Agent-based model (ABM) has been widely used to study infectious disease transmission by simulating behaviors and interactions of autonomous individuals called agents. In the ABM, agent states, for example infected or susceptible, are assigned according to a set of simple rules, and a complex dynamics of disease transmission is described by the collective states of agents over time. Despite the flexibility in real-world modeling, ABMs have received less attention by statisticians because of the intractable likelihood functions which lead to difficulty in estimating parameters and quantifying uncertainty around model outputs. To overcome this limitation, we propose to treat the entire system as a Hidden Markov Model and develop the ABM for infectious disease transmission within the Bayesian framework. The hidden states in the model are represented by individual agent's states over time. We estimate the hidden states and the parameters associated with the model by applying particle Markov Chain Monte Carlo algorithm. Performance of the approach for parameter recovery and prediction along with sensitivity to prior assumptions are evaluated under various simulation conditions. Finally, we apply the proposed approach to the study of COVID-19 outbreak on Diamond Princess cruise ship and examine the differences in transmission by key demographic characteristics, while considering different network structures and the limitations of COVID-19 testing in the cruise.
There are racial disparities in the COVID-19 test positivity rate, suggesting that minorities may be under-tested. Here, drawing on the literature on statistically assessing racial disparities in policing, we 1) illuminate a statistical flaw, known as infra-marginality, in using the positivity rate as a metric for assessing racial disparities in under-testing; 2) develop a new type of Bayesian threshold test to measure disparities in COVID-19 testing and 3) apply the test to measure racial disparities in testing thresholds in a real-world COVID-19 dataset.
This paper describes the Bayesian SIR modeling of the 3 waves of Covid-19 in two contrasting US states during 2020-2021. A variety of models are evaluated at the county level for goodness-of-fit and an assessment of confounding predictors is also made. It is found that models with three deprivation predictors and neighborhood effects are important. In addition the work index from Google mobility was also found to provide increased explanation of the transmission dynamic.
To strengthen inferences meta analyses are commonly used to summarize information from a set of independent studies. In some cases, though, the data may not satisfy the assumptions underlying the meta analysis. Using three Bayesian methods that have a more general structure than the common meta analytic ones, we can show the extent and nature of the pooling that is justified statistically. In this paper, we re-analyze data from several reviews whose objective is to make inference about the COVID-19 asymptomatic infection rate. When it is unlikely that all of the true effect sizes come from a s…
Objective: To estimate the number of deaths in Peru due to COVID-19. Design: With a priori information obtained from the daily number of deaths due to CODIV-19 in China and data from the Peruvian authorities, we constructed a predictive Bayesian non-linear model for the number of deaths in Peru. Exposure: COVID-19. Outcome: Number of deaths. Results: Assuming an intervention level similar to the one implemented in China, the total number of deaths in Peru is expected to be 612 (95%CI: 604.3 - 833.7) persons. Sixty four days after the first reported death, the 99% of expected deaths will be obs…
Obtaining up to date information on the number of UK COVID-19 regional infections is hampered by the reporting lag in positive test results for people with COVID-19 symptoms. In the UK, for "Pillar 2" swab tests for those showing symptoms, it can take up to five days for results to be collated. We make use of the stability of the under reporting process over time to motivate a statistical temporal model that infers the final total count given the partial count information as it arrives. We adopt a Bayesian approach that provides for subjective priors on parameters and a hierarchical structure …
Most COVID-19 predictive modeling efforts use statistical or mathematical models to predict national- and state-level COVID-19 cases or deaths in the future. These approaches assume parameters such as reproduction time, test positivity rate, hospitalization rate, and social intervention effectiveness (masking, distancing, and mobility) are constant. However, the one certainty with the COVID-19 pandemic is that these parameters change over time, as well as vary across counties and states. In fact, the rate of spread over region, hospitalization rate, hospital length of stay and mortality rate, …
Decision making in the face of a disaster requires the consideration of several complex factors. In such cases, Bayesian multi-criteria decision analysis provides a framework for decision making. In this paper, we present how to construct a multi-attribute decision support system for choosing between countermeasure strategies, such as lockdowns, designed to mitigate the effects of COVID-19. Such an analysis can evaluate both the short term and long term efficacy of various candidate countermeasures. The expected utility scores of a countermeasure strategy capture the expected impact of the pol…
