Using a latent Hawkes process for epidemiological modelling.

Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for modelling the infections. Unlike other models, we model the reported cases via a probability distribution driven by the underlying Hawkes process. Modelling the infections via a Hawkes process allows us to estimate by whom an infected individual was infected. We propose a Kernel Density Particle Filter (KDPF) for inference of both latent cases and reproduction number and for predicting the new cases in the near future. The computational effort is proportional to the number of infections making it possible to use particle filter type algorithms, such as the KDPF. We demonstrate the performance of the proposed algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK, and benchmark our model to alternative approaches.

A COVID-19 model for local authorities of the United Kingdom.

We propose a new framework to model the COVID-19 epidemic of the United Kingdom at the local authority level. The model fits within a general framework for semi-mechanistic Bayesian models of the epidemic based on renewal equations, with some important innovations, including a random walk modelling the reproduction number, incorporating information from different sources, including surveys to estimate the time-varying proportion of infections that lead to reported cases or deaths, and modelling the underlying infections as latent random variables. The model is designed to be updated daily using publicly available data. We envisage the model to be useful for now-casting and short-term projections of the epidemic as well as estimating historical trends. The model fits are available on a public website: https://imperialcollegelondon.github.io/covid19local. The model is currently being used by the Scottish government to inform their interventions.

Comparing the responses of the UK, Sweden and Denmark to COVID-19 using counterfactual modelling.

The UK and Sweden have among the worst per-capita COVID-19 mortality in Europe. Sweden stands out for its greater reliance on voluntary, rather than mandatory, control measures. We explore how the timing and effectiveness of control measures in the UK, Sweden and Denmark shaped COVID-19 mortality in each country, using a counterfactual assessment: what would the impact have been, had each country adopted the others' policies? Using a Bayesian semi-mechanistic model without prior assumptions on the mechanism or effectiveness of interventions, we estimate the time-varying reproduction number for the UK, Sweden and Denmark from daily mortality data. We use two approaches to evaluate counterfactuals which transpose the transmission profile from one country onto another, in each country's first wave from 13th March (when stringent interventions began) until 1st July 2020. UK mortality would have approximately doubled had Swedish policy been adopted, while Swedish mortality would have more than halved had Sweden adopted UK or Danish strategies. Danish policies were most effective, although differences between the UK and Denmark were significant for one counterfactual approach only. Our analysis shows that small changes in the timing or effectiveness of interventions have disproportionately large effects on total mortality within a rapidly growing epidemic.

Changing composition of SARS-CoV-2 lineages and rise of Delta variant in England.

BACKGROUND: Since its emergence in Autumn 2020, the SARS-CoV-2 Variant of Concern (VOC) B.1.1.7 (WHO label Alpha) rapidly became the dominant lineage across much of Europe. Simultaneously, several other VOCs were identified globally. Unlike B.1.1.7, some of these VOCs possess mutations thought to confer partial immune escape. Understanding when and how these additional VOCs pose a threat in settings where B.1.1.7 is currently dominant is vital. METHODS: We examine trends in the prevalence of non-B.1.1.7 lineages in London and other English regions using passive-case detection PCR data, cross-sectional community infection surveys, genomic surveillance, and wastewater monitoring. The study period spans from 31st January 2021 to 15th May 2021. FINDINGS: Across data sources, the percentage of non-B.1.1.7 variants has been increasing since late March 2021. This increase was initially driven by a variety of lineages with immune escape. From mid-April, B.1.617.2 (WHO label Delta) spread rapidly, becoming the dominant variant in England by late May. INTERPRETATION: The outcome of competition between variants depends on a wide range of factors such as intrinsic transmissibility, evasion of prior immunity, demographic specificities and interactions with non-pharmaceutical interventions. The presence and rise of non-B.1.1.7 variants in March likely was driven by importations and some community transmission. There was competition between non-B.1.17 variants which resulted in B.1.617.2 becoming dominant in April and May with considerable community transmission. Our results underscore that early detection of new variants requires a diverse array of data sources in community surveillance. Continued real-time information on the highly dynamic composition and trajectory of different SARS-CoV-2 lineages is essential to future control efforts. FUNDING: National Institute for Health Research, Medicines and Healthcare products Regulatory Agency, DeepMind, EPSRC, EA Funds programme, Open Philanthropy, Academy of Medical Sciences Bill,Melinda Gates Foundation, Imperial College Healthcare NHS Trust, The Novo Nordisk Foundation, MRC Centre for Global Infectious Disease Analysis, Community Jameel, Cancer Research UK, Imperial College COVID-19 Research Fund, Medical Research Council, Wellcome Sanger Institute.

