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The genome has evolved since a primitive genome until the present state of the human genome dispatched along the 23 pairs of chromosomes. This evolution has been ruled by the mutation process and also by the physiological and pathological reorganization of the genomic material inside or between the chromosomes, which are conditioning the genomic variability. This reorganization is starting at singular points on the short or long chromosomic arms, called crossing-over, or translocations, insertions, break points. In this paper, we will show that these points, also called weak points or hot spots of the genome are correlated, independently of their origin. In addition, we will give some properties of the genetic interaction matrices in terms of attractors of the genetic expression dynamics. Index Terms--Genetics, interaction matrix, positive and negative circuit, regulatory network, translocation.

Modeling contagious diseases needs to incorporate information about social networks through which the disease spreads as well as data about demographic and genetic changes in the susceptible population. In this paper, we propose a theoretical framework (conceptualization and formalization) which seeks to model obesity as a process of transformation of one's own body determined by individual (physical and psychological), inter-individual (relational, i.e., relative to the relationship between the individual and others) and socio-cultural (environmental, i.e., relative to the relationship between the individual and his milieu) factors. Individual and inter-individual factors are tied to each other in a socio-cultural context whose impact is notably related to the visibility of anybody being exposed on the public stage in a non-contingent way. The question we are dealing with in this article is whether such kind of social diseases, i.e., depending upon socio-environmental exposure, can be considered as “contagious”. In other words, can obesity be propagated from individual to individual or from environmental sources throughout an entire population? [ABSTRACT FROM AUTHOR]

Vaccination has been widely recognized as an effective measure for preventing infectious diseases. To facilitate quantitative research into the activation of adaptive immune responses in the human body by vaccines, it is important to develop an appropriate mathematical model, which can provide valuable guidance for vaccine development. In this study, we constructed a novel mathematical model to simulate the dynamics of antibody levels following vaccination, based on principles from immunology. Our model offers a concise and accurate representation of the kinetics of antibody response. We conducted a comparative analysis of antibody dynamics within the body after administering several common vaccines, including traditional inactivated vaccines, mRNA vaccines, and future attenuated vaccines based on defective interfering viral particles (DVG). Our findings suggest that booster shots play a crucial role in enhancing Immunoglobulin G (IgG) antibody levels, and we provide a detailed discussion on the advantages and disadvantages of different vaccine types. From a mathematical standpoint, our model proposes four essential approaches to guide vaccine design: enhancing antigenic T-cell immunogenicity, directing the production of high-affinity antibodies, reducing the rate of IgG decay, and lowering the peak level of vaccine antigen-antibody complexes. Our study contributes to the understanding of vaccine design and its application by explaining various phenomena and providing guidance in comprehending the interactions between antibodies and antigens during the immune process., (© 2024. The Author(s).)

We hypothesize that the first ancestral "protocell" molecular structures, i.e., the first RNAs and peptides that gradually transformed into real cells once the Earth had cooled sufficiently for organic molecules to appear, have left traces in the RNAs and the genes in present cells. We propose a circular RNA that could have been one of these ancestral structures whose vestigial pentameric subsequences would mark the evolution from this key moment when the protocells began to join with living organisms. In particular, we propose that, in present RNAs (ribosomal or messenger), which play an important role in the metabolism of current cells, we look for traces of the proposed primitive structure in the form of pentamers (or longer fragments) that belong to their nucleotide sequence. The result obtained can be summarized in the existence of a gradient of occurrence of such pentamers, with a high frequency for the most vital functions (protein synthesis, nucleic synthesis, cell respiration, etc.). This gradient is also visible between organisms, from the oldest (Archaea) to the most recent (Eukaryotes) in the evolution of species.

This study introduces a specialized Automatic Speech Recognition (ASR) system, leveraging the Whisper Large-v2 model, specifically adapted for radiological applications in the French language. The methodology focused on adapting the model to accurately transcribe medical terminology and diverse accents within the French language context, achieving a notable Word Error Rate (WER) of 17.121%. This research involved extensive data collection and preprocessing, utilizing a wide range of French medical audio content. The results demonstrate the system's effectiveness in transcribing complex radiological data, underscoring its potential to enhance medical documentation efficiency in French-speaking clinical settings. The discussion extends to the broader implications of this technology in healthcare, including its potential integration with electronic health records (EHRs) and its utility in medical education. This study also explores future research directions, such as tailoring ASR systems to specific medical specialties and languages. Overall, this research contributes significantly to the field of medical ASR systems, presenting a robust tool for radiological transcription in the French language and paving the way for advanced technology-enhanced healthcare solutions.

