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The time-varying effective reproduction number R t is a widely used indicator of transmission dynamics during infectious disease outbreaks. Timely estimates of R t can be obtained from reported cases counted by their date of symptom onset, which is generally closer to the time of infection than the date of report. Case counts by date of symptom onset are typically obtained from line list data, however these data can have missing information and are subject to right truncation. Previous methods have addressed these problems independently by first imputing missing onset dates, then adjusting truncated case counts, and finally estimating the effective reproduction number. This stepwise approach makes it difficult to propagate uncertainty and can introduce subtle biases during real-time estimation due to the continued impact of assumptions made in previous steps. In this work, we integrate imputation, truncation adjustment, and R t estimation into a single generative Bayesian model, allowing direct joint inference of case counts and R t from line list data with missing symptom onset dates. We then use this framework to compare the performance of nowcasting approaches with different stepwise and generative components on synthetic line list data for multiple outbreak scenarios and across different epidemic phases. We find that under reporting delays realistic for hospitalization data (50% of reports delayed by more than a week), intermediate smoothing, as is common practice in stepwise approaches, can bias nowcasts of case counts and R t , which is avoided in a joint generative approach due to shared regularization of all model components. On incomplete line list data, a fully generative approach enables the quantification of uncertainty due to missing onset dates without the need for an initial multiple imputation step. In a real-world comparison using hospitalization line list data from the COVID-19 pandemic in Switzerland, we observe the same qualitative differences between approaches. The generative modeling components developed in this work have been integrated and further extended in the R package epinowcast, providing a flexible and interpretable tool for real-time surveillance.

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most appropriate due to the exponential nature of epidemic processes and the varying magnitudes of observed values across space and time. In this paper, we argue that transforming counts before applying scores such as the CRPS or WIS can effectively mitigate these difficulties and yield epidemiologically meaningful and easily interpretable results. Using the CRPS on log-transformed values as an example, we list three attractive properties: Firstly, it can be interpreted as a probabilistic version of a relative error. Secondly, it reflects how well models predicted the time-varying epidemic growth rate. And lastly, using arguments on variance-stabilizing transformations, it can be shown that under the assumption of a quadratic mean-variance relationship, the logarithmic transformation leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. Applying a transformation of log(x + 1) to data and forecasts from the European COVID-19 Forecast Hub, we find that it changes model rankings regardless of stratification by forecast date, location or target types. Situations in which models missed the beginning of upward swings are more strongly emphasised while failing to predict a downturn following a peak is less severely penalised when scoring transformed forecasts as opposed to untransformed ones. We conclude that appropriate transformations, of which the natural logarithm is only one particularly attractive option, should be considered when assessing the performance of different models in the context of infectious disease incidence.

Mathematical and statistical models can be used to make predictions of how epidemics may progress in the near future and form a central part of outbreak mitigation and control. Renewal equation based models allow inference of epidemiological parameters from historical data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly during the COVID-19 epidemic provide a means to inform interaction between age groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2020 and November 2021. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age group interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020–2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R 0 , variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R 0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R 0 and k (95% CrIs: R 0 1.4-12; k 0.04-0.2); however, the upper bound of R 0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R 0 , variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R 0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R 0 and k (95% CrIs: R 0 1.4-12; k 0.04-0.2); however, the upper bound of R 0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

Estimating the differences in the incubation-period, serial-interval, and generation-interval distributions of SARS-CoV-2 variants is critical to understanding their transmission. However, the impact of epidemic dynamics is often neglected in estimating the timing of infection—for example, when an epidemic is growing exponentially, a cohort of infected individuals who developed symptoms at the same time are more likely to have been infected recently. Here, we reanalyze incubation-period and serial-interval data describing transmissions of the Delta and Omicron variants from the Netherlands at the end of December 2021. Previous analysis of the same dataset reported shorter mean observed incubation period (3.2 d vs. 4.4 d) and serial interval (3.5 d vs. 4.1 d) for the Omicron variant, but the number of infections caused by the Delta variant decreased during this period as the number of Omicron infections increased. When we account for growth-rate differences of two variants during the study period, we estimate similar mean incubation periods (3.8 to 4.5 d) for both variants but a shorter mean generation interval for the Omicron variant (3.0 d; 95% CI: 2.7 to 3.2 d) than for the Delta variant (3.8 d; 95% CI: 3.7 to 4.0 d). The differences in estimated generation intervals may be driven by the “network effect”—higher effective transmissibility of the Omicron variant can cause faster susceptible depletion among contact networks, which in turn prevents late transmission (therefore shortening realized generation intervals). Using up-to-date generation-interval distributions is critical to accurately estimating the reproduction advantage of the Omicron variant.

