Reconstructing a spatially heterogeneous epidemic: Characterising the geographic spread of 2009 A/H1N1pdm infection in England

Contact data and SARS-CoV-2: Retrospective analysis of the estimated impact of the first UK lockdown

To combat the spread of SARS-CoV-2 in March 2020 the United Kingdom (UK) announced a series of restrictions on social interaction, culminating with the introduction of lockdown measures. Estimation of lockdown effectiveness using pandemic models relied on the availability of contact data and choices on how to structure models accordingly. We revisit the Cambridge/Public Health England real-time model (RTM), which was routinely implemented during the pandemic to monitor its development and produce short-term projections. To derive contact matrices, Google Mobility weekly contact data and school attendance data from the Department for Education were combined with information from the POLYMOD study and the UK Time Use Survey. These matrices were combined with susceptibility and transmissibility parameters to estimate effective reproduction numbers, which were taken as indicators of transmission trends. We explore alternative formulations of the RTM, which make fuller use of the available contact data, and assess the impact of each formulation on the conclusions of lockdown effectiveness. Results show that the estimated impact of the lockdown remains unchanged, but also uncover previously uncaptured early epidemic dynamics. This highlights the importance of the timely availability of contact data in understanding transmission dynamics during the early stages of an epidemic and assessing the effectiveness of interventions.

Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study

Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

Real-time nowcasting and forecasting of COVID-19 dynamics in England: the first wave

England has been heavily affected by the SARS-CoV-2 pandemic, with severe 'lockdown' mitigation measures now gradually being lifted. The real-time pandemic monitoring presented here has contributed to the evidence informing this pandemic management throughout the first wave. Estimates on the 10 May showed lockdown had reduced transmission by 75%, the reproduction number falling from 2.6 to 0.61. This regionally varying impact was largest in London with a reduction of 81% (95% credible interval: 77-84%). Reproduction numbers have since then slowly increased, and on 19 June the probability of the epidemic growing was greater than 5% in two regions, South West and London. By this date, an estimated 8% of the population had been infected, with a higher proportion in London (17%). The infection-to-fatality ratio is 1.1% (0.9-1.4%) overall but 17% (14-22%) among the over-75s. This ongoing work continues to be key to quantifying any widespread resurgence, should accrued immunity and effective contact tracing be insufficient to preclude a second wave. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Forecasting the 2017/2018 seasonal influenza epidemic in England using multiple dynamic transmission models: a case study

Background

Since the 2009 A/H1N1 pandemic, Public Health England have developed a suite of real-time statistical models utilising enhanced pandemic surveillance data to nowcast and forecast a future pandemic. Their ability to track seasonal influenza and predict heightened winter healthcare burden in the light of high activity in Australia in 2017 was untested.

Methods

Four transmission models were used in forecasting the 2017/2018 seasonal influenza epidemic in England: a stratified primary care model using daily, region-specific, counts and virological swab positivity of influenza-like illness consultations in general practice (GP); a strain-specific (SS) model using weekly, national GP ILI and virological data; an intensive care model (ICU) using reports of ICU influenza admissions; and a synthesis model that included all data sources. For the first 12 weeks of 2018, each model was applied to the latest data to provide estimates of epidemic parameters and short-term influenza forecasts. The added value of pre-season population susceptibility data was explored.

Results

The combined results provided valuable nowcasts of the state of the epidemic. Short-term predictions of burden on primary and secondary health services were initially highly variable before reaching consensus beyond the observed peaks in activity between weeks 3–4 of 2018. Estimates for R₀ were consistent over time for three of the four models until week 12 of 2018, and there was consistency in the estimation of R₀ across the SPC and SS models, and in the ICU attack rates estimated by the ICU and the synthesis model. Estimation and predictions varied according to the assumed levels of pre-season immunity.

Conclusions

This exercise successfully applied a range of pandemic models to seasonal influenza. Forecasting early in the season remains challenging but represents a crucially important activity to inform planning. Improved knowledge of pre-existing levels of immunity would be valuable.

The UK's pandemic influenza research portfolio: a model for future research on emerging infections

The 2009 influenza A H1N1 pandemic was responsible for considerable global morbidity and mortality. In 2009, several research studies in the UK were rapidly funded and activated for clinical and public health actions. However, some studies were too late for their results to have an early and substantial effect on clinical care, because of the time required to call for research proposals, assess, fund, and set up the projects. In recognition of these inherent delays, a portfolio of projects was funded by the National Institute for Health Research in 2012. These studies have now been set up (ie, with relevant permissions and arrangements made for data collection) and pilot tested where relevant. All studies are now on standby awaiting activation in the event of a pandemic being declared. In this Personal View, we describe the projects that were set up, the challenges of putting these projects into a maintenance-only state, and ongoing activities to maintain readiness for activation, and discuss how to plan research for a range of major incidents.