Background: Hereditary angioedema (HAE) is a potentially life-threatening disorder characterized by recurrent episodes of subcutaneous or submucosal swelling. HAE with normal C1 inhibitor (HAE-nC1-INH) is an underdiagnosed condition. Although the association with genetic variants has been identified for some families, the genetic causes in many patients with HAE-nC1-INH remain unknown. The role of genes associated with bradykinin catabolism is not fully understood., Objective: We sought to investigate the biological parameters and the genes related to kallikrein-kinin system in families with a clinical phenotype of HAE-nC1-INH and presenting with a carboxypeptidase N (CPN) deficiency., Methods: This study includes 4 families presenting with HAE-nC1-INH and CPN deficiency. Patients' clinical records were examined, biological parameters of kallikrein-kinin system were measured, and genetics was analyzed by next-generation sequencing and Sanger sequencing. Predictive algorithms (Human Splicing Finder, Sorting Intolerant From Tolerant, Polymorphism Phenotyping v2, MutationTaster, and ClinPred) were used to classify variants as affecting splicing, as benign to deleterious, or as disease-causing., Results: Patients presented with angioedema and urticaria, mainly on face/lips, but also with abdominal pain or laryngeal symptoms. Affected patients displayed low CPN activity-30% to 50% of median value in plasma. We identified 3 variants of the CPN1 gene encoding the catalytic 55-kDa subunit of CPN: c.533G>A, c.582A>G, and c.734C>T. CPN deficiency associated with genetic variants segregated with HAE-nC1-INH symptoms in affected family members., Conclusions: CPN1 gene variants are associated with CPN deficiency and HAE-nC1-INH symptoms in 4 unrelated families. Genetic CPN deficiency may contribute to bradykinin and anaphylatoxin accumulation, with synergistic effects in angioedema and urticarial symptoms., Competing Interests: This work was supported by an 10.13039/100017732E-Rare-1 research grant attributed within European FP7 (HAEIII; S. Cichon, coordinator) and a French National Agency for Research grant (grant no. EudraCT #38RC09.023). The promoter for the study was CHU Grenoble Alpes (#2009-A00025-52). Funding was also obtained from the French National Blood Service (Etablissement Français du Sang) La Plaine Saint Denis (grant no. APR2016-64), from KininX SAS, and the National Rare Disease Program from the French Ministry of Health (National Reference Center for Angioedema CREAK). F.P. was recipient of a PhD fellowship from Etablissement Français du Sang (#APR2016-64). Disclosure of potential conflict of interest: F. Parsopoulou, G. Loules, and A. Ghannam received grants as stated in the funding section. The rest of the authors declare that they have no relevant conflicts of interest., (© 2024 The Author(s).)

Infectious diseases, such as Dengue fever, pose a significant public health threat. Developing a reliable mathematical model plays a crucial role in quantitatively elucidating the kinetic characteristics of antibody-virus interactions. By integrating previous models and incorporating the antibody dynamic theory, we have constructed a novel and robust model that can accurately simulate the dynamics of antibodies and viruses based on a comprehensive understanding of immunology principles. It explicitly formulates the viral clearance effect of antibodies, along with the positive feedback stimulation of virus-antibody complexes on antibody regeneration. In addition to providing quantitative insights into the dynamics of antibodies and viruses, the model exhibits a high degree of accuracy in capturing the kinetics of viruses and antibodies in Dengue fever patients. This model offers a valuable solution to modeling the differences between primary and secondary Dengue infections concerning IgM/IgG antibodies. Furthermore, it demonstrates that a faster removal rate of antibody-virus complexes might lead to a higher peak viral loading and worse clinical symptom. Moreover, it provides a reasonable explanation for the antibody-dependent enhancement of heterogeneous Dengue infections. Ultimately, this model serves as a foundation for constructing an optimal mathematical model to combat various infectious diseases in the future.

