Prevalence of persistent SARS-CoV-2 in a large community surveillance study.

Persistent SARS-CoV-2 infections may act as viral reservoirs that could seed future outbreaks1-5, give rise to highly divergent lineages6-8 and contribute to cases with post-acute COVID-19 sequelae (long COVID)9,10. However, the population prevalence of persistent infections, their viral load kinetics and evolutionary dynamics over the course of infections remain largely unknown. Here, using viral sequence data collected as part of a national infection survey, we identified 381 individuals with SARS-CoV-2 RNA at high titre persisting for at least 30 days, of which 54 had viral RNA persisting at least 60 days. We refer to these as 'persistent infections' as available evidence suggests that they represent ongoing viral replication, although the persistence of non-replicating RNA cannot be ruled out in all. Individuals with persistent infection had more than 50% higher odds of self-reporting long COVID than individuals with non-persistent infection. We estimate that 0.1-0.5% of infections may become persistent with typically rebounding high viral loads and last for at least 60 days. In some individuals, we identified many viral amino acid substitutions, indicating periods of strong positive selection, whereas others had no consensus change in the sequences for prolonged periods, consistent with weak selection. Substitutions included mutations that are lineage defining for SARS-CoV-2 variants, at target sites for monoclonal antibodies and/or are commonly found in immunocompromised people11-14. This work has profound implications for understanding and characterizing SARS-CoV-2 infection, epidemiology and evolution.

Unsupervised identification of significant lineages of SARS-CoV-2 through scalable machine learning methods.

Since its emergence in late 2019, SARS-CoV-2 has diversified into a large number of lineages and caused multiple waves of infection globally. Novel lineages have the potential to spread rapidly and internationally if they have higher intrinsic transmissibility and/or can evade host immune responses, as has been seen with the Alpha, Delta, and Omicron variants of concern. They can also cause increased mortality and morbidity if they have increased virulence, as was seen for Alpha and Delta. Phylogenetic methods provide the "gold standard" for representing the global diversity of SARS-CoV-2 and to identify newly emerging lineages. However, these methods are computationally expensive, struggle when datasets get too large, and require manual curation to designate new lineages. These challenges provide a motivation to develop complementary methods that can incorporate all of the genetic data available without down-sampling to extract meaningful information rapidly and with minimal curation. In this paper, we demonstrate the utility of using algorithmic approaches based on word-statistics to represent whole sequences, bringing speed, scalability, and interpretability to the construction of genetic topologies. While not serving as a substitute for current phylogenetic analyses, the proposed methods can be used as a complementary, and fully automatable, approach to identify and confirm new emerging variants.

Viral burden is associated with age, vaccination, and viral variant in a population-representative study of SARS-CoV-2 that accounts for time-since-infection-related sampling bias.

In this study, we evaluated the impact of viral variant, in addition to other variables, on within-host viral burden, by analysing cycle threshold (Ct) values derived from nose and throat swabs, collected as part of the UK COVID-19 Infection Survey. Because viral burden distributions determined from community survey data can be biased due to the impact of variant epidemiology on the time-since-infection of samples, we developed a method to explicitly adjust observed Ct value distributions to account for the expected bias. By analysing the adjusted Ct values using partial least squares regression, we found that among unvaccinated individuals with no known prior exposure, viral burden was 44% lower among Alpha variant infections, compared to those with the predecessor strain, B.1.177. Vaccination reduced viral burden by 67%, and among vaccinated individuals, viral burden was 286% higher among Delta variant, compared to Alpha variant, infections. In addition, viral burden increased by 17% for every 10-year age increment of the infected individual. In summary, within-host viral burden increases with age, is reduced by vaccination, and is influenced by the interplay of vaccination status and viral variant.

Correction: Viral burden is associated with age, vaccination, and viral variant in a population-representative study of SARS-CoV-2 that accounts for time-since-infection-related sampling bias.

[This corrects the article DOI: 10.1371/journal.ppat.1011461.].

How effective is the BNT162b2 mRNA vaccine against SARS-CoV-2 transmission and infection? A national programme analysis in Monaco, July 2021 to September 2022.