This work proposes a semi-parametric approach to estimate Covid-19 (SARS-CoV-2) evolution in Spain. Considering the sequences of 14 days cumulative incidence of all Spanish regions, it combines modern Deep Learning (DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma model for counts. DL model provides a suitable description of observed sequences but no reliable uncertainty quantification around it can be obtained. To overcome this we use the prediction from DL as an expert elicitation of the expected number of counts along with their uncertainty and thus obtaining the…
The Covid-19 pandemic has spread across the world since the beginning of 2020. Many regions have experienced its effects. The state of South Carolina in the USA has seen cases since early March 2020 and a primary peak in early April 2020. A lockdown was imposed on April 6th but lifting of restrictions started on April 24th. The daily case and death data as reported by NCHS (deaths) via the New York Times GitHUB repository have been analyzed and approaches to modeling of the data are presented. Prediction is also considered and the role of asymptomatic transmission is assessed as a latent unobs…
The COVID-19 pandemic has caused severe public health consequences in the United States. In this study, we use a hierarchical Bayesian model to estimate the age-specific COVID-19 attributable deaths over time in the United States. The model is specified by a novel non-parametric spatial approach, a low-rank Gaussian Process (GP) projected by regularised B-splines. We show that this projection defines a new GP with attractive smoothness and computational efficiency properties, derive its kernel function, and discuss the penalty terms induced by the projected GP. Simulation analyses and benchmar…
We introduce a Bayesian sequential data assimilation method for COVID-19 forecasting. It is assumed that suitable transmission, epidemic and observation models are available and previously validated and the transmission and epidemic models are coded into a dynamical system. The observation model depends on the dynamical system state variables and parameters, and is cast as a likelihood function. We elicit prior distributions of the effective population size, the dynamical system initial conditions and infectious contact rate, and use Markov Chain Monte Carlo sampling to make inference and pred…
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…
A key challenge in estimating the infection fatality rate (IFR) -- and its relation with various factors of interest -- is determining the total number of cases. The total number of cases is not known because not everyone is tested, but also, more importantly, because tested individuals are not representative of the population at large. We refer to the phenomenon whereby infected individuals are more likely to be tested than non-infected individuals, as "preferential testing." An open question is whether or not it is possible to reliably estimate the IFR without any specific knowledge about th…
The outbreak of Coronavirus Disease 2019 (COVID-19) is an ongoing pandemic affecting over 200 countries and regions. Inference about the transmission dynamics of COVID-19 can provide important insights into the speed of disease spread and the effects of mitigation policies. We develop a novel Bayesian approach to such inference based on a probabilistic compartmental model using data of daily confirmed COVID-19 cases. In particular, we consider a probabilistic extension of the classical susceptible-infectious-recovered model, which takes into account undocumented infections and allows the epide…
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 su…
In this paper, we propose a Susceptible-Infected-Removal (SIR) model with time fused coefficients. In particular, our proposed model discovers the underlying time homogeneity pattern for the SIR model's transmission rate and removal rate via Bayesian shrinkage priors. MCMC sampling for the proposed method is facilitated by the nimble package in R. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze different levels of COVID-19 data in the United States.
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.
The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to Rt estimation, resulting in the state-of-the-art DARt system. With DARt, time misalignment …
In the initial wave of the COVID-19 pandemic we observed great discrepancies in both infection and mortality rates between countries. Besides the biological and epidemiological factors, a multitude of social and economic criteria also influence the extent to which these discrepancies appear. Consequently, there is an active debate regarding the critical socio-economic and health factors that correlate with the infection and mortality rates outcome of the pandemic. Here, we leverage Bayesian model averaging techniques and country level data to investigate the potential of 28 variables, describi…
We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in $\sim$1500 dimensions after discretization. To infer these parameters, we use reported data on t…
Compartmental Disease Models with Time-Varying Transmission Rates: A Bayesian Generalized Hamiltonian Monte Carlo framework with Applications to COVID-19
Basque Center for Applied Mathematics (BCAM)（巴斯克应用数学中心）；Universidad Autonoma de Madrid（马德里自治大学）；Universidade de Vigo（维戈大学）；Galician Center for Mathematical Research and Technology (CITMAga)（加利西亚数学研究与技术中心）；Euskal Herriko Unibertsitatea (EHU)（巴斯克地区大学）；Basque Foundation for Science (IKERBASQUE)（巴斯克科学基金会）
In this report we fit a semi-mechanistic Bayesian hierarchical model to describe the Mexican COVID-19 epidemic. We obtain two epidemiological measures: the number of infections and the reproduction number. Estimations are based on death data. Hence, we expect our estimates to be more accurate than the attack rates estimated from the reported number of cases.