Accurately estimating the effective reproduction number (R t ) of a circulating pathogen is a fundamental challenge in the study of infectious disease. The fields of epidemiology and pathogen phylodynamics both share this goal, but to date, methodologies and data employed by each remain largely distinct. Here we present EpiFusion: a joint approach that can be used to harness the complementary strengths of each field to improve estimation of outbreak dynamics for large and poorly sampled epidemics, such as arboviral or respiratory virus outbreaks, and validate it for retrospective analysis. We propose a model of R t that estimates outbreak trajectories conditional upon both phylodynamic (time-scaled trees estimated from genetic sequences) and epidemiological (case incidence) data. We simulate stochastic outbreak trajectories that are weighted according to epidemiological and phylodynamic observation models and fit using particle Markov Chain Monte Carlo. To assess performance, we test EpiFusion on simulated outbreaks in which transmission and/or surveillance rapidly changes and find that using EpiFusion to combine epidemiological and phylodynamic data maintains accuracy and increases certainty in trajectory and R t estimates, compared to when each data type is used alone. We benchmark EpiFusion’s performance against existing methods to estimate R t and demonstrate advances in speed and accuracy. Importantly, our approach scales efficiently with dataset size. Finally, we apply our model to estimate R t during the 2014 Ebola outbreak in Sierra Leone. EpiFusion is designed to accommodate future extensions that will improve its utility, such as explicitly modelling population structure, accommodations for phylogenetic uncertainty, and the ability to weight the contributions of genomic or case incidence to the inference.

The distribution of the generation time (the interval between individuals becoming infected and transmitting the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to data from the early months of the COVID-19 pandemic (December 2019-March 2020) compared to existing models (Hart et al., 2021). However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March to November 2020 in the UK, we provide updated estimates of the generation time. We considered both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% credible interval 3.3–5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0–8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (5.9 days, 5.2–7.0 days) and a similar standard deviation (4.8 days, 4.0–6.3 days). As well as estimating the generation time using data from the entire study period, we also considered whether the generation time varied temporally. Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, further data collection and analysis is necessary to continue to monitor ongoing transmission and inform future public health policy decisions.

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 nowcasting model using generalised additive models that makes novel use of individual-level patient data to correct the mpox epidemic curve in England. The aim of this model is to correct for backfilling in the epidemic curve 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. The resulting model accurately captured the true shape of the epidemic curve in real time.

Background : The current novel coronavirus outbreak appears to have originated from a point-source exposure event at Huanan seafood wholesale market in Wuhan, China. There is still uncertainty around the scale and duration of this exposure event. This has implications for the estimated transmissibility of the coronavirus and as such, these potential scenarios should be explored.   Methods : We used a stochastic branching process model, parameterised with available data where possible and otherwise informed by the 2002-2003 Severe Acute Respiratory Syndrome (SARS) outbreak, to simulate the Wuhan outbreak. We evaluated scenarios for the following parameters: the size, and duration of the initial transmission event, the serial interval, and the reproduction number (R0). We restricted model simulations based on the number of observed cases on the 25th of January, accepting samples that were within a 5% interval on either side of this estimate. Results : Using a pre-intervention SARS-like serial interval suggested a larger initial transmission event and a higher R0 estimate. Using a SARs-like serial interval we found that the most likely scenario produced an R0 estimate between 2-2.7 (90% credible interval (CrI)). A pre-intervention SARS-like serial interval resulted in an R0 estimate between 2-3 (90% CrI). There were other plausible scenarios with smaller events sizes and longer duration that had comparable R0 estimates. There were very few simulations that were able to reproduce the observed data when R0 was less than 1. Conclusions : Our results indicate that an R0 of less than 1 was highly unlikely unless the size of the initial exposure event was much greater than currently reported. We found that R0 estimates were comparable across scenarios with decreasing event size and increasing duration. Scenarios with a pre-intervention SARS-like serial interval resulted in a higher R0 and were equally plausible to scenarios with SARs-like serial intervals.