BACKGROUND: We quantified SARS-CoV-2 dynamics in different community settings and the direct and indirect effect of the BNT162b2 mRNA vaccine in Monaco for different variants of concern (VOC). METHODS: Between July 2021 and September 2022, we prospectively investigated 20,443 contacts from 6320 index cases using data from the Monaco COVID-19 Public Health Programme. We calculated secondary attack rates (SARs) in households (n = 13,877), schools (n = 2508) and occupational (n = 6499) settings. We used binomial regression with a complementary log-log link function to measure adjusted hazard ratios (aHR) and vaccine effectiveness (aVE) for index cases to infect contacts and contacts to be infected in households. RESULTS: In households, the SAR was 55% (95% CI 54-57) and 50% (48-51) among unvaccinated and vaccinated contacts, respectively. The SAR was 32% (28-36) and 12% (10-13) in workplaces, and 7% (6-9) and 6% (3-10) in schools, among unvaccinated and vaccinated contacts respectively. In household, the aHR was lower in contacts than in index cases (aHR 0.68 [0.55-0.83] and 0.93 [0.74-1.1] for delta; aHR 0.73 [0.66-0.81] and 0.89 [0.80-0.99] for omicron BA.1&2, respectively). Vaccination had no significant effect on either direct or indirect aVE for omicron BA.4&5. The direct aVE in contacts was 32% (17, 45) and 27% (19, 34), and for index cases the indirect aVE was 7% (- 17, 26) and 11% (1, 20) for delta and omicron BA.1&2, respectively. The greatest aVE was in contacts with a previous SARS-CoV-2 infection and a single vaccine dose during the omicron BA.1&2 period (45% [27, 59]), while the lowest were found in contacts with either three vaccine doses (aVE - 24% [- 63, 6]) or one single dose and a previous SARS-CoV-2 infection (aVE - 36% [- 198, 38]) during the omicron BA.4&5 period. CONCLUSIONS: Protection conferred by the BNT162b2 mRNA vaccine against transmission and infection was low for delta and omicron BA.1&2, regardless of the number of vaccine doses and previous SARS-CoV-2 infection. There was no significant vaccine effect for omicron BA.4&5. Health authorities carrying out vaccination campaigns should bear in mind that the current generation of COVID-19 vaccines may not represent an effective tool in protecting individuals from either transmitting or acquiring SARS-CoV-2 infection.

SARS-CoV-2, influenza A/B and respiratory syncytial virus positivity and association with influenza-like illness and self-reported symptoms, over the 2022/23 winter season in the UK: a longitudinal surveillance cohort.

BACKGROUND: Syndromic surveillance often relies on patients presenting to healthcare. Community cohorts, although more challenging to recruit, could provide additional population-wide insights, particularly with SARS-CoV-2 co-circulating with other respiratory viruses. METHODS: We estimated the positivity and incidence of SARS-CoV-2, influenza A/B, and RSV, and trends in self-reported symptoms including influenza-like illness (ILI), over the 2022/23 winter season in a broadly representative UK community cohort (COVID-19 Infection Survey), using negative-binomial generalised additive models. We estimated associations between test positivity and each of the symptoms and influenza vaccination, using adjusted logistic and multinomial models. RESULTS: Swabs taken at 32,937/1,352,979 (2.4%) assessments tested positive for SARS-CoV-2, 181/14,939 (1.2%) for RSV and 130/14,939 (0.9%) for influenza A/B, varying by age over time. Positivity and incidence peaks were earliest for RSV, then influenza A/B, then SARS-CoV-2, and were highest for RSV in the youngest and for SARS-CoV-2 in the oldest age groups. Many test positives did not report key symptoms: middle-aged participants were generally more symptomatic than older or younger participants, but still, only ~ 25% reported ILI-WHO and ~ 60% ILI-ECDC. Most symptomatic participants did not test positive for any of the three viruses. Influenza A/B-positivity was lower in participants reporting influenza vaccination in the current and previous seasons (odds ratio = 0.55 (95% CI 0.32, 0.95)) versus neither season. CONCLUSIONS: Symptom profiles varied little by aetiology, making distinguishing SARS-CoV-2, influenza and RSV using symptoms challenging. Most symptoms were not explained by these viruses, indicating the importance of other pathogens in syndromic surveillance. Influenza vaccination was associated with lower rates of community influenza test positivity.

Lineage replacement and evolution captured by 3 years of the United Kingdom Coronavirus (COVID-19) Infection Survey.

