A method to estimate the serial interval distribution under partially-sampled data.

The serial interval of an infectious disease is an important variable in epidemiology. It is defined as the period of time between the symptom onset times of the infector and infectee in a direct transmission pair. Under partially sampled data, purported infector-infectee pairs may actually be separated by one or more unsampled cases in between. Misunderstanding such pairs as direct transmissions will result in overestimating the length of serial intervals. On the other hand, two cases that are infected by an unseen third case (known as coprimary transmission) may be classified as a direct transmission pair, leading to an underestimation of the serial interval. Here, we introduce a method to jointly estimate the distribution of serial intervals factoring in these two sources of error. We simultaneously estimate the distribution of the number of unsampled intermediate cases between purported infector-infectee pairs, as well as the fraction of such pairs that are coprimary. We also extend our method to situations where each infectee has multiple possible infectors, and show how to factor this additional source of uncertainty into our estimates. We assess our method's performance on simulated data sets and find that our method provides consistent and robust estimates. We also apply our method to data from real-life outbreaks of four infectious diseases and compare our results with published results. With similar accuracy, our method of estimating serial interval distribution provides unique advantages, allowing its application in settings of low sampling rates and large population sizes, such as widespread community transmission tracked by routine public health surveillance.

Phylogenetic identification of influenza virus candidates for seasonal vaccines.

The seasonal influenza (flu) vaccine is designed to protect against those influenza viruses predicted to circulate during the upcoming flu season, but identifying which viruses are likely to circulate is challenging. We use features from phylogenetic trees reconstructed from hemagglutinin (HA) and neuraminidase (NA) sequences, together with a support vector machine, to predict future circulation. We obtain accuracies of 0.75 to 0.89 (AUC 0.83 to 0.91) over 2016-2020. We explore ways to select potential candidates for a seasonal vaccine and find that the machine learning model has a moderate ability to select strains that are close to future populations. However, consensus sequences among the most recent 3 years also do well at this task. We identify similar candidate strains to those proposed by the World Health Organization, suggesting that this approach can help inform vaccine strain selection.

Effective population size in simple infectious disease models.

Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the population likely to be exposed, for example if there are population structures, outbreak controls or other heterogeneities. Although these factors may be taken into account in the model: adding compartments to a compartmental model, variable mixing rates and so on, this makes fitting more challenging, especially if the population complexities are not fully known. In this work we consider the concept of effective population size in outbreak modelling, which we define as the size of the population involved in an outbreak, as an alternative to use of more complex models. Effective population size is an important quantity in genetics for estimation of genetic diversity loss in populations, but it has not been widely applied in epidemiology. Through simulation studies and application to data from outbreaks of COVID-19 in China, we find that simple SIR models with effective population size can provide a good fit to data which are not themselves simple or SIR.

Genomic epidemiology offers high resolution estimates of serial intervals for COVID-19.

Serial intervals - the time between symptom onset in infector and infectee - are a fundamental quantity in infectious disease control. However, their estimation requires knowledge of individuals' exposures, typically obtained through resource-intensive contact tracing efforts. We introduce an alternate framework using virus sequences to inform who infected whom and thereby estimate serial intervals. We apply our technique to SARS-CoV-2 sequences from case clusters in the first two COVID-19 waves in Victoria, Australia. We find that our approach offers high resolution, cluster-specific serial interval estimates that are comparable with those obtained from contact data, despite requiring no knowledge of who infected whom and relying on incompletely-sampled data. Compared to a published serial interval, cluster-specific serial intervals can vary estimates of the effective reproduction number by a factor of 2-3. We find that serial interval estimates in settings such as schools and meat processing/packing plants are shorter than those in healthcare facilities.

COVID-19 endgame: From pandemic to endemic? Vaccination, reopening and evolution in low- and high-vaccinated populations.

COVID-19 remains a major public health concern, with large resurgences even where there has been widespread uptake of vaccines. Waning immunity and the emergence of new variants will shape the long-term burden and dynamics of COVID-19. We explore the transition to the endemic state, and the endemic incidence in British Columbia (BC), Canada and South Africa (SA), to compare low and high vaccination coverage settings with differing public health policies, using a combination of modelling approaches. We compare reopening (relaxation of public health measures) gradually and rapidly as well as at different vaccination levels. We examine how the eventual endemic state depends on the duration of immunity, the rate of importations, the efficacy of vaccines and the transmissibility. These depend on the evolution of the virus, which continues to undergo selection. Slower reopening leads to a lower peak level of incidence and fewer overall infections in the wave following reopening: as much as a 60% lower peak and a 10% lower total in some illustrative simulations; under realistic parameters, reopening when 70% of the population is vaccinated leads to a large resurgence in cases. The long-term endemic behaviour may stabilize as late as January 2023, with further waves of high incidence occurring depending on the transmissibility of the prevalent variant, duration of immunity, and antigenic drift. We find that long term endemic levels are not necessarily lower than current pandemic levels: in a population of 100,000 with representative parameter settings (Reproduction number 5, 1-year duration of immunity, vaccine efficacy at 80% and importations at 3 cases per 100K per day) there are over 100 daily incident cases in the model. Predicted prevalence at endemicity has increased more than twofold after the emergence and spread of Omicron. The consequent burden on health care systems depends on the severity of infection in immunized or previously infected individuals.

