Introduction: About a year and a half after the declaration of the COVID-19 pandemic, almost the entire planet has been affected by SARS-CoV-2 coronavirus and its variants, with serious public health consequences and other repercussions not yet thoroughly evaluated or foreseen in terms of economic, financial and social disruption throughout communities. Therefore, it is of utmost importance to understand the geography of the evolution of successive pandemic waves. Particularly in European countries, where, in recent decades, more advanced models for cohesion and competitiveness of a whole with more than 400 million inhabitants have been achieved, with ambitious challenges for horizon 2030 regarding this vast territory’s economic, social, and environmental sustainability. Objective: The main objective of this research is to describe the multivariate trajectories of COVID-19 incidence, mortality, hospital admissions, ICU admissions and testing, over three successive waves, covering all European Union (EU) countries with more than two million inhabitants, over 14-days periods before May 4 2020, until February 22 2021. Methods: This research includes 22 European countries representing about 98.8% of the EU population, described by six epidemiological variables over 43 time periods from the ECDC database: the 14-day notification rate Biometrics & Biostatistics International Journal Research Article Open Access of new cases reported for 100,000 inhabitants; the 14-day notification rate of reported deaths per one million inhabitants; the mean and the rate for 100,000 population of hospital occupancy and ICU occupancy; the testing rate per 100,000 population; and the 14-days percentage of test positivity An exploratory data analysis of each epidemiological variable identified a typology of countries profiles evolution. Multivariate exploratory statistical methods, namely a 3-way data analysis (double principal components and rank principal components analyses), were applied with software R version 4.1.0. Results: The multivariate evolution profile of the COVID-19 pandemic in the EU over the studied period highlighted 3 phases: the first phase over 24 time periods, with a relatively low COVID-19 incidence, hitting only part of EU countries; a second phase at the beginning of the second wave, when COVID-19 spread to most countries, with a higher impact on national health systems; lastly, a third phase coincident with the peak of the second wave and the onset of the third wave, a particularly reactive phase from the public authorities, with intensified testing of the population. These results are clear from the principal component analysis of the centres of gravity of the 43 time periods (interstructure). The multivariate statistical analysis of the global dataset of all countries over the 43 time periods additionally provides the main factorial representation of the trajectories of COVID-19 for each country in direct comparison with the global average ranked values reached by the six epidemiological variables over the whole period under study (intrastructure). These trajectories make it possible to identify different country profiles throughout the successive pandemic waves and counter-cyclical behaviours, partly explained by the insufficient harmonisation of public policies to tackle the pandemic within the EU.

The increasing difficulties in financing the welfare state and in particular public retirement pensions have been one of the outcomes both of the decrease of fertility and birth rates combined with the increase of life expectancy. The dynamics of retirement pensions are usually studied in Economics using overlapping generation models. These models are based on simplifying assumptions like the use of a representative agent to ease the problem of tractability. Alternatively, we propose to use agent-based modelling (ABM), relaxing the need for those assumptions and enabling the use of interacting and heterogeneous agents assigning special importance to the study of inter-generational relations. We treat pension dynamics both in economics and political perspectives. The model we build, following the ODD protocol, will try to understand the dynamics of choice of public versus private retirement pensions resulting from the conflicting preferences of different agents but also from the cooperation between them. The aggregation of these individual preferences is done by voting. We combine a microsimulation approach following the evolution of synthetic populations along time, with the ABM approach studying the interactions between the different agent types. Our objective is to depict the conditions for the survival of the public pensions system emerging from the relation between egoistic and altruistic individual and collective behaviours.