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Register a new userAnalyzing initial stage of COVID-19 transmission through Bayesian time-varying model
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Added by
Arkaprava Roy
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Recent outbreak of the novel coronavirus COVID-19 has affected all of our lives in one way or the other. While medical researchers are working hard to find a cure and doctors/nurses to attend the affected individuals, measures such as `lockdown, `stay-at-home, `social distancing are being implemented in different parts of the world to curb its further spread. To model the non-stationary spread, we propose a novel time-varying semiparametric AR$(p)$ model for the count valued time-series of newly affected cases, collected every day and also extend it to propose a novel time-varying INGARCH model. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We substantiate our methods by simulations that show superiority compared to some of the close existing methods. Finally we analyze the daily time series data of newly confirmed cases to study its spread through different government interventions.
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Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compartmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a real-world disease. Different models of disease including the SIR, SIRm and SEIR model are compared with respect to their ability to predict disease spread. Physical distancing impacts and personal protection equipment use will be discussed in relevance to the COVID-19 spread.
In this short technical report we model, within the Bayesian framework, the rate of positive tests reported by the the State of Indiana, accounting also for the substantial variability (and overdispeartion) in the daily count of the tests performed. The approach we take, results with a simple procedure for prediction, a posteriori, of this rate of positivity and allows for an easy and a straightforward adaptation by any agency tracking daily results of COVID-19 tests. The numerical results provided herein were obtained via an updatable R Markdown document.
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.
We analyze risk factors correlated with the initial transmission growth rate of the recent COVID-19 pandemic in different countries. The number of cases follows in its early stages an almost exponential expansion; we chose as a starting point in each country the first day $d_i$ with 30 cases and we fitted for 12 days, capturing thus the early exponential growth. We looked then for linear correlations of the exponents $alpha$ with other variables, for a sample of 126 countries. We find a positive correlation, {it i.e. faster spread of COVID-19}, with high confidence level with the following variables, with respective $p$-value: low Temperature ($4cdot10^{-7}$), high ratio of old vs.~working-age people ($3cdot10^{-6}$), life expectancy ($8cdot10^{-6}$), number of international tourists ($1cdot10^{-5}$), earlier epidemic starting date $d_i$ ($2cdot10^{-5}$), high level of physical contact in greeting habits ($6 cdot 10^{-5}$), lung cancer prevalence ($6 cdot 10^{-5}$), obesity in males ($1 cdot 10^{-4}$), share of population in urban areas ($2cdot10^{-4}$), cancer prevalence ($3 cdot 10^{-4}$), alcohol consumption ($0.0019$), daily smoking prevalence ($0.0036$), UV index ($0.004$, 73 countries). We also find a correlation with low Vitamin D levels ($0.002-0.006$, smaller sample, $sim 50$ countries, to be confirmed on a larger sample). There is highly significant correlation also with blood types: positive correlation with types RH- ($3cdot10^{-5}$) and A+ ($3cdot10^{-3}$), negative correlation with B+ ($2cdot10^{-4}$). Several of the above variables are intercorrelated and likely to have common interpretations. We performed a Principal Component Analysis, in order to find their significant independent linear combinations. We also analyzed a possible bias: countries with low GDP-per capita might have less testing and we discuss correlation with the above variables.
We describe the population-based SEIR (susceptible, exposed, infected, removed) model developed by the Irish Epidemiological Modelling Advisory Group (IEMAG), which advises the Irish government on COVID-19 responses. The model assumes a time-varying effective contact rate (equivalently, a time-varying reproduction number) to model the effect of non-pharmaceutical interventions. A crucial technical challenge in applying such models is their accurate calibration to observed data, e.g., to the daily number of confirmed new cases, as the past history of the disease strongly affects predictions of future scenarios. We demonstrate an approach based on inversion of the SEIR equations in conjunction with statistical modelling and spline-fitting of the data, to produce a robust methodology for calibration of a wide class of models of this type.
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