An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling.

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe, mechanistically, changes in extrinsic environmental factors including public behaviour and seasonal fluctuations. An elegant approach to capturing environmental stochasticity is to model the force of infection as a stochastic process. However, inference in this context requires solving a computationally expensive "missing data" problem, using data-augmentation techniques. We propose to model the time-varying transmission-potential as an approximate diffusion process using a path-wise series expansion of Brownian motion. This approximation replaces the "missing data" imputation step with the inference of the expansion coefficients: a simpler and computationally cheaper task. We illustrate the merit of this approach through three examples: modelling influenza using a canonical SIR model, capturing seasonality using a SIRS model, and the modelling of COVID-19 pandemic using a multi-type SEIR model.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges.

The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Ct threshold values, a proxy for viral load in community SARS-CoV-2 cases, demonstrate wide variation across populations and over time.

Background: Information on SARS-CoV-2 in representative community surveillance is limited, particularly cycle threshold (Ct) values (a proxy for viral load). Methods: We included all positive nose and throat swabs 26 April 2020 to 13 March 2021 from the UK's national COVID-19 Infection Survey, tested by RT-PCR for the N, S, and ORF1ab genes. We investigated predictors of median Ct value using quantile regression. Results: Of 3,312,159 nose and throat swabs, 27,902 (0.83%) were RT-PCR-positive, 10,317 (37%), 11,012 (40%), and 6550 (23%) for 3, 2, or 1 of the N, S, and ORF1ab genes, respectively, with median Ct = 29.2 (~215 copies/ml; IQR Ct = 21.9-32.8, 14-56,400 copies/ml). Independent predictors of lower Cts (i.e. higher viral load) included self-reported symptoms and more genes detected, with at most small effects of sex, ethnicity, and age. Single-gene positives almost invariably had Ct > 30, but Cts varied widely in triple-gene positives, including without symptoms. Population-level Cts changed over time, with declining Ct preceding increasing SARS-CoV-2 positivity. Of 6189 participants with IgG S-antibody tests post-first RT-PCR-positive, 4808 (78%) were ever antibody-positive; Cts were significantly higher in those remaining antibody negative. Conclusions: Marked variation in community SARS-CoV-2 Ct values suggests that they could be a useful epidemiological early-warning indicator. Funding: Department of Health and Social Care, National Institutes of Health Research, Huo Family Foundation, Medical Research Council UK; Wellcome Trust.

Tracking elimination of HIV transmission in men who have sex with men in England: a modelling study.

BACKGROUND: To manage the HIV epidemic among men who have sex with men (MSM) in England, treatment as prevention strategies based on test and treat were strengthened between 2011 and 2015, and supplemented from 2015 by scale-up of pre-exposure prophylaxis (PrEP). We examined the effect of these interventions on HIV incidence and investigated whether internationally agreed targets for HIV control and elimination of HIV transmission by 2030 might be within reach among MSM in England. METHODS: We used a novel, age-stratified, CD4-staged Bayesian back-calculation model to estimate HIV incidence and undiagnosed infections among adult MSM (age ≥15 years) during the 10-year period between 2009 and 2018. The model used data on HIV and AIDS diagnoses routinely collected via the national HIV and AIDS Reporting System in England, and knowledge on the progression of HIV through CD4-defined disease stages. Estimated incidence trends were extrapolated, assuming a constant MSM population from 2018 onwards, to quantify the likelihood of achieving elimination of HIV transmission, defined as less than one newly aquired infection per 10 000 MSM per year, by 2030. FINDINGS: The peak in HIV incidence in MSM in England was estimated with 80% certainty to have occurred in 2012 or 2013, at least 1 year before the observed peak in new diagnoses in 2014. Results indicated a steep decrease in the annual number of new infections among MSM, from 2770 (95% credible interval 2490-3040) in 2013 to 1740 (1500-2010) in 2015, followed by a steadier decrease from 2016, down to 854 (441-1540) infections in 2018. A decline in new infections was consistently estimated in all age groups, and was particularly marked in MSM aged 25-34 years, and slowest in those aged 45 years or older. Similar trends were estimated in the number of undiagnosed infections, with the greatest decrease after 2013 in the 25-34 years age group. Under extrapolation assumptions, we calculated a 40% probability of achieving the defined target elimination threshold by 2030. INTERPRETATION: The sharp decrease in HIV incidence, estimated to have begun before the scale up of PrEP, indicates the success of strengthening treatment as prevention measures among MSM in England. To achieve the 2030 elimination threshold, targeted policies might be required to reach those aged 45 years or older, in whom incidence is decreasing at the slowest rate. FUNDING: UK Medical Research Council, UK National Institute of Health Research Health Protection Unit in Behavioural Science and Evaluation, and Public Health England.