The potential of genomics for infectious disease forecasting.

Genomic technologies have led to tremendous gains in understanding how pathogens function, evolve and interact. Pathogen diversity is now measurable at high precision and resolution, in part because over the past decade, sequencing technologies have increased in speed and capacity, at decreased cost. Alongside this, the use of models that can forecast emergence and size of infectious disease outbreaks has risen, highlighted by the coronavirus disease 2019 pandemic but also due to modelling advances that allow for rapid estimates in emerging outbreaks to inform monitoring, coordination and resource deployment. However, genomics studies have remained largely retrospective. While they contain high-resolution views of pathogen diversification and evolution in the context of selection, they are often not aligned with designing interventions. This is a missed opportunity because pathogen diversification is at the core of the most pressing infectious public health challenges, and interventions need to take the mechanisms of virulence and understanding of pathogen diversification into account. In this Perspective, we assess these converging fields, discuss current challenges facing both surveillance specialists and modellers who want to harness genomic data, and propose next steps for integrating longitudinally sampled genomic data with statistical learning and interpretable modelling to make reliable predictions into the future.

Quantifying transmissibility of SARS-CoV-2 and impact of intervention within long-term healthcare facilities.

Estimates of the basic reproduction number (R 0) for COVID-19 are particularly variable in the context of transmission within locations such as long-term healthcare (LTHC) facilities. We sought to characterize the heterogeneity of R 0 across known outbreaks within these facilities. We used a unique comprehensive dataset of all outbreaks that occurred within LTHC facilities in British Columbia, Canada as of 21 September 2020. We estimated R 0 in 18 LTHC outbreaks with a novel Bayesian hierarchical dynamic model of susceptible, exposed, infected and recovered individuals, incorporating heterogeneity of R 0 between facilities. We further compared these estimates to those obtained with standard methods that use the exponential growth rate and maximum likelihood. The total size of outbreaks varied dramatically, with range of attack rates 2%-86%. The Bayesian analysis provided an overall estimate of R 0 = 2.51 (90% credible interval 0.47-9.0), with individual facility estimates ranging between 0.56 and 9.17. Uncertainty in these estimates was more constrained than standard methods, particularly for smaller outbreaks informed by the population-level model. We further estimated that intervention led to 61% (52%-69%) of all potential cases being averted within the LTHC facilities, or 75% (68%-79%) when using a model with multi-level intervention effect. Understanding of transmission risks and impact of intervention are essential in planning during the ongoing global pandemic, particularly in high-risk environments such as LTHC facilities.

Long time frames to detect the impact of changing COVID-19 measures, Canada, March to July 2020.

BackgroundMany countries have implemented population-wide interventions to control COVID-19, with varying extent and success. Many jurisdictions have moved to relax measures, while others have intensified efforts to reduce transmission.AimWe aimed to determine the time frame between a population-level change in COVID-19 measures and its impact on the number of cases.MethodsWe examined how long it takes for there to be a substantial difference between the number of cases that occur following a change in COVID-19 physical distancing measures and those that would have occurred at baseline. We then examined how long it takes to observe this difference, given delays and noise in reported cases. We used a susceptible-exposed-infectious-removed (SEIR)-type model and publicly available data from British Columbia, Canada, collected between March and July 2020.ResultsIt takes 10 days or more before we expect a substantial difference in the number of cases following a change in COVID-19 control measures, but 20-26 days to detect the impact of the change in reported data. The time frames are longer for smaller changes in control measures and are impacted by testing and reporting processes, with delays reaching ≥ 30 days.ConclusionThe time until a change in control measures has an observed impact is longer than the mean incubation period of COVID-19 and the commonly used 14-day time period. Policymakers and practitioners should consider this when assessing the impact of policy changes. Rapid, consistent and real-time COVID-19 surveillance is important to minimise these time frames.

How much leeway is there to relax COVID-19 control measures?

