Generic probabilistic modelling and non-homogeneity issues for the UK epidemic of COVID-19
Anatoly Zhigljavsky, Roger Whitaker, Ivan Fesenko, Kobi Kremnizer, Jack Noonan, Paul Harper, Jonathan Gillard, Thomas Woolley, Daniel Gartner, Jasmine Grimsley,… 展开作者
Anatoly Zhigljavsky, Roger Whitaker, Ivan Fesenko, Kobi Kremnizer, Jack Noonan, Paul Harper, Jonathan Gillard, Thomas Woolley, Daniel Gartner, Jasmine Grimsley, Edilson de Arruda, Val Fedorov, Tom Crick MBE
Coronavirus COVID-19 spreads through the population mostly based on social contact. To gauge the potential for widespread contagion, to cope with associated uncertainty and to inform its mitigation, more accurate and robust modelling is centrally important for policy making. We provide a flexible modelling approach that increases the accuracy with which insights can be made. We use this to analyse different scenarios relevant to the COVID-19 situation in the UK. We present a stochastic model that captures the inherently probabilistic nature of contagion between population members. The computational nature of our model means that spatial constraints (e.g., communities and regions), the susceptibility of different age groups and other factors such as medical pre-histories can be incorporated with ease. We analyse different possible scenarios of the COVID-19 situation in the UK. Our model is robust to small changes in the parameters and is flexible in being able to deal with different scenarios.
This approach goes beyond the convention of representing the spread of an epidemic through a fixed cycle of susceptibility, infection and recovery (SIR). It is important to emphasise that standard SIR-type models, unlike our model, are not flexible enough and are also not stochastic and hence should be used with extreme caution. Our model allows both heterogeneity and inherent uncertainty to be incorporated. Due to the scarcity of verified data, we draw insights by calibrating our model using parameters from other relevant sources, including agreement on average (mean field) with parameters in SIR-based models.
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
We study the spatial heterogeneity effect on regional COVID-19 pandemic timing and severity by analyzing the COVID-19 growth rate curves in the United States. We propose a geographically detailed functional data grouping method equipped with a functional conditional autoregressive (CAR) prior to fully capture the spatial correlation in the pandemic curves. The spatial homogeneity pattern can then be detected by a geographically weighted Chinese restaurant process prior which allows both locally spatially contiguous groups and globally discontiguous groups. We design an efficient Markov chain M…
We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the population. We find that a correct assessment of the amount of under-detection is important to obtain reliable estimates of the critical model parameters. Moreover, a single SIR model over the whole epidemic period is unable to correctly describe the behaviour of the pandemic. Then, the adaptation of the model in every time-interval between relevant governmen…
An analysis of the COVID-19 epidemic is proposed on the basis of the epiMOX dashboard (publicly accessible at https://www.epimox.polimi.it) that deals with data of the epidemic trends and outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development, together with its current trends by fostering a deeper interpretation of available data through several critical epidemic indicators. In addition, we complement the epiMOX dashboard with a predictive tool based on an epidemiological compartmental model, named SUIHTER, for the forecast …
The ongoing COVID-19 pandemic has progressed with varying degrees of intensity in individual countries, suggesting it is important to analyse factors that vary between them. We study measures of `population-weighted density', which capture density as perceived by a randomly chosen individual. These measures of population density can significantly explain variation in the initial rate of spread of COVID-19 between countries within Europe. However, such measures do not explain differences on a global scale, particularly when considering countries in East Asia, or looking later into the epidemics…
Coronavirus disease (COVID-2019) is a severe ongoing novel pandemic that is spreading quickly across the world. Italy, that is widely considered one of the main epicenters of the pandemic, has registered the highest COVID-2019 death rates and death toll in the world, to the present day. In this article I estimate an autoregressive integrated moving average (ARIMA) model to forecast the epidemic trend over the period after April 4, 2020, by using the Italian epidemiological data at national and regional level. The data refer to the number of daily confirmed cases officially registered by the It…
We review epidemiological models for the propagation of the COVID-19 pandemic during the early months of the outbreak: from February to May 2020. The aim is to propose a methodological review that highlights the following characteristics: (i) the epidemic propagation models, (ii) the modeling of intervention strategies, (iii) the models and estimation procedures of the epidemic parameters and (iv) the characteristics of the data used. We finally selected 80 articles from open access databases based on criteria such as the theoretical background, the reproducibility, the incorporation of interv…