Community prevalence of SARS-CoV-2 in England from April to November, 2020: results from the ONS Coronavirus Infection Survey.

BACKGROUND: Decisions about the continued need for control measures to contain the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) rely on accurate and up-to-date information about the number of people testing positive for SARS-CoV-2 and risk factors for testing positive. Existing surveillance systems are generally not based on population samples and are not longitudinal in design. METHODS: Samples were collected from individuals aged 2 years and older living in private households in England that were randomly selected from address lists and previous Office for National Statistics surveys in repeated cross-sectional household surveys with additional serial sampling and longitudinal follow-up. Participants completed a questionnaire and did nose and throat self-swabs. The percentage of individuals testing positive for SARS-CoV-2 RNA was estimated over time by use of dynamic multilevel regression and poststratification, to account for potential residual non-representativeness. Potential changes in risk factors for testing positive over time were also assessed. The study is registered with the ISRCTN Registry, ISRCTN21086382. FINDINGS: Between April 26 and Nov 1, 2020, results were available from 1 191 170 samples from 280 327 individuals; 5231 samples were positive overall, from 3923 individuals. The percentage of people testing positive for SARS-CoV-2 changed substantially over time, with an initial decrease between April 26 and June 28, 2020, from 0·40% (95% credible interval 0·29-0·54) to 0·06% (0·04-0·07), followed by low levels during July and August, 2020, before substantial increases at the end of August, 2020, with percentages testing positive above 1% from the end of October, 2020. Having a patient-facing role and working outside your home were important risk factors for testing positive for SARS-CoV-2 at the end of the first wave (April 26 to June 28, 2020), but not in the second wave (from the end of August to Nov 1, 2020). Age (young adults, particularly those aged 17-24 years) was an important initial driver of increased positivity rates in the second wave. For example, the estimated percentage of individuals testing positive was more than six times higher in those aged 17-24 years than in those aged 70 years or older at the end of September, 2020. A substantial proportion of infections were in individuals not reporting symptoms around their positive test (45-68%, dependent on calendar time. INTERPRETATION: Important risk factors for testing positive for SARS-CoV-2 varied substantially between the part of the first wave that was captured by the study (April to June, 2020) and the first part of the second wave of increased positivity rates (end of August to Nov 1, 2020), and a substantial proportion of infections were in individuals not reporting symptoms, indicating that continued monitoring for SARS-CoV-2 in the community will be important for managing the COVID-19 pandemic moving forwards. FUNDING: Department of Health and Social Care.

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.

Efficient Real-Time Monitoring of an Emerging Influenza Pandemic: How Feasible?

A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here, we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter nonidentifiability.

Extending Bayesian back-calculation to estimate age and time specific HIV incidence.

CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their inter-related contribution to the observed surveillance data. This paper, extends existing approaches to age-specific settings, permitting the joint estimation of age- and time-specific incidence and diagnosis rates and the derivation of other epidemiological quantities of interest. This allows the identification of specific age-groups at higher risk of infection, which is crucial in directing public health interventions. We investigate, through simulation studies, the suitability of various bivariate splines for the non-parametric modelling of the latent age- and time-specific incidence and illustrate our method on routinely collected data from the HIV epidemic among gay and bisexual men in England and Wales.

Exploiting routinely collected severe case data to monitor and predict influenza outbreaks.

