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Register a new userEstimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update
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Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, wide-scale social distancing including local and national lockdowns. In this technical update, we extend a semi-mechanistic Bayesian hierarchical model that infers the impact of these interventions and estimates the number of infections over time. Our methods assume that changes in the reproductive number - a measure of transmission - are an immediate response to these interventions being implemented rather than broader gradual changes in behaviour. Our model estimates these changes by calculating backwards from temporal data on observed to estimate the number of infections and rate of transmission that occurred several weeks prior, allowing for a probabilistic time lag between infection and death. In this update we extend our original model [Flaxman, Mishra, Gandy et al 2020, Report #13, Imperial College London] to include (a) population saturation effects, (b) prior uncertainty on the infection fatality ratio, (c) a more balanced prior on intervention effects and (d) partial pooling of the lockdown intervention covariate. We also (e) included another 3 countries (Greece, the Netherlands and Portugal). The model code is available at https://github.com/ImperialCollegeLondon/covid19model/ We are now reporting the results of our updated model online at https://mrc-ide.github.io/covid19estimates/ We estimated parameters jointly for all M=14 countries in a single hierarchical model. Inference is performed in the probabilistic programming language Stan using an adaptive Hamiltonian Monte Carlo (HMC) sampler.
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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. Yet, due to the exponential nature of epidemic growth, the error due to this simplification can be rapidly amplified and lead to inaccurate predictions and/or risk evaluation. From the statistical modeling perspective, the magnitude of the impact of this averaging remains an open question: how can this intrinsic variability be percolated into epidemic models, and how can its impact on uncertainty quantification and predictive scenarios be better quantified? In this paper, we propose to study this question through a Bayesian perspective, creating a bridge between the agent-based and compartmental approaches commonly used in the literature. After deriving a Bayesian model that captures at scale the heterogeneity of a population and environmental conditions, we simulate the spread of the epidemic as well as the impact of different social distancing strategies, and highlight the strong impact of this added variability on the reported results. We base our discussion on both synthetic experiments -- thereby quantifying of the reliability and the magnitude of the effects -- and real COVID-19 data.
We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its sub-regions in order to account for the wide disparities in population size and density. Without prior information on non-pharmaceutical interventions (NPIs), the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing Stay-at-Home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.
Infectious diseases and human behavior are intertwined. On one side, our movements and interactions are the engines of transmission. On the other, the unfolding of viruses might induce changes to our daily activities. While intuitive, our understanding of such feedback loop is still limited. Before COVID-19 the literature on the subject was mainly theoretical and largely missed validation. The main issue was the lack of empirical data capturing behavioral change induced by diseases. Things have dramatically changed in 2020. Non-pharmaceutical interventions (NPIs) have been the key weapon against the SARS-CoV-2 virus and affected virtually any societal process. Travels bans, events cancellation, social distancing, curfews, and lockdowns have become unfortunately very familiar. The scale of the emergency, the ease of survey as well as crowdsourcing deployment guaranteed by the latest technology, several Data for Good programs developed by tech giants, major mobile phone providers, and other companies have allowed unprecedented access to data describing behavioral changes induced by the pandemic. Here, I aim to review some of the vast literature written on the subject of NPIs during the COVID-19 pandemic. In doing so, I analyze 347 articles written by more than 2518 of authors in the last $12$ months. While the large majority of the sample was obtained by querying PubMed, it includes also a hand-curated list. Considering the focus, and methodology I have classified the sample into seven main categories: epidemic models, surveys, comments/perspectives, papers aiming to quantify the effects of NPIs, reviews, articles using data proxies to measure NPIs, and publicly available datasets describing NPIs. I summarize the methodology, data used, findings of the articles in each category and provide an outlook highlighting future challenges as well as opportunities
We analysed publicly available data on place of occurrence of COVID-19 deaths from national statistical agencies in the UK between March 9 2020 and February 28 2021. We introduce a modified Weibull model that describes the deaths due to COVID-19 at a national and place of occurrence level. We observe similar trends in the UK where deaths due to COVID-19 first peak in Homes, followed by Hospitals and Care Homes 1-2 weeks later in the first and second waves. This is in line with the infectious period of the disease, indicating a possible transmission vehicle between the settings. Our results show that the first wave is characterised by fast growth and a slow reduction after the peak in deaths due to COVID-19. The second and third waves have the converse property, with slow growth and a rapid decrease from the peak. This difference may result from behavioural changes in the population (social distancing, masks, etc). Finally, we introduce a double logistic model to describe the dynamic proportion of COVID-19 deaths occurring in each setting. This analysis reveals that the proportion of COVID-19 deaths occurring in Care Homes increases from the start of the pandemic and past the peak in total number of COVID-19 deaths in the first wave. After the catastrophic impact in the first wave, the proportion of COVID-19 deaths occurring in Care Homes gradually decreased from is maximum after the first wave indicating residence were better protected in the second and third waves compared to the first.
We develop a novel hybrid epidemiological model and a specific methodology for its calibration to distinguish and assess the impact of mobility restrictions (given by Apples mobility trends data) from other complementary non-pharmaceutical interventions (NPIs) used to control the spread of COVID-19. Using the calibrated model, we estimate that mobility restrictions contribute to 47 % (US States) and 47 % (worldwide) of the overall suppression of the disease transmission rate using data up to 13/08/2020. The forecast capacity of our model was evaluated doing four-weeks ahead predictions. Using data up to 30/06/20 for calibration, the mean absolute percentage error (MAPE) of the prediction of cumulative deceased individuals was 5.0 % for the United States (51 states) and 6.7 % worldwide (49 countries). This MAPE was reduced to 3.5% for the US and 3.8% worldwide using data up to 13/08/2020. We find that the MAPE was higher for the total confirmed cases at 11.5% worldwide and 10.2% for the US States using data up to 13/08/2020. Our calibrated model achieves an average R-Squared value for cumulative confirmed and deceased cases of 0.992 using data up to 30/06/20 and 0.98 using data up to 13/08/20.
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