DVGs (Defective Viral Genomes) are prevalent in RNA virus infections. In this investigation, we conducted an analysis of high-throughput sequencing data and observed widespread presence of DVGs in SARS-CoV-2. Comparative analysis between SARS-CoV-2 and diverse DNA viruses revealed heightened susceptibility to damage and increased sequencing sample heterogeneity within the SARS-CoV-2 genome. Whole-genome sequencing depth variability analysis exhibited a higher coefficient of variation for SARS-CoV-2, while DVG analysis indicated a significant proportion of recombination sites, signifying notable genome heterogeneity and suggesting that a large proportion of assembled virus particles contain incomplete RNA sequences. Moreover, our investigation explored the sequencing depth and DVG content differences among various strains. Our findings revealed that as the virus evolves, there is a notable increase in the proportion of intact genomes within virus particles, as evidenced by third-generation sequencing data. Specifically, the proportion of intact genome in the Omicron strain surpassed that of the Delta and Alpha strains. This observation effectively elucidates the heightened infectiousness of the Omicron strain compared to the Delta and Alpha strains. We also postulate that this improvement in completeness stems from enhanced virus assembly capacity, as the Omicron strain can promptly facilitate the binding of RNA and capsid protein, thereby reducing the exposure time of vulnerable virus RNA in the host environment and significantly mitigating its degradation. Finally, employing mathematical modeling, we simulated the impact of DVG effects under varying environmental factors on infection characteristics and population evolution. Our findings provide an explanation for the close association between symptom severity and the extent of virus invasion, as well as the substantial disparity in population infection characteristics caused by the same strain under distinct environmental conditions. This study presents a novel approach for future virus research and vaccine development., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Xu, Peng, Song, Zhang, Wei, Demongeot and Zeng.)

Background: The current ribosome has evolved from the primitive stages of life on Earth. Its function is to build proteins and on the basis of this role, we are looking for a universal common ancestor to the ribosome which could: i) present optimal combinatorial properties, and ii) have left vestiges in the current molecules composing the ribosome (rRNA or r-proteins) or helping in its construction and functioning., Methods: Genomic public databases are used for finding the nucleotide sequences of rRNAs and mRNA of r-proteins and statistical calculations are performed on the occurrence in these genes of some pentamers belonging to the RNA proposed as optimal ribosome ancestor., Results: After having exhibited a possible solution to the problem of an RNA capable of catalyzing peptide genesis, traces of this RNA are found in many rRNAs and mRNA of r-proteins, as well as in factors contributing to the construction of the current ribosome., Conclusions: The existence of an optimal primordial RNA whose function is to facilitate the creation of peptide bonds between amino acids may have contributed to accelerate the emergence of the first vital processes. Its traces should be found in many living species inside structures structurally and functionally close to the ribosome, which is already the case in the species studied in this article.

The development of phylogenetic trees based on RNA or DNA sequences generally requires a precise and limited choice of important RNAs, e.g., messenger RNAs of essential proteins or ribosomal RNAs (like 16S), but rarely complete genomes, making it possible to explain evolution and speciation. In this article, we propose revisiting a classic phylogeny of archaea from only the information on the succession of nucleotides of their entire genome. For this purpose, we use a new tool, the unsupervised classifier Maxwell, whose principle lies in the Burrows-Wheeler compression transform, and we show its efficiency in clustering whole archaeal genomes., Competing Interests: Joël Gardes, Christophe Maldivi and Denis Boisset were employed by the company Orange Labs. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The chronological age used in demography describes the linear evolution of the life of a living being. The chronological age cannot give precise information about the exact developmental stage or aging processes an organism has reached. On the contrary, the biological age (or epigenetic age) represents the true evolution of the tissues and organs of the living being. Biological age is not always linear and sometimes proceeds by discontinuous jumps. These jumps can be negative (we then speak of rejuvenation) or positive (in the event of premature aging), and they can be dependent on endogenous events such as pregnancy (negative jump) or stroke (positive jump) or exogenous ones such as surgical treatment (negative jump) or infectious disease (positive jump). The article proposes a mathematical model of the biological age by defining a valid model for the two types of jumps (positive and negative). The existence and uniqueness of the solution are solved, and its temporal dynamic is analyzed using a moments equation. We also provide some individual-based stochastic simulations.