Modelling the impact of the tier system on SARS-CoV-2 transmission in the UK between the first and second national lockdowns.

OBJECTIVE: To measure the effects of the tier system on the COVID-19 pandemic in the UK between the first and second national lockdowns, before the emergence of the B.1.1.7 variant of concern. DESIGN: This is a modelling study combining estimates of real-time reproduction number Rt (derived from UK case, death and serological survey data) with publicly available data on regional non-pharmaceutical interventions. We fit a Bayesian hierarchical model with latent factors using these quantities to account for broader national trends in addition to subnational effects from tiers. SETTING: The UK at lower tier local authority (LTLA) level. 310 LTLAs were included in the analysis. PRIMARY AND SECONDARY OUTCOME MEASURES: Reduction in real-time reproduction number Rt . RESULTS: Nationally, transmission increased between July and late September, regional differences notwithstanding. Immediately prior to the introduction of the tier system, Rt averaged 1.3 (0.9-1.6) across LTLAs, but declined to an average of 1.1 (0.86-1.42) 2 weeks later. Decline in transmission was not solely attributable to tiers. Tier 1 had negligible effects. Tiers 2 and 3, respectively, reduced transmission by 6% (5%-7%) and 23% (21%-25%). 288 LTLAs (93%) would have begun to suppress their epidemics if every LTLA had gone into tier 3 by the second national lockdown, whereas only 90 (29%) did so in reality. CONCLUSIONS: The relatively small effect sizes found in this analysis demonstrate that interventions at least as stringent as tier 3 are required to suppress transmission, especially considering more transmissible variants, at least until effective vaccination is widespread or much greater population immunity has amassed.

Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England.

The SARS-CoV-2 lineage B.1.1.7, designated variant of concern (VOC) 202012/01 by Public Health England1, was first identified in the UK in late summer to early autumn 20202. Whole-genome SARS-CoV-2 sequence data collected from community-based diagnostic testing for COVID-19 show an extremely rapid expansion of the B.1.1.7 lineage during autumn 2020, suggesting that it has a selective advantage. Here we show that changes in VOC frequency inferred from genetic data correspond closely to changes inferred by S gene target failures (SGTF) in community-based diagnostic PCR testing. Analysis of trends in SGTF and non-SGTF case numbers in local areas across England shows that B.1.1.7 has higher transmissibility than non-VOC lineages, even if it has a different latent period or generation time. The SGTF data indicate a transient shift in the age composition of reported cases, with cases of B.1.1.7 including a larger share of under 20-year-olds than non-VOC cases. We estimated time-varying reproduction numbers for B.1.1.7 and co-circulating lineages using SGTF and genomic data. The best-supported models did not indicate a substantial difference in VOC transmissibility among different age groups, but all analyses agreed that B.1.1.7 has a substantial transmission advantage over other lineages, with a 50% to 100% higher reproduction number.

Age groups that sustain resurging COVID-19 epidemics in the United States.

After initial declines, in mid-2020 a resurgence in transmission of novel coronavirus disease (COVID-19) occurred in the United States and Europe. As efforts to control COVID-19 disease are reintensified, understanding the age demographics driving transmission and how these affect the loosening of interventions is crucial. We analyze aggregated, age-specific mobility trends from more than 10 million individuals in the United States and link these mechanistically to age-specific COVID-19 mortality data. We estimate that as of October 2020, individuals aged 20 to 49 are the only age groups sustaining resurgent SARS-CoV-2 transmission with reproduction numbers well above one and that at least 65 of 100 COVID-19 infections originate from individuals aged 20 to 49 in the United States. Targeting interventions-including transmission-blocking vaccines-to adults aged 20 to 49 is an important consideration in halting resurgent epidemics and preventing COVID-19-attributable deaths.

Genomics and epidemiology of the P 1 SARS-CoV-2 lineage in Manaus, Brazil

Cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in Manaus, Brazil, resurged in late 2020 despite previously high levels of infection. Genome sequencing of viruses sampled in Manaus between November 2020 and January 2021 revealed the emergence and circulation of a novel SARS-CoV-2 variant of concern. Lineage P.1 acquired 17 mutations, including a trio in the spike protein (K417T, E484K, and N501Y) associated with increased binding to the human ACE2 (angiotensin-converting enzyme 2) receptor. Molecular clock analysis shows that P.1 emergence occurred around mid-November 2020 and was preceded by a period of faster molecular evolution. Using a two-category dynamical model that integrates genomic and mortality data, we estimate that P.1 may be 1.7- to 2.4-fold more transmissible and that previous (non-P.1) infection provides 54 to 79% of the protection against infection with P.1 that it provides against non-P.1 lineages. Enhanced global genomic surveillance of variants of concern, which may exhibit increased transmissibility and/or immune evasion, is critical to accelerate pandemic responsiveness.

