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Register a new userRevealing the Transmission Dynamics of COVID-19: A Bayesian Framework for $R_t$ Estimation
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In epidemiological modelling, the instantaneous reproduction number, $R_t$, is important to understand the transmission dynamics of infectious diseases. Current $R_t$ estimates often suffer from problems such as lagging, averaging and uncertainties demoting the usefulness of $R_t$. To address these problems, we propose a new method in the framework of sequential Bayesian inference where a Data Assimilation approach is taken for $R_t$ estimation, resulting in the state-of-the-art DAR$_t$ system for $R_t$ estimation. With DAR$_t$, the problem of time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and $R_t$; the drawback of averaging is improved by instantaneous updating upon new observations and a model selection mechanism capturing abrupt changes caused by interventions; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DAR$_t$ through simulations and demonstrate its power in revealing the transmission dynamics of COVID-19.
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We propose a general Bayesian approach to modeling epidemics such as COVID-19. The approach grew out of specific analyses conducted during the pandemic, in particular an analysis concerning the effects of non-pharmaceutical interventions (NPIs) in reducing COVID-19 transmission in 11 European countries. The model parameterizes the time varying reproduction number $R_t$ through a regression framework in which covariates can e.g be governmental interventions or changes in mobility patterns. This allows a joint fit across regions and partial pooling to share strength. This innovation was critical to our timely estimates of the impact of lockdown and other NPIs in the European epidemics, whose validity was borne out by the subsequent course of the epidemic. Our framework provides a fully generative model for latent infections and observations deriving from them, including deaths, cases, hospitalizations, ICU admissions and seroprevalence surveys. One issue surrounding our models use during the COVID-19 pandemic is the confounded nature of NPIs and mobility. We use our framework to explore this issue. We have open sourced an R package epidemia implementing our approach in Stan. Versions of the model are used by New York State, Tennessee and Scotland to estimate the current situation and make policy decisions.
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 the COVID-19 pandemic, among the more controversial issues is the use of face coverings. To address this we show that the underlying physics ensures particles with diameters & 1 $mu$m are efficiently filtered out by a simple cotton or surgical mask. For particles in the submicron range the efficiency depends on the material properties of the masks, though generally the filtration efficiency in this regime varies between 30 to 60 % and multi-layered cotton masks are expected to be comparable to surgical masks. Respiratory droplets are conventionally divided into coarse droplets (> 5-10 $mu$m) responsible for droplet transmission and aerosols (< 5-10 $mu$m) responsible for airborne transmission. Masks are thus expected to be highly effective at preventing droplet transmission, with their effectiveness limited only by the mask fit, compliance and appropriate usage. By contrast, knowledge of the size distribution of bioaerosols and the likelihood that they contain virus is essential to understanding their effectiveness in preventing airborne transmission. We argue from literature data on SARS-CoV-2 viral loads that the finest aerosols (< 1 $mu$m) are unlikely to contain even a single virion in the majority of cases; we thus expect masks to be effective at reducing the risk of airborne transmission in most settings.
In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, $mathcal{R}_{0}$. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when $mathcal{R}_{0}<1$ via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of $mathcal{R}_{0}$ since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by $mathcal{R}_{0} = 3.110$, with the 95% confidence interval being $2.042 leq mathcal{R}_0 leq 3.240$, and the mean value being $mathcal{R}_{0}=2.623$. Of the 32 parameters in the model, we find that just six have a significant influence on $mathcal{R}_{0}$, these include the rate of testing, where an increasing testing rate contributes to the reduction of $mathcal{R}_{0}$.
Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models parameters and can give misleading choices. One approach that uses the full posterior distribution is to compute the ratio of two models normalising constants, known as the Bayes factor. Often in realistic problems, this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a variation of the TI method, referred to as referenced TI, which computes a single models normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with explicit pedagogical 1 and 2D examples. Benchmarking is presented with comparable methods and we find favourable convergence performance. The approach is shown to be useful in practice when applied to a real problem - to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.
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