BACKGROUND: Influenza remains a significant burden on health systems. Effective responses rely on the timely understanding of the magnitude and the evolution of an outbreak. For monitoring purposes, data on severe cases of influenza in England are reported weekly to Public Health England. These data are both readily available and have the potential to provide valuable information to estimate and predict the key transmission features of seasonal and pandemic influenza. METHODS: We propose an epidemic model that links the underlying unobserved influenza transmission process to data on severe influenza cases. Within a Bayesian framework, we infer retrospectively the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including: the effective reproduction number; the initial susceptibility; the probability of admission to intensive care given infection; and the effect of school closure on transmission. The model is also implemented in real time to assess whether early forecasting of the number of admissions to intensive care is possible. RESULTS: Our model of admissions data allows reconstruction of the underlying transmission dynamics revealing: increased transmission during the season 2013/14 and a noticeable effect of the Christmas school holiday on disease spread during seasons 2012/13 and 2014/15. When information on the initial immunity of the population is available, forecasts of the number of admissions to intensive care can be substantially improved. CONCLUSION: Readily available severe case data can be effectively used to estimate epidemiological characteristics and to predict the evolution of an epidemic, crucially allowing real-time monitoring of the transmission and severity of the outbreak.

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.

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.

Haemodynamic changes with paracetamol in critically-ill children.

PURPOSE: Paracetamol has been associated with a reduction in blood pressure, especially in febrile, critically-ill adults. We hypothesised that blood pressure would fall following administration of paracetamol in critically-ill children and this effect would be greater during fever and among children with a high body surface area to weight ratio. METHODS: A 12-month prospective observational study of children (0-16years) admitted to paediatric intensive care, who underwent pulse contour analysis and received paracetamol concurrently. RESULTS: Mean arterial blood pressure decreased significantly by 4.7% from baseline (95% CI 1.75-8.07%) in 31 children following 148 doses of paracetamol. The nadir was 2-hour post-dose. The effect was pronounced in children with fever at baseline (6.4%, 95% CI 2.8-10%), although this was not statistically significant. There was no simple relationship between this effect and body surface area to weight ratio. The association between a change in blood pressure and changes in heart rate or measured stroke volume was poor; therefore it was likely that a change in the systemic vascular resistance contributes most to this effect. CONCLUSION: There is a significant but modest reduction in blood pressure post-paracetamol in critically-ill children. This is likely related to a change in systemic vascular resistance.

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

Understanding how the geographic distribution of and movements within a population influence the spatial spread of infections is crucial for the design of interventions to curb transmission. Existing knowledge is typically based on results from simulation studies whereas analyses of real data remain sparse. The main difficulty in quantifying the spatial pattern of disease spread is the paucity of available data together with the challenge of incorporating optimally the limited information into models of disease transmission. To address this challenge the role of routine migration on the spatial pattern of infection during the epidemic of 2009 pandemic influenza in England is investigated here through two modelling approaches: parallel-region models, where epidemics in different regions are assumed to occur in isolation with shared characteristics; and meta-region models where inter-region transmission is expressed as a function of the commuter flux between regions. Results highlight that the significantly less computationally demanding parallel-region approach is sufficiently flexible to capture the underlying dynamics. This suggests that inter-region movement is either inaccurately characterized by the available commuting data or insignificant once its initial impact on transmission has subsided.

Four key challenges in infectious disease modelling using data from multiple sources.

Public health-related decision-making on policies aimed at controlling epidemics is increasingly evidence-based, exploiting multiple sources of data. Policy makers rely on complex models that are required to be robust, realistically approximating epidemics and consistent with all relevant data. Meeting these requirements in a statistically rigorous and defendable manner poses a number of challenging problems. How to weight evidence from different datasets and handle dependence between them, efficiently estimate and critically assess complex models are key challenges that we expound in this paper, using examples from influenza modelling.

Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in the Netherlands.

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1-4 years: 0.00096 (95%CrI: 0.00078-0.0012); 5-19 years: 0.00036 (0.00031-0.0044); 20-64 years: 0.0015 (0.00091-0.0020); 65+ years: 0.0084 (0.0028-0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29-82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.