The Office for National Statistics Coronavirus (COVID-19) Infection Survey (ONS-CIS) is the largest surveillance study of SARS-CoV-2 positivity in the community, and collected data on the United Kingdom (UK) epidemic from April 2020 until March 2023 before being paused. Here, we report on the epidemiological and evolutionary dynamics of SARS-CoV-2 determined by analysing the sequenced samples collected by the ONS-CIS during this period. We observed a series of sweeps or partial sweeps, with each sweeping lineage having a distinct growth advantage compared to their predecessors, although this was also accompanied by a gradual fall in average viral burdens from June 2021 to March 2023. The sweeps also generated an alternating pattern in which most samples had either S-gene target failure (SGTF) or non-SGTF over time. Evolution was characterized by steadily increasing divergence and diversity within lineages, but with step increases in divergence associated with each sweeping major lineage. This led to a faster overall rate of evolution when measured at the between-lineage level compared to within lineages, and fluctuating levels of diversity. These observations highlight the value of viral sequencing integrated into community surveillance studies to monitor the viral epidemiology and evolution of SARS-CoV-2, and potentially other pathogens.

A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic.

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

EpiBeds: Data informed modelling of the COVID-19 hospital burden in England.

The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

Symptoms and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Positivity in the General Population in the United Kingdom.

BACKGROUND: "Classic" symptoms (cough, fever, loss of taste/smell) prompt severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) polymerase chain reaction (PCR) testing in the United Kingdom. Studies have assessed the ability of different symptoms to identify infection, but few have compared symptoms over time (reflecting variants) and by vaccination status. METHODS: Using the COVID-19 Infection Survey, sampling households across the United Kingdom, we compared symptoms in PCR-positives vs PCR-negatives, evaluating sensitivity of combinations of 12 symptoms (percentage symptomatic PCR-positives reporting specific symptoms) and tests per case (TPC) (PCR-positives or PCR-negatives reporting specific symptoms/ PCR-positives reporting specific symptoms). RESULTS: Between April 2020 and August 2021, 27 869 SARS-CoV-2 PCR-positive episodes occurred in 27 692 participants (median 42 years), of whom 13 427 (48%) self-reported symptoms ("symptomatic PCR-positives"). The comparator comprised 3 806 692 test-negative visits (457 215 participants); 130 612 (3%) self-reported symptoms ("symptomatic PCR-negatives"). Symptom reporting in PCR-positives varied by age, sex, and ethnicity, and over time, reflecting changes in prevalence of viral variants, incidental changes (eg, seasonal pathogens (with sore throat increasing in PCR-positives and PCR-negatives from April 2021), schools reopening) and vaccination rollout. After May 2021 when Delta emerged, headache and fever substantially increased in PCR-positives, but not PCR-negatives. Sensitivity of symptom-based detection increased from 74% using "classic" symptoms, to 81% adding fatigue/weakness, and 90% including all 8 additional symptoms. However, this increased TPC from 4.6 to 5.3 to 8.7. CONCLUSIONS: Expanded symptom combinations may provide modest benefits for sensitivity of PCR-based case detection, but this will vary between settings and over time, and increases tests/case. Large-scale changes to targeted PCR-testing approaches require careful evaluation given substantial resource and infrastructure implications.

Omicron-associated changes in SARS-CoV-2 symptoms in the United Kingdom.

BACKGROUND: The SARS-CoV-2 Delta variant has been replaced by the highly transmissible Omicron BA.1 variant, and subsequently by Omicron BA.2. It is important to understand how these changes in dominant variants affect reported symptoms, while also accounting for symptoms arising from other co-circulating respiratory viruses. METHODS: In a nationally representative UK community study, the COVID-19 Infection Survey, we investigated symptoms in PCR-positive infection episodes vs. PCR-negative study visits over calendar time, by age and vaccination status, comparing periods when the Delta, Omicron BA.1 and BA.2 variants were dominant. RESULTS: Between October-2020 and April-2022, 120,995 SARS-CoV-2 PCR-positive episodes occurred in 115,886 participants, with 70,683 (58%) reporting symptoms. The comparator comprised 4,766,366 PCR-negative study visits (483,894 participants); 203,422 (4%) reporting symptoms. Symptom reporting in PCR-positives varied over time, with a marked reduction in loss of taste/smell as Omicron BA.1 dominated, maintained with BA.2 (44%/45% 17 October 2021, 16%/13% 2 January 2022, 15%/12% 27 March 2022). Cough, fever, shortness of breath, myalgia, fatigue/weakness and headache also decreased after Omicron BA.1 dominated, but sore throat increased, the latter to a greater degree than concurrent increases in PCR-negatives. Fatigue/weakness increased again after BA.2 dominated, although to a similar degree to concurrent increases in PCR-negatives. Symptoms were consistently more common in adults aged 18-65 years than in children or older adults. CONCLUSIONS: Increases in sore throat (also common in the general community), and a marked reduction in loss of taste/smell, make Omicron harder to detect with symptom-based testing algorithms, with implications for institutional and national testing policies.

Hospital length of stay for COVID-19 patients: Data-driven methods for forward planning.

BACKGROUND: Predicting hospital length of stay (LoS) for patients with COVID-19 infection is essential to ensure that adequate bed capacity can be provided without unnecessarily restricting care for patients with other conditions. Here, we demonstrate the utility of three complementary methods for predicting LoS using UK national- and hospital-level data. METHOD: On a national scale, relevant patients were identified from the COVID-19 Hospitalisation in England Surveillance System (CHESS) reports. An Accelerated Failure Time (AFT) survival model and a truncation corrected method (TC), both with underlying Weibull distributions, were fitted to the data to estimate LoS from hospital admission date to an outcome (death or discharge) and from hospital admission date to Intensive Care Unit (ICU) admission date. In a second approach we fit a multi-state (MS) survival model to data directly from the Manchester University NHS Foundation Trust (MFT). We develop a planning tool that uses LoS estimates from these models to predict bed occupancy. RESULTS: All methods produced similar overall estimates of LoS for overall hospital stay, given a patient is not admitted to ICU (8.4, 9.1 and 8.0 days for AFT, TC and MS, respectively). Estimates differ more significantly between the local and national level when considering ICU. National estimates for ICU LoS from AFT and TC were 12.4 and 13.4 days, whereas in local data the MS method produced estimates of 18.9 days. CONCLUSIONS: Given the complexity and partiality of different data sources and the rapidly evolving nature of the COVID-19 pandemic, it is most appropriate to use multiple analysis methods on multiple datasets. The AFT method accounts for censored cases, but does not allow for simultaneous consideration of different outcomes. The TC method does not include censored cases, instead correcting for truncation in the data, but does consider these different outcomes. The MS method can model complex pathways to different outcomes whilst accounting for censoring, but cannot handle non-random case missingness. Overall, we conclude that data-driven modelling approaches of LoS using these methods is useful in epidemic planning and management, and should be considered for widespread adoption throughout healthcare systems internationally where similar data resources exist.

Bayesian belief network modelling of household food security in rural South Africa.

BACKGROUND: Achieving food security remains a key challenge for public policy throughout the world. As such, understanding the determinants of food insecurity and the causal relationships between them is an important scientific question. We aim to construct a Bayesian belief network model of food security in rural South Africa to act as a tool for decision support in the design of interventions. METHODS: Here, we use data from the Agincourt Health and Socio-demographic Surveillance System (HDSS) study area, which is close to the Mozambique border in a low-income region of South Africa, together with Bayesian belief network (BBN) methodology to address this question. RESULTS: We find that a combination of expert elicitation and learning from data produces the most credible set of causal relationships, as well as the greatest predictive performance with 10-fold cross validation resulting in a Briers score 0.0846, information reward of 0.5590, and Bayesian information reward of 0.0057. We report the resulting model as a directed acyclic graph (DAG) that can be used to model the expected effects of complex interventions to improve food security. Applications to sensitivity analyses and interventional simulations show ways the model can be applied as tool for decision support for human experts in deciding on interventions. CONCLUSIONS: The resulting models can form the basis of the iterative generation of a robust causal model of household food security in the Agincourt HDSS study area and in other similar populations.

Airflow Characteristics in Aeromedical Aircraft: Considerations During COVID-19.

OBJECTIVE: The aeromedical transport of coronavirus patients presents risks to clinicians and aircrew. Patient positioning and physical barriers may provide additional protection during flight. This paper describes airflow testing undertaken on fixed wing and rotary wing aeromedical aircraft. METHODS: Airflow testing was undertaken on a stationary Hawker Beechcraft B200C and Leonardo Augusta Westland 139. Airflow was simulated using a Trainer 101 (MSS Professional A/S, Odense Sø, Syddanmark, Denmark) Smoke machine. Different cabin configurations were used along with variations in heating, cooling, and ventilation systems. RESULTS: For the Hawker Beechcraft B200C, smoke generated within the forward section of the cabin was observed to fill the cabin to a fluid boundary located in-line with the forward edge of the cargo door. With the curtain closed, smoke was only observed to enter the cockpit in very small quantities. For the Leonardo AW139, smoke generated within the cabin was observed to expand to fill the cabin evenly before dissipating. With the curtain closed, smoke was observed to enter the cockpit only in small quantities CONCLUSION: The use of physical barriers in fixed wing and rotary wing aeromedical aircraft provides some protection to aircrew. Optimal positioning of the patient is on the aft stretcher on the Beechcraft B200C and on a laterally orientated stretcher on the AW139. The results provide a baseline for further investigation into methods to protect aircrew during the coronavirus pandemic.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Scabies in residential care homes: Modelling, inference and interventions for well-connected population sub-units.