Objective: The objective of this article is to develop a robust method for forecasting the transition from endemic to epidemic phases in contagious diseases using COVID-19 as a case study., Methods: Seven indicators are proposed for detecting the endemic/epidemic transition: variation coefficient, entropy, dominant/subdominant spectral ratio, skewness, kurtosis, dispersion index and normality index. Then, principal component analysis (PCA) offers a score built from the seven proposed indicators as the first PCA component, and its forecasting performance is estimated from its ability to predict the entrance in the epidemic exponential growth phase., Results: This score is applied to the retro-prediction of endemic/epidemic transitions of COVID-19 outbreak in seven various countries for which the first PCA component has a good predicting power., Conclusion: This research offers a valuable tool for early epidemic detection, aiding in effective public health responses.

We have employed mathematical modeling techniques to construct a comprehensive framework for elucidating the intricate response mechanisms of the immune system, facilitating a deeper understanding of B-cell clonal deletion and somatic hypermutation. Our improved model introduces innovative mechanisms that shed light on positive and negative selection processes during T-cell and B-cell development. Notably, clonal deletion is attributed to the attenuated immune stimulation exerted by self-antigens with high binding affinities, rendering them less effective in eliciting subsequent B-cell maturation and differentiation. Secondly, our refined model places particular emphasis on the crucial role played by somatic hypermutation in modulating the immune system's functionality. Through extensive investigation, we have determined that somatic hypermutation not only expedites the production of highly specific antibodies pivotal in combating microbial infections but also serves as a regulatory mechanism to dampen autoimmunity and enhance self-tolerance within the organism. Lastly, our model advances the understanding of the implications of antibody in vivo evolution in the overall process of organismal aging. With the progression of time, the age-associated amplification of autoimmune activity becomes apparent. While somatic hypermutation effectively delays this process, mitigating the levels of autoimmune response, it falls short of reversing this trajectory entirely. In conclusion, our advanced mathematical model offers a comprehensive and scholarly approach to comprehend the intricacies of the immune system. By encompassing novel mechanisms for selection, emphasizing the functional role of somatic hypermutation, and illuminating the consequences of in vivo antibody evolution, our model expands the current understanding of immune responses and their implications in aging.

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

There are several theories on the origin of life, which differ by choosing the preponderant factor of emergence: main function (autocatalysis versus replication), initial location (black smokers versus ponds) or first molecule (RNA versus DNA). Among the two last ones, the first assumes that an RNA world involving a collaboration of small RNAs with amino-acids pre-existed and the second that DNA-enzyme-lipid complexes existed first. The debate between these classic theories is not closed and the arguments for one or the other of these theories have recently fueled a debate in which the two have a high degree of likelihood. It therefore seems interesting to propose a third intermediate way, based on the existence of an RNA that may have existed before the latter stages postulated by these theories, and therefore may be the missing link towards a common origin of them. To search for a possible ancestral structure, we propose as candidate a small RNA existing in ring or hairpin form in the early stages of life, which could have acted as a "proto-ribosome" by favoring the synthesis of the first peptides. Remnants of this putative candidate RNA exist in molecules nowadays involved in the ribosomal factory, the concentrations of these relics depending on the seniority of these molecules within the translation process.

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction−diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction−diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh−Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model’s effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.

Background: The adventure of the mRNA vaccine began thirty years ago in the context of influenza. This consisted in encapsulating the mRNA coding for a viral protein in a lipid particle. We show how the mRNA encoding S protein has been modified for that purpose in the context of the anti-SARS-CoV-2 vaccination., Results: by using data coming from genetic and epidemiologic databases, we show the theoretical possibility of fragmentation of this mRNA into small RNA sequences capable of inhibiting important bio-syntheses such as the production of beta-globin., Discussion: we discuss two aspects related to mRNA vaccine: (i) the plausibility of mRNA fragmentation, and (ii) the role of liposomal nanoparticles (LNPs) used in the vaccine and their impact on mRNA biodistribution., Conclusion: we insist on the need to develop lipid nanoparticles allowing personalized administration of vaccines and avoiding adverse effects due to mRNA fragmentation and inefficient biodistribution. Hence, we recommend (i) adapting the mRNA of vaccines to the least mutated virus proteins and (ii) personalizing its administration to the categories of chronic patients at risk most likely to suffer from adverse effects.