Prospects of elimination of HIV with test-and-treat strategy.

Recently, there has been much debate about the prospects of eliminating HIV from high endemic countries by a test-and-treat strategy. This strategy entails regular HIV testing in the entire population and starting antiretroviral treatment immediately in all who are found to be HIV infected. We present the concept of the elimination threshold and investigate under what conditions of treatment uptake and dropout elimination of HIV is feasible. We used a deterministic model incorporating an accurate description of disease progression and variable infectivity. We derived explicit expressions for the basic reproduction number and the elimination threshold. Using estimates of exponential growth rates of HIV during the initial phase of epidemics, we investigated for which populations elimination is within reach. The concept of the elimination threshold allows an assessment of the prospects of elimination of HIV from information in the early phase of the epidemic. The relative elimination threshold quantifies prospects of elimination independently of the details of the transmission dynamics. Elimination of HIV by test-and-treat is only feasible for populations with very low reproduction numbers or if the reproduction number is lowered significantly as a result of additional interventions. Allowing low infectiousness during primary infection, the likelihood of elimination becomes somewhat higher. The elimination threshold is a powerful tool for assessing prospects of elimination from available data on epidemic growth rates of HIV. Empirical estimates of the epidemic growth rate from phylogenetic studies were used to assess the potential for elimination in specific populations.

HIV incidence in men who have sex with men in England and Wales 2001-10: a nationwide population study.

BACKGROUND: Control of HIV transmission could be achievable through an expansion of HIV testing of at-risk populations together with ready access and adherence to antiretroviral therapy. To examine whether increases in testing rates and antiretroviral therapy coverage correspond to the control of HIV transmission, we estimated HIV incidence in men who have sex with men (MSM) in England and Wales since 2001. METHODS: A CD4-staged back-calculation model of HIV incidence was used to disentangle the competing contributions of time-varying rates of diagnosis and HIV incidence to observed HIV diagnoses. Estimated trends in time to diagnosis, incidence, and undiagnosed infection in MSM were interpreted against a backdrop of increased HIV testing rates and antiretroviral-therapy coverage over the period 2001-10. FINDINGS: The observed 3·7 fold expansion in HIV testing in MSM was mirrored by a decline in the estimated mean time-to-diagnosis interval from 4·0 years (95% credible interval [CrI] 3·8-4·2) in 2001 to 3·2 years (2·6-3·8) by the end of 2010. However, neither HIV incidence (2300-2500 annual infections) nor the number of undiagnosed HIV infections (7370, 95% CrI 6990-7800, in 2001, and 7690, 5460-10 580, in 2010) changed throughout the decade, despite an increase in antiretroviral uptake from 69% in 2001 to 80% in 2010. INTERPRETATION: CD4 cell counts at HIV diagnosis are fundamental to the production of robust estimates of incidence based on HIV diagnosis data. Improved frequency and targeting of HIV testing, as well as the introduction of ART at higher CD4 counts than is currently recommended, could begin a decline in HIV transmission among MSM in England and Wales. FUNDING: UK Medical Research Council, UK Health Protection Agency.

Bayesian modeling to unmask and predict influenza A/H1N1pdm dynamics in London.

The tracking and projection of emerging epidemics is hindered by the disconnect between apparent epidemic dynamics, discernible from noisy and incomplete surveillance data, and the underlying, imperfectly observed, system. Behavior changes compound this, altering both true dynamics and reporting patterns, particularly for diseases with nonspecific symptoms, such as influenza. We disentangle these effects to unravel the hidden dynamics of the 2009 influenza A/H1N1pdm pandemic in London, where surveillance suggests an unusual dominant peak in the summer. We embed an age-structured model into a bayesian synthesis of multiple evidence sources to reveal substantial changes in contact patterns and health-seeking behavior throughout the epidemic, uncovering two similar infection waves, despite large differences in the reported levels of disease. We show how this approach, which allows for real-time learning about model parameters as the epidemic progresses, is also able to provide a sequence of nested projections that are capable of accurately reflecting the epidemic evolution.