title: Time-evolution of age-dependent mortality patterns in mathematical model of heterogeneous human population.
abstract: The widely-known Gompertz law of mortality states the exponential increase of mortality with age in human populations. Such an exponential increase is observed at the adulthood span, roughly after the reproductive period, while mortality data at young and extremely old ages deviate from it. The heterogeneity of human populations, i.e. the existence of subpopulations with different mortality dynamics, is a useful consideration that can explain age-dependent mortality patterns across the whole life-course. A simple mathematical model combining the heterogeneity of populations with an assumption that the mortality in each subpopulation grows exponentially with age has been proven to be capable of reproducing the entire mortality pattern in a human population including the observed peculiarities at early- and late-life intervals. In this work we fit this model to actual (Swedish) mortality data for consecutive periods and consequently describe the evolution of mortality dynamics in terms of the evolution of the model parameters over time. We have found that the evolution of the model parameters validates the applicability of the compensation law of mortality to each subpopulation separately. Furthermore, our study has indicated that the population structure changes so that the population tends to become more homogeneous over time. Finally, our analysis of the decrease of the overall mortality in a population over time has shown that this decrease is mainly due to a change in the population structure and to a lesser extent to a reduction of mortality in each of the subpopulations, the latter being represented by an alteration of the parameters that outline the exponential dynamics.
authors.affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
authors.forename: Demetris
authors.initials: D
authors.lastname: Avraam
authors.affiliation: Department of Actuarial Science, Faculty of Business and Economics (HEC Lausanne), University of Lausanne, Lausanne, Switzerland.
authors.forename: Séverine
authors.initials: S
authors.lastname: Arnold-Gaille
authors.affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
authors.forename: Dyfan
authors.initials: D
authors.lastname: Jones
authors.affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. Electronic address: bnvasiev@liv.ac.uk.
authors.forename: Bakhtier
authors.initials: B
authors.lastname: Vasiev
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000375:Aging; D002648:Child; D002675:Child, Preschool; D016208:Databases, Factual; D005260:Female; D006801:Humans; D007223:Infant; D007231:Infant, Newborn; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D008962:Models, Theoretical; D009026:Mortality / Q000639:trends*; D011157:Population Dynamics; D013548:Sweden / Q000453:epidemiology; D055815:Young Adult
keywords: Compensation law of mortality; Gompertz law; Mathematical model; Model fitting; Mortality dynamics