterns over time by fitting the proposed model to (Swedish) mortality data of consecutive periods across the 20th century. The evolution of mortality is described in terms of the changes of model parameters estimated by fitting the model to data from different time periods. We show that the evolution of model parameters confirms the applicability of the compensation law of mortality to each constituent subpopulation separately. The compensation law states an inverse relationship between the scale and the shape parameter of Gompertz law. Our analysis also indicates a change in the structure of this population over time in a way that the population tends to become more homogeneous by the end of the 20th century. This change in structure is reflected in changes to the initial proportions of the constituent subpopulations. These two observations, namely the validity of the compensation effect and the homogenisation of the population, imply that the alteration of model parameters (which reflect demographic terms) can explain the decrease of the overall mortality over time. It is shown that the decrease in mortality across the 20th century is mainly due to changes in the structure of the population, and to a lesser extent, to a reduction in mortality for each of the subpopulations. The outcomes of our research show that the consideration of heterogeneity is efficient for the description of various features of a population’s mortality. The idea of “pure” subpopulations, such that in each of them exponential law is held for all ages, has been used as a convenient mathematical constraint which allows very accurate reproduction of the entire mortality patterns. This provides a justification for the deviation of mortality from its exponential increase at young and very-old ages and for the decrease of mortality over time. In the last part of this thesis we propose that the proposed heterogeneity is not only a convenient tool for fitting mortality data but indeed reflects the true heterogeneous structure of the population. Particularly we demonstrate that the model of a heterogeneous population fits mortality data better than most of the other commonly used models if the data are taken for the entire lifespan and better than all other models if we consider only old ages. Also, we show that the model can reproduce seemingly contradicting observations in late-life mortality dynamics like deceleration, levelling-off and mortality decline. Finally, assuming that the differences between subpopulations reflect genetic variations within the population and using the Swedish mortality data for the 20th century, we show that evolutionary processes resulting in changes of allele frequencies, can explain the homogenisation of the population as predicted by the model.