Unifying incidence and prevalence under a time-varying general branching process.

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.

Application of referenced thermodynamic integration to Bayesian model selection.

Evaluating normalising constants is important across a range of topics in statistical learning, notably Bayesian model selection. However, in many realistic problems this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a simple but under-appreciated variation of the TI method, here referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with pedagogical 1 and 2D examples. The approach is shown to be useful in practice when applied to a real problem -to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.

Estimating the COVID-19 infection fatality ratio accounting for seroreversion using statistical modelling.

Background: The infection fatality ratio (IFR) is a key statistic for estimating the burden of coronavirus disease 2019 (COVID-19) and has been continuously debated throughout the COVID-19 pandemic. The age-specific IFR can be quantified using antibody surveys to estimate total infections, but requires consideration of delay-distributions from time from infection to seroconversion, time to death, and time to seroreversion (i.e. antibody waning) alongside serologic test sensitivity and specificity. Previous IFR estimates have not fully propagated uncertainty or accounted for these potential biases, particularly seroreversion. Methods: We built a Bayesian statistical model that incorporates these factors and applied this model to simulated data and 10 serologic studies from different countries. Results: We demonstrate that seroreversion becomes a crucial factor as time accrues but is less important during first-wave, short-term dynamics. We additionally show that disaggregating surveys by regions with higher versus lower disease burden can inform serologic test specificity estimates. The overall IFR in each setting was estimated at 0.49-2.53%. Conclusion: We developed a robust statistical framework to account for full uncertainties in the parameters determining IFR. We provide code for others to apply these methods to further datasets and future epidemics.

Genomic characterization and epidemiology of an emerging SARS-CoV-2 variant in Delhi, India.

Delhi, the national capital of India, experienced multiple severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) outbreaks in 2020 and reached population seropositivity of >50% by 2021. During April 2021, the city became overwhelmed by COVID-19 cases and fatalities, as a new variant, B.1.617.2 (Delta), replaced B.1.1.7 (Alpha). A Bayesian model explains the growth advantage of Delta through a combination of increased transmissibility and reduced sensitivity to immune responses generated against earlier variants (median estimates: 1.5-fold greater transmissibility and 20% reduction in sensitivity). Seropositivity of an employee and family cohort increased from 42% to 87.5% between March and July 2021, with 27% reinfections, as judged by increased antibody concentration after a previous decline. The likely high transmissibility and partial evasion of immunity by the Delta variant contributed to an overwhelming surge in Delhi.

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.

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.

Genomics and epidemiology of a novel SARS-CoV-2 lineage in Manaus, Brazil.

Cases of SARS-CoV-2 infection in Manaus, Brazil, resurged in late 2020, despite high levels of previous infection there. Through genome sequencing of viruses sampled in Manaus between November 2020 and January 2021, we identified the emergence and circulation of a novel SARS-CoV-2 variant of concern, lineage P.1, that acquired 17 mutations, including a trio in the spike protein (K417T, E484K and N501Y) associated with increased binding to the human ACE2 receptor. Molecular clock analysis shows that P.1 emergence occurred around early 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 1.4-2.2 times more transmissible and 25-61% more likely to evade protective immunity elicited by previous infection with 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.

Reduction in mobility and COVID-19 transmission.

In response to the COVID-19 pandemic, countries have sought to control SARS-CoV-2 transmission by restricting population movement through social distancing interventions, thus reducing the number of contacts. Mobility data represent an important proxy measure of social distancing, and here, we characterise the relationship between transmission and mobility for 52 countries around the world. Transmission significantly decreased with the initial reduction in mobility in 73% of the countries analysed, but we found evidence of decoupling of transmission and mobility following the relaxation of strict control measures for 80% of countries. For the majority of countries, mobility explained a substantial proportion of the variation in transmissibility (median adjusted R-squared: 48%, interquartile range - IQR - across countries [27-77%]). Where a change in the relationship occurred, predictive ability decreased after the relaxation; from a median adjusted R-squared of 74% (IQR across countries [49-91%]) pre-relaxation, to a median adjusted R-squared of 30% (IQR across countries [12-48%]) post-relaxation. In countries with a clear relationship between mobility and transmission both before and after strict control measures were relaxed, mobility was associated with lower transmission rates after control measures were relaxed indicating that the beneficial effects of ongoing social distancing behaviours were substantial.

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.

Anonymised and aggregated crowd level mobility data from mobile phones suggests that initial compliance with COVID-19 social distancing interventions was high and geographically consistent across the UK.