We investigate patterns of COVID-19 mortality across 20 Italian regions and their association with mobility, positivity, and socio-demographic, infrastructural and environmental covariates. Notwithstanding limitations in accuracy and resolution of the data available from public sources, we pinpoint significant trends exploiting information in curves and shapes with Functional Data Analysis techniques. These depict two starkly different epidemics; an "exponential" one unfolding in Lombardia and the worst hit areas of the north, and a milder, "flat(tened)" one in the rest of the country -- inclu…
We portray the evolution of the Covid-19 epidemic during the crisis of March-April 2020 in the Paris area, by analyzing the medical emergency calls received by the EMS of the four central departments of this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between these departments. We show that the logarithm of each epidemic observable can be approximated by a piecewise linear function of time. This allows us to distinguish the different phases of the epidemic, and to identify the delay between sanitary measures and their influence on the load of EMS. This …
Clinical trials of a vaccine during an epidemic face particular challenges, such as the pressure to identify an effective vaccine quickly to control the epidemic, and the effect that time-space-varying infection incidence has on the power of a trial. We illustrate how the operating characteristics of different trial design elements may be evaluated using a network epidemic and trial simulation model, based on COVID-19 and individually randomised two-arm trials with a binary outcome. We show that "ring" recruitment strategies, prioritising participants at high risk of infection, can result in s…
Governments around the world have implemented preventive measures against the spread of the coronavirus disease (COVID-19). In this study, we consider a multivariate discrete-time Markov model to analyze the propagation of COVID-19 across 33 provincial regions in China. This approach enables us to evaluate the effect of mobility restriction policies on the spread of the disease. We use data on daily human mobility across regions and apply the Bayesian framework to estimate the proposed model. The results show that the spread of the disease in China was predominately driven by community transmi…
A novel yet simple extension of the symmetric logistic distribution is proposed by introducing a skewness parameter. It is shown how the three parameters of the ensuing skew logistic distribution may be estimated using maximum likelihood. The skew logistic distribution is then extended to the skew bi-logistic distribution to allow the modelling of multiple waves in epidemic time series data. The proposed skew-logistic model is validated on COVID-19 data from the UK, and is evaluated for goodness-of-fit against the logistic and normal distributions using the recently formulated empirical surviv…
We propose a detailed discrete-time model of COVID-19 epidemics coming in two flavours, mean-field and probabilistic. The main contribution lies in several extensions of the basic model that capture i) user mobility - distinguishing routing, i.e. change of residence, from commuting, i.e. daily mobility - and ii) contact tracing procedures. We confront this model to public data on daily hospitalizations, and discuss its application as well as underlying estimation procedures.
Spatio-temporal models for infection counts generally follow themes of the broader disease mapping literature, but may need to address specific features of spatio-temporal infection data including considerable time fluctuations (with epidemic phases) and spatial diffusion. Low order autoregression is a feature of several recent spatio-temporal studies of infection data, possibly with lags on both within area infections and on infections in adjacent areas. Many epidemic time series show a period of relatively stable infection levels (possibly characterized as endemicity), followed by a sudden s…
The ongoing COVID-19 pandemic calls for a multi-faceted public health response comprising complementary interventions to control the spread of the disease while vaccines and therapies are developed. Many of these interventions need to be informed by epidemic risk predictions given available data, including symptoms, contact patterns, and environmental factors. Here we propose a novel probabilistic formalism based on Individual-Level Models (ILMs) that offers rigorous formulas for the probability of infection of individuals, which can be parameterised via Maximum Likelihood Estimation (MLE) app…
In response to the novel coronavirus disease (COVID-19), governments have introduced severe policy measures with substantial effects on human behavior. Here, we perform a large-scale, spatio-temporal analysis of human mobility during the COVID-19 epidemic. We derive human mobility from anonymized, aggregated telecommunication data in a nationwide setting (Switzerland; February 10 - April 26, 2020), consisting of ~1.5 billion trips. In comparison to the same time period from 2019, human movement in Switzerland dropped by 49.1%. The strongest reduction is linked to bans on gatherings of more tha…
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.