Background: The age of infection plays an important role in assessing an individual's daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article's main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model., Results: We present some results of the parameters' identification of the model when all the eigenvalues are known. This method was applied to Japan's third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month., Conclusion: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.

It was noticed that the mortality rate of SARS-CoV-2 infection experienced a significant declination in the early stage of the epidemic. We suspect that the sharp deterioration of virus toxicity is related to the deletion of the untranslated region (UTR) of the virus genome. It was found that the genome length of SARS-CoV-2 engaged a significant truncation due to UTR deletion after a mega-sequence analysis. Sequence similarity analysis further indicated that short UTR strains originated from its long UTR ancestors after an irreversible deletion. A good correlation was discovered between genome length and mortality, which demonstrated that the deletion of the virus UTR significantly affected the toxicity of the virus. This correlation was further confirmed in a significance analysis of the genetic influence on the clinical outcomes. The viral genome length of hospitalized patients was significantly more extensive than that of asymptomatic patients. In contrast, the viral genome length of asymptomatic was considerably longer than that of ordinary patients with symptoms. A genome-level mutation scanning was performed to systematically evaluate the influence of mutations at each position on virulence. The results indicated that UTR deletion was the primary driving force in alternating virus virulence in the early evolution. In the end, we proposed a mathematical model to explain why this UTR deletion was not continuous.

It is not entirely clear why, at some stage in its evolution, terrestrial life adopted double-stranded DNA as the hereditary material. To explain this, we propose that small, double-stranded, polynucleotide circlets have special catalytic properties. We then use this proposal as the basis for a 'view from here' that we term the Circlet hypothesis as part of a broader Ring World. To maximize the potential explanatory value of this hypothesis, we speculate boldly about the origins of several of the fundamental characteristics and briefly describe the main methods or treatments applied. The principal prediction of the paper is that the highly constrained, conformational changes will occur preferentially in dsDNA, dsRNA and hybrid RNA-DNA circlets that are below a critical size (e.g., 306 bp) and that these will favor the polymerization of precursors into RNA and DNA. We conclude that the Circlet hypothesis and the Ring World therefore have the attraction of offering the same solution to the fundamental problems probably confronting both the earliest cells and the most recent ones.

The end of the acute phase of the COVID-19 pandemic is near in some countries as declared by World Health Organization (WHO) in January 2022 based on some studies in Europe and South Africa despite unequal distribution of vaccines to combat the disease spread globally. The heterogeneity in individual age and the reaction to biological and environmental changes that has been observed in COVID-19 dynamics in terms of different reaction to vaccination by age group, severity of infection per age group, hospitalization and Intensive Care Unit (ICU) records show different patterns, and hence, it is important to improve mathematical models for COVID-19 pandemic prediction to account for different proportions of ages in the population, which is a major factor in epidemic history. We aim in this paper to estimate, using the Usher model, the lifespan loss due to viral infection and ageing which could result in pathological events such as infectious diseases. Exploiting epidemiology and demographic data firstly from Cameroon and then from some other countries, we described the ageing in the COVID-19 outbreak in human populations and performed a graphical representation of the proportion of sensitivity of some of the model parameters which we varied. The result shows a coherence between the orders of magnitude of the calculated and observed incidence numbers during the epidemic wave, which constitutes a semi-quantitative validation of the mathematical modelling approach at the population level. To conclude, the age heterogeneity of the populations involved in the COVID-19 outbreak needs the consideration of models in age groups with specific susceptibilities to infection.

Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible−Infectious−Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0−19 years, 20−64 years, and >64 years, but in this article, we only consider two (20−64 years and >64 years) age groups because the group 0−19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible−Infectious−Goneanewsusceptible−Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-19 epidemics from reported cases data. Given an epidemiological model, we developed in previous studies a method that allowed the computation of an instantaneous transmission rate that produced an exact fit of reported cases data of the COVID-19 outbreak. In this article, we improve the method by incorporating vaccination data. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below 3.5 from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below 3.5, which implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate 75-80% to eliminate COVID-19 in each state or country.