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Register a new userMorphology and numerical characteristics of epidemic curves for SARS-Cov-II using Moyal distribution
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In this paper, it is shown that the Moyal distribution is an excelent tool to study the SARS-Cov-II (Covid-19) epidemiological associated curves and its propagation. The Moyal parameters give all the information to describe the form and the impact of the illness outbreak in the different affected countries and its global impact. We checked that the Moyal distribution can accurately fit the daily report of {it{new confirmed cases of infected people}} (NCC) per country, in that places where the contagion is reaching their final phase, describing the beginning, the most intense phase and the descend of the contagion, simultaneously . In order to achieve the purpose of this work, it is important to work with a complete and well compilated set of the data to be used to fit the curves. Data from European countries like France, Spain, Italy Belgium, Sweden, United Kingdom, Denmark and others like USA and China, have been used. Also, the correlation between the parameters of the Moyal distribution fitting and the general public health measures imposed in each country, have been discussed. A relation between those policies and the features of the Moyal distribution, in terms of their parameters and critical points, is shown; from that, it can be seen that the knowledge of the time evolution of the epidemiological curve, their critical points, superposition properties and rates of the rising and the ending, could help to find a way to estimate the efficiency of social distancing measures, imposed in each country, and anticipate the different phases of the pandemic.
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A number of epidemics, including the SARS-CoV-1 epidemic of 2002-2004, have been known to exhibit superspreading, in which a small fraction of infected individuals is responsible for the majority of new infections. The existence of superspreading implies a fat-tailed distribution of infectiousness (new secondary infections caused per day) among different individuals. Here, we present a simple method to estimate the variation in infectiousness by examining the variation in early-time growth rates of new cases among different subpopulations. We use this method to estimate the mean and variance in the infectiousness, $beta$, for SARS-CoV-2 transmission during the early stages of the pandemic within the United States. We find that $sigma_beta/mu_beta gtrsim 3.2$, where $mu_beta$ is the mean infectiousness and $sigma_beta$ its standard deviation, which implies pervasive superspreading. This result allows us to estimate that in the early stages of the pandemic in the USA, over 81% of new cases were a result of the top 10% of most infectious individuals.
Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.
SARS-CoV-2 causing COVID-19 disease has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used and misused to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, is dominated by a small number of individuals, and is driven by super-spreading events (SSEs). The distinct transmission features, such as high stochasticity under low prevalence, and the central role played by SSEs on transmission dynamics, should not be overlooked. Many explosive SSEs have occurred in indoor settings stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, fish factories, cruise ships, family gatherings, parties and night clubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity that outbreak can be effectively contained with targeted interventions to eliminate SSEs. Here, we describe the potential types of SSEs, how they influence transmission, and give recommendations for control of SARS-CoV-2.
SARS-CoV-2, like any other virus, continues to mutate as it spreads, according to an evolutionary process. Unlike any other virus, the number of currently available sequences of SARS-CoV-2 in public databases such as GISAID is already several million. This amount of data has the potential to uncover the evolutionary dynamics of a virus like never before. However, a million is already several orders of magnitude beyond what can be processed by the traditional methods designed to reconstruct a viruss evolutionary history, such as those that build a phylogenetic tree. Hence, new and scalable methods will need to be devised in order to make use of the ever increasing number of viral sequences being collected. Since identifying variants is an important part of understanding the evolution of a virus, in this paper, we propose an approach based on clustering sequences to identify the current major SARS-CoV-2 variants. Using a $k$-mer based feature vector generation and efficient feature selection methods, our approach is effective in identifying variants, as well as being efficient and scalable to millions of sequences. Such a clustering method allows us to show the relative proportion of each variant over time, giving the rate of spread of each variant in different locations -- something which is important for vaccine development and distribution. We also compute the importance of each amino acid position of the spike protein in identifying a given variant in terms of information gain. Positions of high variant-specific importance tend to agree with those reported by the USAs Centers for Disease Control and Prevention (CDC), further demonstrating our approach.
In a previous article [1] we have described the temporal evolution of the Sars- Cov-2 in Italy in the time window February 24-April 1. As we can see in [1] a generalized logistic equation captures both the peaks of the total infected and the deaths. In this article our goal is to study the missing peak, i.e. the currently infected one (or total currently positive). After the April 7 the large increase in the number of swabs meant that the logistical behavior of the infected curve no longer worked. So we decided to generalize the model, introducing new parameters. Moreover, we adopt a similar approach used in [1] (for the estimation of deaths) in order to evaluate the recoveries. In this way, introducing a simple conservation law, we define a model with 4 populations: total infected, currently positives, recoveries and deaths. Therefore, we propose an alternative method to a classical SIRD model for the evaluation of the Sars-Cov-2 epidemic. However, the method is general and thus applicable to other diseases. Finally we study the behavior of the ratio infected over swabs for Italy, Germany and USA, and we show as studying this parameter we recover the generalized Logistic model used in [1] for these three countries. We think that this trend could be useful for a future epidemic of this coronavirus.
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