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In many epidemiological and ecological contexts, there is a trade-off between infections and interaction. This arises because the links between individuals capable of spreading infections are also often associated with beneficial activities. Here, we consider how the presence of explicit network structure changes the optimal solution of a class of infection-interaction trade-offs. In order to do this, we develop and analyse a low-dimensional dynamical system approximating the network SIS epidemic. We find that network structure in the form of heterogeneous numbers of contacts can have a significant impact on the optimal number of contacts that comes out of a trade-off model., Comment: 16 pages; 5 figures

During the SARS-CoV-2 pandemic, polymerase chain reaction (PCR) and lateral flow device (LFD) tests were frequently deployed to detect the presence of SARS-CoV-2. Many of these tests were singleplex, and only tested for the presence of a single pathogen. Multiplex tests can test for the presence of several pathogens using only a single swab, which can allow for: surveillance of more pathogens, targeting of antiviral interventions, a reduced burden of testing, and lower costs. Test sensitivity however, particularly in LFD tests, is highly conditional on the viral concentration dynamics of individuals. To inform the use of multiplex testing in outbreak detection it is therefore necessary to investigate the interactions between outbreak detection strategies and the differing viral concentration trajectories of key pathogens. Viral concentration trajectories are estimated for SARS-CoV-2, and Influenza A/B. Testing strategies for the first five symptomatic cases in an outbreak are then simulated and used to evaluate key performance indicators. Strategies that use a combination of multiplex LFD and PCR tests achieve; high levels of detection, detect outbreaks rapidly, and have the lowest burden of testing across multiple pathogens. Influenza B was estimated to have lower rates of detection due to its modelled viral concentration dynamics., Comment: 29 pages, 17 Figures

Epidemiological delays, such as incubation periods, serial intervals, and hospital lengths of stay, are among key quantities in infectious disease epidemiology that inform public health policy and clinical practice. This information is used to inform mathematical and statistical models, which in turn can inform control strategies. There are three main challenges that make delay distributions difficult to estimate. First, the data are commonly censored (e.g., symptom onset may only be reported by date instead of the exact time of day). Second, delays are often right truncated when being estimated in real time (not all events that have occurred have been observed yet). Third, during a rapidly growing or declining outbreak, overrepresentation or underrepresentation, respectively, of recently infected cases in the data can lead to bias in estimates. Studies that estimate delays rarely address all these factors and sometimes report several estimates using different combinations of adjustments, which can lead to conflicting answers and confusion about which estimates are most accurate. In this work, we formulate a checklist of best practices for estimating and reporting epidemiological delays with a focus on the incubation period and serial interval. We also propose strategies for handling common biases and identify areas where more work is needed. Our recommendations can help improve the robustness and utility of reported estimates and provide guidance for the evaluation of estimates for downstream use in transmission models or other analyses.

Hospitalisations from COVID-19 with Omicron sub-lineages have put a sustained pressure on the English healthcare system. Understanding the expected healthcare demand enables more effective and timely planning from public health. We collect syndromic surveillance sources, which include online search data, NHS 111 telephonic and online triages. Incorporating this data we explore generalised additive models, generalised linear mixed-models, penalised generalised linear models and model ensemble methods to forecast over a two-week forecast horizon at an NHS Trust level. Furthermore, we showcase how model combinations improve forecast scoring through a mean ensemble, weighted ensemble, and ensemble by regression. Validated over multiple Omicron waves, at different spatial scales, we show that leading indicators can improve performance of forecasting models, particularly at epidemic changepoints. Using a variety of scoring rules, we show that ensemble approaches outperformed all individual models, providing higher performance at a 21-day window than the corresponding individual models at 14-days. We introduce a modelling structure used by public health officials in England in 2022 to inform NHS healthcare strategy and policy decision making. This paper explores the significance of ensemble methods to improve forecasting performance and how novel syndromic surveillance can be practically applied in epidemic forecasting., Comment: arXiv admin note: substantial text overlap with arXiv:2303.12037

Objectives: To identify and quantify risk factors that contribute to clusters of COVID-19 in the workplace. Methods: We identified clusters of COVID-19 cases in the workplace and investigated the characteristics of the individuals, the workplaces, the areas they work, and the methods of commute to work, through data linkages based on Middle Layer Super Output Areas (MSOAs) in England between 20/06/2021 and 20/02/2022. We estimated associations between potential risk factors and workplace clusters, adjusting for plausible confounders identified using a Directed Acyclic Graph (DAG). Results: For most industries, increased physical proximity in the workplace was associated with increased risk of COVID-19 clusters, while increased vaccination was associated with reduced risk. Commuter demographic risk factors varied across industry, but for the majority of industries, a higher proportion of black/african/caribbean ethnicities, and living in deprived areas, was associated with increased cluster risk. A higher proportion of commuters in the 60-64 age group was associated with reduced cluster risk. There were significant associations between gender, work commute methods, and staff contract type with cluster risk, but these were highly variable across industries. Conclusions: This study has used novel national data linkages to identify potential risk factors of workplace COVID-19 clusters, including possible protective effects of vaccination and increased physical distance at work. The same methodological approach can be applied to wider occupational and environmental health research.