Background: Since early March 2020, the COVID-19 epidemic across the United Kingdom has led to a range of social distancing policies, which have resulted in reduced mobility across different regions. Crowd level data on mobile phone usage can be used as a proxy for actual population mobility patterns and provide a way of quantifying the impact of social distancing measures on changes in mobility. Methods: Here, we use two mobile phone-based datasets (anonymised and aggregated crowd level data from O2 and from the Facebook app on mobile phones) to assess changes in average mobility, both overall and broken down into high and low population density areas, and changes in the distribution of journey lengths. Results: We show that there was a substantial overall reduction in mobility, with the most rapid decline on the 24th March 2020, the day after the Prime Minister's announcement of an enforced lockdown. The reduction in mobility was highly synchronized across the UK. Although mobility has remained low since 26th March 2020, we detect a gradual increase since that time. We also show that the two different datasets produce similar trends, albeit with some location-specific differences. We see slightly larger reductions in average mobility in high-density areas than in low-density areas, with greater variation in mobility in the high-density areas: some high-density areas eliminated almost all mobility. Conclusions: These analyses form a baseline from which to observe changes in behaviour in the UK as social distancing is eased and inform policy towards the future control of SARS-CoV-2 in the UK.

Potential impact of the COVID-19 pandemic on HIV, tuberculosis, and malaria in low-income and middle-income countries: a modelling study.

BACKGROUND: COVID-19 has the potential to cause substantial disruptions to health services, due to cases overburdening the health system or response measures limiting usual programmatic activities. We aimed to quantify the extent to which disruptions to services for HIV, tuberculosis, and malaria in low-income and middle-income countries with high burdens of these diseases could lead to additional loss of life over the next 5 years. METHODS: Assuming a basic reproduction number of 3·0, we constructed four scenarios for possible responses to the COVID-19 pandemic: no action, mitigation for 6 months, suppression for 2 months, or suppression for 1 year. We used established transmission models of HIV, tuberculosis, and malaria to estimate the additional impact on health that could be caused in selected settings, either due to COVID-19 interventions limiting activities, or due to the high demand on the health system due to the COVID-19 pandemic. FINDINGS: In high-burden settings, deaths due to HIV, tuberculosis, and malaria over 5 years could increase by up to 10%, 20%, and 36%, respectively, compared with if there was no COVID-19 pandemic. The greatest impact on HIV was estimated to be from interruption to antiretroviral therapy, which could occur during a period of high health system demand. For tuberculosis, the greatest impact would be from reductions in timely diagnosis and treatment of new cases, which could result from any prolonged period of COVID-19 suppression interventions. The greatest impact on malaria burden could be as a result of interruption of planned net campaigns. These disruptions could lead to a loss of life-years over 5 years that is of the same order of magnitude as the direct impact from COVID-19 in places with a high burden of malaria and large HIV and tuberculosis epidemics. INTERPRETATION: Maintaining the most critical prevention activities and health-care services for HIV, tuberculosis, and malaria could substantially reduce the overall impact of the COVID-19 pandemic. FUNDING: Bill & Melinda Gates Foundation, Wellcome Trust, UK Department for International Development, and Medical Research Council.

Evolution and epidemic spread of SARS-CoV-2 in Brazil.

Brazil currently has one of the fastest-growing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemics in the world. Because of limited available data, assessments of the impact of nonpharmaceutical interventions (NPIs) on this virus spread remain challenging. Using a mobility-driven transmission model, we show that NPIs reduced the reproduction number from >3 to 1 to 1.6 in São Paulo and Rio de Janeiro. Sequencing of 427 new genomes and analysis of a geographically representative genomic dataset identified >100 international virus introductions in Brazil. We estimate that most (76%) of the Brazilian strains fell in three clades that were introduced from Europe between 22 February and 11 March 2020. During the early epidemic phase, we found that SARS-CoV-2 spread mostly locally and within state borders. After this period, despite sharp decreases in air travel, we estimated multiple exportations from large urban centers that coincided with a 25% increase in average traveled distances in national flights. This study sheds new light on the epidemic transmission and evolutionary trajectories of SARS-CoV-2 lineages in Brazil and provides evidence that current interventions remain insufficient to keep virus transmission under control in this country.

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.

Density functional theory study of rutile VO2 surfaces.

We present the results of a density functional theory investigation of the surfaces of rutile-like vanadium dioxide, VO(2)(R). We calculate the surface energies of low Miller index planes and find that the most stable surface orientation is the (110). The equilibrium morphology of a VO(2)(R) particle has an acicular shape, laterally confined by (110) planes and topped by (011) planes. The redox properties of the (110) surface are investigated by calculating the relative surface free energies of the non-stoichiometric compositions as a function of oxygen chemical potential. It is found that the VO(2)(110) surface is oxidized with respect to the stoichiometric composition, not only at ambient conditions but also at the more reducing conditions under which bulk VO(2) is stable in comparison with bulk V(2)O(5). The adsorbed oxygen forms surface vanadyl species much more favorably than surface peroxo species.