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Home  >  Medical Research Archives  >  Issue 149  > Omicron Waves in Few European Countries till June 2022 Modeled by a New Version of a Tracking Approach with Successive and Superimposed Waves
Published in the Medical Research Archives
Jul 2023 Issue

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

Published on Jul 06, 2023




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.

Author info

Pavel Petkov

By about mid of 2022, the importance of the COVID-19 Pandemic’s issue was not needing any special argumentation 1. Since the first signals for the seriousness of that Pandemic worldwide in the beginning of 2020 2, much has been learned about the SARS-CoV-2 virus itself, though this process is not finished because new virus variants/mutations appear with time, with different properties, including much increased contagiousness sometimes. This is the case with the Omicron variant identified in late November 2021 3. Later, other sub-variants of it were found responsible for provoking new (or secondary) waves spreading out even faster and whose peaks lie at varying time intervals further away from the primary peak, but sometimes also very close 4,5. As matter of fact the first Omicron variant which became of importance (labeled shortly BA.1 in the literature) and the sub-variant labeled BA.2 which became dominant since February 2022 worldwide, were detected nearly simultaneously in South Africa and Botswana (joined also by BA.3). The present work is concerned with some mathematical aspects of addressing and modeling the Omicron-stage of the Pandemic 6 in retros- pective. However, one should never forget that dealing with the development of Epidemics is a multidisciplinary subject. Epidemiologists, specialists in infections, virologists, medics with different specializations, pharmaceutics, immunologists, molecular biologists etc. naturally participate by addressing their relevant specialized issues. Thus, the modeling remains just a more or less reliable quest for mathematical apparatus able for short and/or long term forecasting or a posteriori description. In this way, it is possible to address more efficiently the issue of the health, social and economic price that societies have to pay to stop/control the Pandemic. Very recently, during the finalization of the present work in May 2023, the WHO declared 7 that the COVID-19 pandemic is now an established and ongoing health issue which no longer constitutes a public health emergency of international concern.

A bit more than an year earlier, in the beginning of March 2022, the Omicron wave has reached in many countries a maximum and decreasing trends were observed. Therefore the question of lifting different restrictions then raised again. At that time, there were objective and real preconditions which have been met and which have made reasonable such a program of return to the normal. However, this general trend cannot be a basis for automatism in dealing with the problem, within about the same nature and tempo of lifting restrictions everywhere. On the contrary, this should be done with taking into account the specific features of the situation at every place (country or even region, may be). Later, new developments occurred, to some extent related to the initialized processes of lifting restriction, but mainly to the spread of new sub-variants of Omicron 4,5 described as being even more contagious than the original one. The present work, on the basis of improvements of the tracking model published recently in Ref.8 aims to reproduce in retrospective the data on the new daily infection cases in three European countries: the UK, Germany and France till June 2022. The improvements compared to Ref8, consist in more continuous interconnection between consecutive waves and superposition of the waves related to pathogens with different properties. The paper is built as follows. After the introduction, the method used for the calculations is presented including the newly incorporated and improved features. Then, the results for the three countries are presented, and later discussed and compared, also to similar data for the USA. Finally, the conclusions of the present study are given.

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