Tufts University（塔夫茨大学）；Tufts Medical Center（塔夫茨医学中心）
We consider the problem of forecasting the daily number of hospitalized COVID-19 patients at a single hospital site, in order to help administrators with logistics and planning. We develop several candidate hierarchical Bayesian models which directly capture the count nature of data via a generalized Poisson likelihood, model time-series dependencies via autoregressive and Gaussian process latent processes, and share statistical strength across related sites. We demonstrate our approach on public datasets for 8 hospitals in Massachusetts, U.S.A. and 10 hospitals in the United Kingdom. Further …
While vaccines are crucial to end the COVID-19 pandemic, public confidence in vaccine safety has always been vulnerable. Many statistical methods have been applied to VAERS (Vaccine Adverse Event Reporting System) database to study the safety of COVID-19 vaccines. However, all these methods ignored the adverse event (AE) ontology. AEs are naturally related; for example, events of retching, dysphagia, and reflux are all related to an abnormal digestive system. Explicitly bringing AE relationships into the model can aid in the detection of true AE signals amid the noise while reducing false posi…
We analyze repeated cross-sectional survey data collected by the Institute of Global Health Innovation, to characterize the perception and behavior of the Italian population during the Covid-19 pandemic, focusing on the period that spans from April to November 2020. To accomplish this goal, we propose a Bayesian dynamic latent-class regression model, that accounts for the effect of sampling bias including survey weights into the likelihood function. According to the proposed approach, attitudes towards Covid-19 are described via three ideal behaviors that are fixed over time, corresponding to …
Currently, novel coronavirus disease 2019 (COVID-19) is a big threat to global health. The rapid spread of the virus has created pandemic, and countries all over the world are struggling with a surge in COVID-19 infected cases. There are no drugs or other therapeutics approved by the US Food and Drug Administration to prevent or treat COVID-19: information on the disease is very limited and scattered even if it exists. This motivates the use of data integration, combining data from diverse sources and eliciting useful information with a unified view of them. In this paper, we propose a Bayesia…
We study the effects of physical distancing measures for the spread of COVID-19 in regional areas within British Columbia, using the reported cases of the five provincial Health Authorities. Building on the Bayesian epidemiological model of Anderson et al. (2020), we propose a hierarchical regional Bayesian model with time-varying regional parameters between March to December of 2020. In the absence of COVID-19 variants and vaccinations during this period, we examine the regionalized basic reproduction number, modelled prevalence, relative reduction in contact due to physical distancing, and p…
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…
In this paper, we investigate the classical and Bayesian estimation of unknown parameters of the Gumbel type-II distribution based on adaptive type-II progressive hybrid censored sample (AT-II PHCS). The maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) are developed and computed numerically using Newton-Raphson method. Bayesian approaches are employed to estimate parameters under symmetric and asymmetric loss functions. Bayesian estimates are not in explicit forms. Thus, Bayesian estimates are obtained by using Markov chain Monte Carlo (MCMC) method along with …
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 m…
A full Bayesian approach to the estimation of Vaccine Efficacy is presented, which is an improvement over the currently used exact method conditional on the total number of cases. As an example, we reconsider the statistical sections of the BioNTech/Pfizer protocol, which in 2020 has led to the first approved anti-Covid-19 vaccine.