State-level tracking of COVID-19 in the United States.

As of 1st June 2020, the US Centres for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly model the US epidemic at the state-level, using publicly available death data within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We use changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on the rate of transmission of SARS-CoV-2. We estimate that Rt was only below one in 23 states on 1st June. We also estimate that 3.7% [3.4%-4.0%] of the total population of the US had been infected, with wide variation between states, and approximately 0.01% of the population was infectious. We demonstrate good 3 week model forecasts of deaths with low error and good coverage of our credible intervals.

Inference of COVID-19 epidemiological distributions from Brazilian hospital data.

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalized with COVID-19 using a large dataset (N = 21 000 - 157 000) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2 and 17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalized lognormal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.

Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe.

Following the detection of the new coronavirus1 severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics of coronavirus disease 2019 (COVID-19). In response, many European countries have implemented non-pharmaceutical interventions, such as the closure of schools and national lockdowns. Here we study the effect of major interventions across 11 European countries for the period from the start of the COVID-19 epidemics in February 2020 until 4 May 2020, when lockdowns started to be lifted. Our model calculates backwards from observed deaths to estimate transmission that occurred several weeks previously, allowing for the time lag between infection and death. We use partial pooling of information between countries, with both individual and shared effects on the time-varying reproduction number (Rt). Pooling allows for more information to be used, helps to overcome idiosyncrasies in the data and enables more-timely estimates. Our model relies on fixed estimates of some epidemiological parameters (such as the infection fatality rate), does not include importation or subnational variation and assumes that changes in Rt are an immediate response to interventions rather than gradual changes in behaviour. Amidst the ongoing pandemic, we rely on death data that are incomplete, show systematic biases in reporting and are subject to future consolidation. We estimate that-for all of the countries we consider here-current interventions have been sufficient to drive Rt below 1 (probability Rt < 1.0 is greater than 99%) and achieve control of the epidemic. We estimate that across all 11 countries combined, between 12 and 15 million individuals were infected with SARS-CoV-2 up to 4 May 2020, representing between 3.2% and 4.0% of the population. Our results show that major non-pharmaceutical interventions-and lockdowns in particular-have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.

An omnibus CUSUM chart for monitoring time to event data.

A non-parametric method is proposed for monitoring time-to-event data. A cumulative sum chart is constructed that is able to detect an unknown out-of-control state. This method exploits the absolute differences between the Kaplan-Meier estimator and the in-control distribution over specific time intervals. The efficiency of the algorithm is studied via a simulation and a real data study. The new method is also tested via the simulation study against existing methods.

Model checks for Cox-type regression models based on optimally weighted martingale residuals.

We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. "Directed" means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions.We derive optimal tests against certain competing models which include Cox-type regression models with different covariates and/or a different link function. We report results from several simulation studies and apply our test to a real dataset.

Global tests in the additive hazards regression model.

In this article, we discuss testing for the effect of several covariates in the additive hazards regression model. Bhattacharyya and Klein (Statist. Med. 2005; 24(14):2235-2240) note that an ad hoc weight function suggested by Aalen (Statist. Med. 1989; 8:907-925) is inconsistent when used as a global test for comparing groups since the test statistic depends on which group is used as the baseline group. We will suggest a simple alternative test that does not exhibit this problem. This test is a natural extension of the logrank test. We shall also discuss an alternative covariance estimator. The tests are applied to a data set and a simulation study is performed.

Checking a semiparametric additive risk model.

McKeague and Sasieni [A partly parametric additive risk model. Biometrika 81 (1994) 501] propose a restriction of Aalen's additive risk model by the additional hypothesis that some of the covariates have time-independent influence on the intensity of the observed counting process. We introduce goodness-of-fit tests for this semiparametric Aalen model. The asymptotic distribution properties of the test statistics are derived by means of martingale techniques. The tests can be adjusted to detect particular alternatives. As one of the most important alternatives we consider Cox's proportional hazards model. We present simulation studies and an application to a real data set.