The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating $R_0$ from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition. We show that by conditioning a `deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory., Comment: To be published in Infectious Disease Modelling

Following the UK Government's Living with COVID-19 Strategy and the end of universal testing, hospital admissions are an increasingly important measure of COVID-19 pandemic pressure. Understanding leading indicators of admissions at National Health Service (NHS) Trust, regional and national geographies help health services plan capacity needs and prepare for ongoing pressures. We explored the spatio-temporal relationships of leading indicators of hospital pressure across successive waves of SARS-CoV-2 incidence in England. This includes an analysis of internet search volume values from Google Trends, NHS triage calls and online queries, the NHS COVID-19 App, lateral flow devices and the ZOE App. Data sources were analysed for their feasibility as leading indicators using linear and non-linear methods; granger causality, cross correlations and dynamic time warping at fine spatial scales. Consistent temporal and spatial relationships were found for some of the leading indicators assessed across resurgent waves of COVID-19. Google Trends and NHS queries consistently led admissions in over 70% of Trusts, with lead times ranging from 5-20 days, whereas an inconsistent relationship was found for the ZOE app, NHS COVID-19 App, and rapid testing, that diminished with granularity, showing limited autocorrelation of leads between -7 to 7 days. This work shows that novel syndromic surveillance data has utility for understanding the expected hospital burden at fine spatial scales. The analysis shows at low level geographies that some surveillance sources can predict hospital admissions, though care must be taken in relying on the lead times and consistency between waves.

Background: Seasonal influenza causes a substantial burden on healthcare services over the winter period when these systems are already under pressure. Policies during the COVID-19 pandemic supressed the transmission of season influenza, making the timing and magnitude of a potential resurgence difficult to predict. Methods: We developed a hierarchical generalised additive model (GAM) for the short-term forecasting of hospital admissions with a positive test for the influenza virus sub-regionally across England. The model incorporates a multi-level structure of spatio-temporal splines, weekly seasonality, and spatial correlation. Using multiple performance metrics including interval score, coverage, bias, and median absolute error, the predictive performance is evaluated for the 2022/23 seasonal wave. Performance is measured against an autoregressive integrated moving average (ARIMA) time series model. Results: The GAM method outperformed the ARIMA model across scoring rules at both high and low-level geographies, and across the different phases of the epidemic wave including the turning point. The performance of the GAM with a 14-day forecast horizon was comparable in error to the ARIMA at 7 days. The performance of the GAM is found to be most sensitive to the flexibility of the smoothing function that measures the national epidemic trend. Interpretation: This study introduces a novel approach to short-term forecasting of hospital admissions with influenza using hierarchical, spatial, and temporal components. The model is data-driven and practical to deploy using information realistically available at time of prediction, addressing key limitations of epidemic forecasting approaches. This model was used across the winter for healthcare operational planning by the UK Health Security Agency and the National Health Service in England.

In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was characterised by substantial delays in the reporting of the symptom onset date and specimen collection date for confirmed positive cases. These delays led to substantial backfilling in the epidemic curve, making it challenging to interpret the epidemic trajectory in real-time. Many nowcasting models exist to tackle this challenge in epidemiological data, but these lacked sufficient flexibility. We have developed a novel nowcasting model using generalised additive models to correct the mpox epidemic curve in England, and provide real-time characteristics of the state of the epidemic, including the real-time growth rate. This model benefited from close collaboration with individuals involved in collecting and processing the data, enabling temporal changes in the reporting structure to be built into the model, which improved the robustness of the nowcasts generated.

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

The COVID-19 pandemic has had high mortality rates in the elderly and frail worldwide, particularly in care homes. This is driven by the difficulty of isolating care homes from the wider community, the large population sizes within care facilities (relative to typical households), and the age/frailty of the residents. To quantify the mortality risk posed by disease, the case fatality risk (CFR) is an important tool. This quantifies the proportion of cases that result in death. Throughout the pandemic, CFR amongst care home residents in England has been monitored closely. To estimate CFR, we apply both novel and existing methods to data on deaths in care homes, collected by Public Health England and the Care Quality Commission. We compare these different methods, evaluating their relative strengths and weaknesses. Using these methods, we estimate temporal trends in the instantaneous CFR (at both daily and weekly resolutions) and the overall CFR across the whole of England, and dis-aggregated at regional level. We also investigate how the CFR varies based on age and on the type of care required, dis-aggregating by whether care homes include nursing staff and by age of residents. This work has contributed to the summary of measures used for monitoring the UK epidemic.

The first year of the COVID-19 pandemic put considerable strain on the national healthcare system in England. 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, which was coupled to a model of the generalised epidemic. We named this model EpiBeds. 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 different clinical pathways, and the reproduction number of the generalised epidemic. 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 has provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland.

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitness, a measure of reproductive success used in evolutionary graph theory, is related to the life-history of individuals in terms of their birth and death rates. In simple networks, these ecologically motivated dynamics are used to provide new insight into the spread of adaptive mutations, both with and without clonal interference. For example, the star network, which is known to be an amplifier of selection in evolutionary graph theory, can inhibit the spread of adaptive mutations when individuals can die naturally.

During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.

Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduction number for initiating interventions. This observation has particular implications for the low- and middle-income countries currently in the early stages of their local epidemics., Comment: Main text: 13 pages (1-13), 3 figures, 1 table; Supplementary Information: 9 pages (14-22), 4 figures, 1 table

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes.