A tentative tracking of the SARS-Cov2 pandemic in France, based on a corrected SIR model including vaccination effects

We developed successive extensions of the SIR model in order to track the dynamics of the SARS-Cov2 disease. The analysis of health system available data is published in a chronicle accessible on the net: https://corona-circule.github. io/lettres/. This chronicle was initiated on late march 2020 and up to now contains 50 issues. A constant concern was the reliability of the data: for instance, we very soon evidenced that the number of confirmed cases, because of the asymptomatic carriers and the erratic testing policy, was hugely underestimated. By the end of 2020 we made a basic change in the model which consisted in accounting for a constant contagiousness time (SIR-tcc) instead of the probabilistic evolution of the end of the infection assumed so far. Recently we completed this SIR-tcc model for the vaccination effects in order to properly track the evolution of the group immunity threshold. Calculations were performed using the Excel facility (Microsoft), allowing a manual fitting of the model parameters. The results have dealt with a large number of countries, but we focus here on the data regarding France. Further pieces of information are also presented, in order to help elucidating some the factors responsible for the complex history of the pandemic dynamics. (submitted dec 14th 2021) 1 The epidemiological context 1.1 The SARS-Cov2 virus The 21st century saw the emergence of three coronaviruses responsible for deadly severe acute respiratory syndromes in humans (SARS): SARSCoV [1,2], MERS-CoV [3], and SARS-CoV-2 [4,5] which is causing the COVID-19 disease. As for the first two, the reservoir host for SARS-CoV-2 is the bat [6]. Whereas palm civets [7] and dromedary camels [8] are recognized for the transmission of, respectively, SARSCoV and MERS-CoV from bats to humans, the SARSCoV-2 intermediate host is still not known. Like other respiratory pathogens, including influenza and rhinovirus, coronavirus transmission occurs through airborne droplets produced by sneezing, coughing, and breathing [9]. Coronaviruses are ribonucleic acid (RNA) viruses, their genetic material is a single-stranded RNA molecule, carrying four main structural proteins Spike, envelope, membrane, nucleocapsid and several nonstructural proteins [10]. The spike surface protein of the coronaviruses mediates their entry into host cells through a variety of receptors and entry mechanisms [11]. Like SARS-CoV, SARS-CoV-2 uses the angiotensin-converting enzyme 2 (ACE2) as a receptor to enter cells [12,13]. Inside the host cell, viral RNA is translated into non-structural proteins that supress the host genes expression in favour of the virus ones [14,15]. Then, viral RNA is replicated, translated and new virus particles are formed that will strike other host cells [16]. Infected cell fuses to neighbouring cells expressing ACE2, giving rise to massive individual respiratory cells that prosper for long and produce more and more new virus particles [17]. Beside the rapid virus replication, the innate immune cells response takes place with the secretion of pro-inflammatory cytokines and proteases [18]. This excessive inflammation, called “cytokine storm”, leads to acute respiratory distress syndrome and pulmonary oedema [6]. However, since the virus supresses the host genes expression, including those encoding proteins that alert the immune system, it escapes the immune response of the host. The consequences of Sars-CoV-2 infection vary greatly from one person to another. While 90% of the infected individuals are not very symptomatic or asymptomatic, 10% develop severe, or even critical, forms with pneumonia requiring an intensive care stay. The viral load is obviously a major risk factor. Age is also a major risk factor for the development of severe forms, with individuals over 65 years having the greatest risk of requiring intensive care [19], and men are more susceptible than women [20]. Nearly 25% of severe forms are due to a deficiency in the type 1 interferon (INF1) pathway, a cytokine usually produced rapidly by the immune system in response to a viral infection and whose main effect is to inhibit virus replication in infected cells). With 3-4% of INF1 gene alterations [21] and 15-20% of presence of autoantibodies neutralizing IFN1 and blocking its antiviral action [22-23]. The EPJ Web of Conferences 263, 01002 (2022) https://doi.org/10.1051/epjconf/202226301002 8 Complexity-Disorder Days 2021 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). presence of INF1 neutralizing autoantibodies is very rare before age 65 (0.2 to 0.5%) and then increases exponentially with aging to reach 4% between 70 and 79 years, and 7% between 80 and 85 years. The causes and mechanisms of this increase in the general population remain to be elucidated, but it partly explains why age is a major risk factor in the development of severe forms of Covid-19. Defects in the gene encoding the toll-like receptor 7 (TLR7), an RNA intracellular receptor playing a major role in INF1 production, are found in 1.8% of men with severe forms under age 65 [24]. The TLR7 gene being on the X chromosome explains why men are more frequently affected by severe Covid-19 than women. 1.2 SARS-CoV-2 variants The SARS-CoV-2 virus is constantly mutating and numerous SARS-CoV-2 variants have emerged, naturally selected for their higher transmissibility, lethality or capacity to escape the host’s immune response in comparison with the original virus (Table 1). Transmissibility is related to permeability and represents the ability of the virus to enter host cells. Lethality is the proportion of infected individuals who die from the infection in a given place, at a given time. Lethality is to be differentiated from virulence which corresponds to the propensity of the virus to harm its host. Virulence is quantified in the absence of specific care. The same variant will have a different lethality from one country to another depending, for example, on the quality of the hospital system, but its virulence will be unchanged. Table 1. Effects of the main SARS-CoV-2 variants, in comparison with the original virus, on their transmissibility, lethality, and ability to escape the host immune response [25-28]. Variant Transmissibility Lethality Immune escape Alpha B.1.1.7 43-90% higher No change Slightly increased Beta B.1. 351 1.5x higher Possibility increased fatality rate Higher Kappa & Delta B.1. 617.1 &2 2.6 x higher Elevated in Brazil (may be due only to healthcare system overload) Higher Gamma P.1 1.7-2.4 x higher Higher Higher Epsilon B.1. 427& 429 19-24% higher Yet not known Slightly increased The most recent variant which is in the headlines at the end of 2021, Omicron (B.1.1.529), carries many mutations present in other variants. Of the 32 Omicron mutations in the spike protein, 16 are in the Delta variant. These known mutations seem worrying since they are linked to a greater infectivity and a better ability to escape the immune response. And numerous new mutations seem able to contribute to a further escape ability, and a more efficient virus replication [29-31]. Nevertheless, there is still a lot to understand about the Omicron variant at the biological, clinical, vaccination and epidemiological level.