The coronavirus disease 2019 (COVID-19) global pandemic has led many countries to impose unprecedented lockdown measures in order to slow down the outbreak. Questions on whether governments have acted promptly enough, and whether lockdown measures can be lifted soon have since been central in public discourse. Data-driven models that predict COVID-19 fatalities under different lockdown policy scenarios are essential for addressing these questions and informing governments on future policy directions. To this end, this paper develops a Bayesian model for predicting the effects of COVID-19 lockd…
Multiple studies have suggested the spread of COVID-19 is affected by factors such as climate, BCG vaccinations, pollution and blood type. We perform a joint study of these factors using the death growth rates of 40 regions worldwide with both machine learning and Bayesian methods. We find weak, non-significant (< 3$σ$) evidence for temperature and relative humidity as factors in the spread of COVID-19 but little or no evidence for BCG vaccination prevalence or $\text{PM}_{2.5}$ pollution. The only variable detected at a statistically significant level (>3$σ$) is the rate of positive COVID-19 …
Tufts University（塔夫茨大学）；Tufts Medical Center（塔夫茨医疗中心）
We address the problem of modeling constrained hospital resources in the midst of the COVID-19 pandemic in order to inform decision-makers of future demand and assess the societal value of possible interventions. For broad applicability, we focus on the common yet challenging scenario where patient-level data for a region of interest are not available. Instead, given daily admissions counts, we model aggregated counts of observed resource use, such as the number of patients in the general ward, in the intensive care unit, or on a ventilator. In order to explain how individual patient trajector…
We consider latent Gaussian fields for modelling spatial dependence in the context of both spatial point patterns and areal data, providing two different applications. The inhomogeneous Log-Gaussian Cox Process model is specified to describe a seismic sequence occurred in Greece, resorting to the Stochastic Partial Differential Equations. The Besag-York-Mollie model is fitted for disease mapping of the Covid-19 infection in the North of Italy. These models both belong to the class of Bayesian hierarchical models with latent Gaussian fields whose posterior is not available in closed form. There…
In this paper, we build a mechanistic system to understand the relation between a reduction in human mobility and Covid-19 spread dynamics within New York City. To this end, we propose a multivariate compartmental model that jointly models smartphone mobility data and case counts during the first 90 days of the epidemic. Parameter calibration is achieved through the formulation of a general Bayesian hierarchical model to provide uncertainty quantification of resulting estimates. The open-source probabilistic programming language Stan is used for the requisite computation. Through sensitivity a…
Heidelberg University（海德堡大学）；Chinese Academy of Medical Sciences and Peking Union Medical College（中国医学科学院与北京协和医学院）；University Hospital Bonn（波恩大学医院）；University Hospital Heidelberg（海德堡大学医院）；Harvard T.H. Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）；Africa Health Research Institute（非洲健康研究所）
Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and intervention measures during an ongoing outbreak. However, reliably inferring the dynamics of ongoing outbreaks by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address …
As the coronavirus disease 2019 (COVID-19) has shown profound effects on public health and the economy worldwide, it becomes crucial to assess the impact on the virus transmission and develop effective strategies to address the challenge. A new statistical model derived from the SIR epidemic model with functional parameters is proposed to understand the impact of weather and government interventions on the virus spread in the presence of asymptomatic infections among eight metropolitan areas in the United States. The model uses Bayesian inference with Gaussian process priors to study the funct…
A finite mixture model is used to learn trends from the currently available data on coronavirus (COVID-19). Data on the number of confirmed COVID-19 related cases and deaths for European countries and the United States (US) are explored. A semi-supervised clustering approach with positive equivalence constraints is used to incorporate country and state information into the model. The analysis of trends in the rates of cases and deaths is carried out jointly using a mixture of multivariate Gaussian non-linear regression models with a mean trend specified using a generalized logistic function. T…
The correct evaluation of the reproductive number $R$ for COVID-19 -- which characterizes the average number of secondary cases generated by each typical primary case -- is central in the quantification of the potential scope of the pandemic and the selection of an appropriate course of action. In most models, $R$ is modeled as a universal constant for the virus across outbreak clusters and individuals -- effectively averaging out the inherent variability of the transmission process due to varying individual contact rates, population densities, demographics, or temporal factors amongst many. Y…
We propose a Bayesian Heterogeneity Learning approach for Susceptible-Infected-Removal-Susceptible (SIRS) model that allows underlying clustering patterns for transmission rate, recovery rate, and loss of immunity rate for the latest coronavirus (COVID-19) among different regions. Our proposed method provides simultaneously inference on parameter estimation and clustering information which contains both number of clusters and cluster configurations. Specifically, our key idea is to formulates the SIRS model into a hierarchical form and assign the Mixture of Finite mixtures priors for heterogen…