Real-time modelling of a pandemic influenza outbreak

BACKGROUND

Real-time modelling is an essential component of the public health response to an outbreak of pandemic influenza in the UK. A model for epidemic reconstruction based on realistic epidemic surveillance data has been developed, but this model needs enhancing to provide spatially disaggregated epidemic estimates while ensuring that real-time implementation is feasible.

OBJECTIVES

To advance state-of-the-art real-time pandemic modelling by (1) developing an existing epidemic model to capture spatial variation in transmission, (2) devising efficient computational algorithms for the provision of timely statistical analysis and (3) incorporating the above into freely available software.

METHODS

Markov chain Monte Carlo (MCMC) sampling was used to derive Bayesian statistical inference using 2009 pandemic data from two candidate modelling approaches: (1) a parallel-region (PR) approach, splitting the pandemic into non-interacting epidemics occurring in spatially disjoint regions; and (2) a meta-region (MR) approach, treating the country as a single meta-population with long-range contact rates informed by census data on commuting. Model discrimination is performed through posterior mean deviance statistics alongside more practical considerations. In a real-time context, the use of sequential Monte Carlo (SMC) algorithms to carry out real-time analyses is investigated as an alternative to MCMC using simulated data designed to sternly test both algorithms. SMC-derived analyses are compared with 'gold-standard' MCMC-derived inferences in terms of estimation quality and computational burden.

RESULTS

The PR approach provides a better and more timely fit to the epidemic data. Estimates of pandemic quantities of interest are consistent across approaches and, in the PR approach, across regions (e.g. R₀ is consistently estimated to be 1.76-1.80, dropping by 43-50% during an over-summer school holiday). A SMC approach was developed, which required some tailoring to tackle a sudden 'shock' in the data resulting from a pandemic intervention. This semi-automated SMC algorithm outperforms MCMC, in terms of both precision of estimates and their timely provision. Software implementing all findings has been developed and installed within Public Health England (PHE), with key staff trained in its use.

LIMITATIONS

The PR model lacks the predictive power to forecast the spread of infection in the early stages of a pandemic, whereas the MR model may be limited by its dependence on commuting data to describe transmission routes. As demand for resources increases in a severe pandemic, data from general practices and on hospitalisations may become unreliable or biased. The SMC algorithm developed is semi-automated; therefore, some statistical literacy is required to achieve optimal performance.

CONCLUSIONS

Following the objectives, this study found that timely, spatially disaggregate, real-time pandemic inference is feasible, and a system that assumes data as per pandemic preparedness plans has been developed for rapid implementation.

FUTURE WORK RECOMMENDATIONS

Modelling studies investigating the impact of pandemic interventions (e.g. vaccination and school closure); the utility of alternative data sources (e.g. internet searches) to augment traditional surveillance; and the correct handling of test sensitivity and specificity in serological data, propagating this uncertainty into the real-time modelling.

TRIAL REGISTRATION

Current Controlled Trials ISRCTN40334843.

FUNDING

This project was funded by the National Institute for Health Research (NIHR) Health Technology programme and will be published in full in Health Technology Assessment; Vol. 21, No. 58. See the NIHR Journals Library website for further project information. Daniela De Angelis was supported by the UK Medical Research Council (Unit Programme Number U105260566) and by PHE. She received funding under the NIHR grant for 10% of her time. The rest of her salary was provided by the MRC and PHE jointly.

Evidence Synthesis for Stochastic Epidemic Models

In recent years, the role of epidemic models in informing public health policies has progressively grown. Models have become increasingly realistic and more complex, requiring the use of multiple data sources to estimate all quantities of interest. This review summarises the different types of stochastic epidemic models that use evidence synthesis and highlights current challenges.

Detecting a Surprisingly Low Transmission Distance in the Early Phase of the 2009 Influenza Pandemic

The spread of the 2009 H1N1 influenza pandemic in England was characterized by two major waves of infections: the first one was highly spatially localized (mainly in the London area), while the second one spread homogeneously through the entire country. The reasons behind this complex spatiotemporal dynamics have yet to be clarified. In this study, we perform a Bayesian analysis of five models entailing different hypotheses on the possible determinants of the observed pattern. We find a consensus among all models in showing a surprisingly low transmission distance (defined as the geographic distance between the place of residence of the infectors and her/his infectees) during the first wave: about 1.5 km (2.2 km if infections linked to household and school transmission are excluded). The best-fitting model entails a change in human activity regarding contacts not related to household and school. By using this model we estimate that the transmission distance sharply increased to 5.3 km (10 km when excluding infections linked to household and school transmission) during the second wave. Our study reveals a possible explanation for the observed pattern and highlights the need of better understanding human mobility and activity patterns under the pressure posed by a pandemic threat.