The widely spread CoronaVirus Disease (COVID)-19 is one of the worst infectious disease outbreaks in history and has become an emergency of primary international concern. As the pandemic evolves, academic communities have been actively involved in various capacities, including accurate epidemic estimation, fast clinical diagnosis, policy effectiveness evaluation and development of contract tracing technologies. There are more than 23,000 academic papers on the COVID-19 outbreak, and this number is doubling every 20 days while the pandemic is still on-going [1]. The literature, however, at its …
The evolution of the COVID-19 epidemic has been accompanied by accumulating evidence on the underlying epidemiological parameters. Hence there is potential for models providing mid-term forecasts of the epidemic trajectory using such information. The effectiveness of lockdown interventions can also be assessed by modelling later epidemic stages, possibly using a multiphase epidemic model. Commonly applied methods to analyze epidemic trajectories include phenomenological growth models (e.g. the Richards), and variants of the susceptible-infected-recovered (SIR) compartment model. Here we focus …
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…
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 …
One of the key indicators used in tracking the evolution of an infectious disease isthe reproduction number. This quantity is usually computed using the reportednumber of cases, but ignoring that many more individuals may be infected (e.g.asymptomatics). We propose a statistical procedure to quantify the impact of un-detected infectious cases on the determination of the effective reproduction number. Our approach is stochastic, data-driven and not relying on any compartmentalmodel. It is applied to the COVID-19 case in eight different countries and all Italianregions, showing that the effect o…
Mass antigen testing has been proposed as a possible cost-effective tool to contain the Covid-19 pandemic. We test the impact of a voluntary mass testing campaign implemented in the Italian region of South Tyrol on the spread of the virus in the following months. We do so by using an innovative empirical approach which embeds a semi-parametric growth model - where Covid-19 transmission dynamics are allowed to vary across regions and to be impacted by the implementation of the mass testing campaign - into a synthetic control framework which creates an appropriate control group of other Italian …
Various measures have been taken in different countries to mitigate the Covid-19 epidemic. But, throughout the world, many citizens don't understand well how these measures are taken and even question the decisions taken by their government. Should the measures be more (or less) restrictive? Are they taken for a too long (or too short) period of time? To provide some quantitative elements of response to these questions, we consider the well-known SEIR model for the Covid-19 epidemic propagation and propose a pragmatic model of the government decision-making operation. Although simple and obvio…
One of the difficulties in monitoring an ongoing pandemic is deciding on the metric that best describes its status when multiple intercorrelated measurements are available. Having a single measure, such as the effective reproduction number R, has been a simple and useful metric for tracking the epidemic and for imposing policy interventions to curb the increase when R >1. While R is easy to interpret in a fully susceptible population, it is more difficult to interpret for a population with heterogeneous prior immunity, e.g., from vaccination and prior infection. We propose an additional metric…
Epidemics are a serious public health threat, and the resources for mitigating their effects are typically limited. Decision-makers face challenges in forecasting the supply and demand for these resources as prior information about the disease is often not available, the behaviour of the disease can periodically change (either naturally or as a result of public health policies) and can differ by geographical region. Randomized controlled trials (RCTs) using scarce resources such as blood products as a randomized intervention are affected by epidemics. In this work, we discuss a model that is s…
Background: Travel is a potent force in the emergence of disease. We discussed how the traveler case reports could aid in a timely detection of a disease outbreak. Methods: Using the traveler data, we estimated a few indicators of the epidemic that affected decision making and policy, including the exponential growth rate, the doubling time, and the probability of severe cases exceeding the hospital capacity, in the initial phase of the COVID-19 epidemic in multiple countries. We imputed the arrival dates when they were missing. We compared the estimates from the traveler data to the ones from…
Institute for Data, Systems, and Society, MIT（麻省理工学院数据、系统与社会研究所）
The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics of disease, whereas non-mechanistic models make assumptions on the form of observed time series. Here, we introduce a simple mixture-based model which bridges the two approaches while retaining benefits of both. The model represents time series of cases and fatalities as a mixture of Gaussian curves, providing a flexible function class to learn from data comp…
