Omicron Waves in Few European Countries till June 2022 Modeled by a New Version of a Tracking Approach with Successive and Superimposed Waves

Abstract

Our objective is a mathematical modeling in retrospective of the COVID-19 Omicron waves in the UK, France and Germany till mid June 2022. The aim is two-fold: ensure a good reproduction of the data with consistent parameters, also by comparing the results to the ones from an earlier study for the USA, and check the usefulness of a new, improved version of a recently published model. The main novelty of the approach used is the dynamical tracking of successive generations of infected people instead of treating the evolution of few large compartments within which the total population is partitioned. Because of the stronger transmission of Omicron, its waves start to dominate the Pandemic, and then the new model can be easily employed. The formalism is improved by employing better conditions for continuity when interconnecting solutions of differential equations and a superposition of waves related to independent pathogens. The daily observed new infection cases are described over a large time scale in a reasonable way after normalization, with deviations and differences due to country-specific factors. The time-position of the first calculated Pandemic peaks indicates a transition from the third to the fourth generation of infected people. The derived infection and recovery rates are consistent with those deduced for the USA. A correlation exists between initialization of relaxing restrictions and begin of a new wave or simply a jump up of the data locally. However, very often it happens nearby that a new independent wave emerges related to a different variant of the pathogen. Another important result is that describing in a reasonable way Epidemics by using consecutive waves and superposition of waves caused by different pathogen variants opens the possibility to investigate the COVID-19 Pandemic in its full time range, since early 2020 to present. In the future, we intend to work on that problem to obtain additional useful information on that particular Pandemic in some country (or region) and to develop further the model (and software) toward readiness to meet next possible challenges when they come.