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Register a new userModeling the Heterogeneity in COVID-19s Reproductive Number and its Impact on Predictive Scenarios
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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.
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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.
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.
The ongoing COVID-19 pandemic has created a global crisis of massive scale. Prior research indicates that human mobility is one of the key factors involved in viral spreading. Indeed, in a connected planet, rapid world-wide spread is enabled by long-distance air-, land- and sea-transportation among countries and continents, and subsequently fostered by commuting trips within densely populated cities. While early travel restrictions contribute to delayed disease spread, their utility is much reduced if the disease has a long incubation period or if there is asymptomatic transmission. Given the lack of vaccines, public health officials have mainly relied on non-pharmaceutical interventions, including social distancing measures, curfews, and stay-at-home orders. Here we study the impact of city organization on its susceptibility to disease spread, and amenability to interventions. Cities can be classified according to their mobility in a spectrum between compact-hierarchical and decentralized-sprawled. Our results show that even though hierarchical cities are more susceptible to the rapid spread of epidemics, their organization makes mobility restrictions quite effective. Conversely, sprawled cities are characterized by a much slower initial spread, but are less responsive to mobility restrictions. These findings hold globally across cities in diverse geographical locations and a broad range of sizes. Our empirical measurements are confirmed by a simulation of COVID-19 spread in urban areas through a compartmental model. These results suggest that investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove most helpful in containing and reducing the impact of present and future pandemics.
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 Bayesian model with time-varying regional parameters to account for the relative reduction in contact due to physical distancing and increased testing from 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, fraction of normal contacts, proportion of anticipated cases, and we observed significant differences between the provincial-wide and regional models.
Large-scale testing is considered key to assess the state of the current COVID-19 pandemic. Yet, the link between the reported case numbers and the true state of the pandemic remains elusive. We develop mathematical models based on competing hypotheses regarding this link, thereby providing different prevalence estimates based on case numbers, and validate them by predicting SARS-CoV-2-attributed death rate trajectories. Assuming that individuals were tested based solely on a predefined risk of being infectious implies the absolute case numbers reflect the prevalence, but turned out to be a poor predictor, consistently overestimating growth rates at the beginning of two COVID-19 epidemic waves. In contrast, assuming that testing capacity is fully exploited performs better. This leads to using the percent-positive rate as a more robust indicator of epidemic dynamics, however we find it is subject to a saturation phenomenon that needs to be accounted for as the number of tests becomes larger.
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