In the context of an ageing population, understanding the transmission of infectious diseases such as scabies through well-connected sub-units of the population, such as residential care homes, is particularly important for the design of efficient interventions to mitigate against the effects of those diseases. Here, we present a modelling methodology based on the efficient solution of a large-scale system of linear differential equations that allows statistical calibration of individual-based random models to real data on scabies in residential care homes. In particular, we review and benchmark different numerical methods for the integration of the differential equation system, and then select the most appropriate of these methods to perform inference using Markov chain Monte Carlo. We test the goodness-of-fit of this model using posterior predictive intervals and propagate forward the resulting parameter uncertainty in a Bayesian framework to consider the economic cost of delayed interventions against scabies, quantifying the benefits of prompt action in the event of detection. We also revisit the previous methodology used to assess the safety of treatments in small population sub-units-in this context ivermectin-and demonstrate that even a very slight relaxation of the implicit assumption of homogeneous death rates significantly increases the plausibility of the hypothesis that ivermectin does not cause excess mortality based upon the data of Barkwell and Shields.

The impact of surveillance and control on highly pathogenic avian influenza outbreaks in poultry in Dhaka division, Bangladesh.

In Bangladesh, the poultry industry is an economically and socially important sector, but it is persistently threatened by the effects of H5N1 highly pathogenic avian influenza. Thus, identifying the optimal control policy in response to an emerging disease outbreak is a key challenge for policy-makers. To inform this aim, a common approach is to carry out simulation studies comparing plausible strategies, while accounting for known capacity restrictions. In this study we perform simulations of a previously developed H5N1 influenza transmission model framework, fitted to two separate historical outbreaks, to assess specific control objectives related to the burden or duration of H5N1 outbreaks among poultry farms in the Dhaka division of Bangladesh. In particular, we explore the optimal implementation of ring culling, ring vaccination and active surveillance measures when presuming disease transmission predominately occurs from premises-to-premises, versus a setting requiring the inclusion of external factors. Additionally, we determine the sensitivity of the management actions under consideration to differing levels of capacity constraints and outbreaks with disparate transmission dynamics. While we find that reactive culling and vaccination policies should pay close attention to these factors to ensure intervention targeting is optimised, across multiple settings the top performing control action amongst those under consideration were targeted proactive surveillance schemes. Our findings may advise the type of control measure, plus its intensity, that could potentially be applied in the event of a developing outbreak of H5N1 amongst originally H5N1 virus-free commercially-reared poultry in the Dhaka division of Bangladesh.

Modelling fertility in rural South Africa with combined nonlinear parametric and semi-parametric methods.

BACKGROUND: Central to the study of populations, and therefore to the analysis of the development of countries undergoing major transitions, is the calculation of fertility patterns and their dependence on different variables such as age, education, and socio-economic status. Most epidemiological research on these matters rely on the often unjustified assumption of (generalised) linearity, or alternatively makes a parametric assumption (e.g. for age-patterns). METHODS: We consider nonlinearity of fertility in the covariates by combining an established nonlinear parametric model for fertility over age with nonlinear modelling of fertility over other covariates. For the latter, we use the semi-parametric method of Gaussian process regression which is a popular methodology in many fields including machine learning, computer science, and systems biology. We applied the method to data from the Agincourt Health and Socio-Demographic Surveillance System, annual census rounds performed on a poor rural region of South Africa since 1992, to analyse fertility patterns over age and socio-economic status. RESULTS: We capture a previously established age-pattern of fertility, whilst being able to more robustly model the relationship between fertility and socio-economic status without unjustified a priori assumptions of linearity. Peak fertility over age is shown to be increasing over time, as well as for adolescents but not for those later in life for whom fertility is generally decreasing over time. CONCLUSIONS: Combining Gaussian process regression with nonlinear parametric modelling of fertility over age allowed for the incorporation of further covariates into the analysis without needing to assume a linear relationship. This enabled us to provide further insights into the fertility patterns of the Agincourt study area, in particular the interaction between age and socio-economic status.

Extinction times in the subcritical stochastic SIS logistic epidemic.

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as [Formula: see text] but more slowly than [Formula: see text]. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.