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

Summary This thesis deals with the probabilistic modeling of the heterogeneity of human populations and its impact on longevity. In recent years, numerous studies have shown an alarming increase in geographic and socioeconomic mortality inequalities. This paradigm shift poses problems that traditional demographic models cannot solve, and whose formalization requires a fine observation of data in a multidisciplinary context. With population dynamics models as a guideline, this thesis proposes to illustrate this complexity from different points of view: The first one proposes to show the link between heterogeneity and nonlinearity in the presence of changes in population composition. The process called Birth Death Swap is defined by an equation directed by a Poisson measure using a trajectory comparison result. When swaps are faster than demographic events, an averaging result is established by stable convergence and comparison. In particular, the aggregate population tends towards non-linear dynamics. We then study empirically the impact of heterogeneity on aggregate mortality, using data from the English population structured by age and socioeconomic circumstances. We show through numerical simulations how heterogeneity can compensate for the reduction of a cause of mortality. The last point of view is an interdisciplinary review on the determinants of longevity, accompanied by a reflection on the evolution of the tools to analyze it and the new modeling challenges in the face of this paradigm shift.