New paradigms in heterogeneous population dynamics: trajectory modeling, aggregation, and empirical data.

Summary This thesis deals with the probabilistic modeling of heterogeneity in human populations and of its impact on longevity. Over the past few years, numerous studies have shown a significant increase in geographical and socioeconomic inequalities in mortality. New issues have emerged from this paradigm shift that traditional demographic models are not able solve, and whose formalization requires a careful analysis of the data, in a multidisciplinary environment. Using the framework of population dynamics, this thesis aims at illustrating this complexity according to different points of view: We explore the link between heterogeneity and non-linearity in the presence of composition changes in the population, from a mathematical modeling viewpoint. The population dynamics, called Birth Death Swap, is built as the solution of a stochastic equation driven by a Poisson measure, using a more general pathwise comparison result. When swaps occur at a faster rate than demographic events, an averaging result is obtained by stable convergence and comparison. In particular, the aggregated population converges towards a nonlinear dynamic. In the second part, the impact of heterogeneity on aggregate mortality is studied from an empirical viewpoint, using English population data structured by age and socioeconomic circumstances. Based on numerical simulations, we show how a cause of death reduction could be compensated in presence of heterogeneity. The last point of view is an interdisciplinary survey on the determinants of longevity, accompanied by an analysis on the evolution of tools to analyze it and on new modeling issues in the face of this paradigm shift.