Following successful non-pharmaceutical interventions (NPI) aiming to control COVID-19, many jurisdictions reopened their economies and borders. As little immunity had developed in most populations, re-establishing higher contact carried substantial risks, and therefore many locations began to see resurgence in COVID-19 cases. We present a Bayesian method to estimate the leeway to reopen, or alternatively the strength of change required to re-establish COVID-19 control, in a range of jurisdictions experiencing different COVID-19 epidemics. We estimated the timing and strength of initial control measures such as widespread distancing and compared the leeway jurisdictions had to reopen immediately after NPI measures to later estimates of leeway. Finally, we quantified risks associated with reopening and the likely burden of new cases due to introductions from other jurisdictions. We found widely varying leeway to reopen. After initial NPI measures took effect, some jurisdictions had substantial leeway (e.g., Japan, New Zealand, Germany) with > 0.99 probability that contact rates were below 80% of the threshold for epidemic growth. Others had little leeway (e.g., the United Kingdom, Washington State) and some had none (e.g., Sweden, California). For most such regions, increases in contact rate of 1.5-2 fold would have had high (> 0.7) probability of exceeding past peak sizes. Most jurisdictions experienced June-August trajectories consistent with our projections of contact rate increases of 1-2-fold. Under such relaxation scenarios for some regions, we projected up to ∼100 additional cases if just one case were imported per week over six weeks, even between jurisdictions with comparable COVID-19 risk. We provide an R package covidseir to enable jurisdictions to estimate leeway and forecast cases under different future contact patterns. Estimates of leeway can establish a quantitative basis for decisions about reopening. We recommend a cautious approach to reopening economies and borders, coupled with strong monitoring for changes in transmission.

Pair-based likelihood approximations for stochastic epidemic models.

Fitting stochastic epidemic models to data is a non-standard problem because data on the infection processes defined in such models are rarely observed directly. This in turn means that the likelihood of the observed data is intractable in the sense that it is very computationally expensive to obtain. Although data-augmented Markov chain Monte Carlo (MCMC) methods provide a solution to this problem, employing a tractable augmented likelihood, such methods typically deteriorate in large populations due to poor mixing and increased computation time. Here, we describe a new approach that seeks to approximate the likelihood by exploiting the underlying structure of the epidemic model. Simulation study results show that this approach can be a serious competitor to data-augmented MCMC methods. Our approach can be applied to a wide variety of disease transmission models, and we provide examples with applications to the common cold, Ebola, and foot-and-mouth disease.

Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing.

Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide. It is therefore urgent to estimate the impact such measures are having. We introduce a Bayesian epidemiological model in which a proportion of individuals are willing and able to participate in distancing, with the timing of distancing measures informed by survey data on attitudes to distancing and COVID-19. We fit our model to reported COVID-19 cases in British Columbia (BC), Canada, and five other jurisdictions, using an observation model that accounts for both underestimation and the delay between symptom onset and reporting. We estimated the impact that physical distancing (social distancing) has had on the contact rate and examined the projected impact of relaxing distancing measures. We found that, as of April 11 2020, distancing had a strong impact in BC, consistent with declines in reported cases and in hospitalization and intensive care unit numbers; individuals practising physical distancing experienced approximately 0.22 (0.11-0.34 90% CI [credible interval]) of their normal contact rate. The threshold above which prevalence was expected to grow was 0.55. We define the "contact ratio" to be the ratio of the estimated contact rate to the threshold rate at which cases are expected to grow; we estimated this contact ratio to be 0.40 (0.19-0.60) in BC. We developed an R package 'covidseir' to make our model available, and used it to quantify the impact of distancing in five additional jurisdictions. As of May 7, 2020, we estimated that New Zealand was well below its threshold value (contact ratio of 0.22 [0.11-0.34]), New York (0.60 [0.43-0.74]), Washington (0.84 [0.79-0.90]) and Florida (0.86 [0.76-0.96]) were progressively closer to theirs yet still below, but California (1.15 [1.07-1.23]) was above its threshold overall, with cases still rising. Accordingly, we found that BC, New Zealand, and New York may have had more room to relax distancing measures than the other jurisdictions, though this would need to be done cautiously and with total case volumes in mind. Our projections indicate that intermittent distancing measures-if sufficiently strong and robustly followed-could control COVID-19 transmission. This approach provides a useful tool for jurisdictions to monitor and assess current levels of distancing relative to their threshold, which will continue to be essential through subsequent waves of this pandemic.

Transmission analysis of a large tuberculosis outbreak in London: a mathematical modelling study using genomic data.

Outbreaks of tuberculosis (TB) - such as the large isoniazid-resistant outbreak centred on London, UK, which originated in 1995 - provide excellent opportunities to model transmission of this devastating disease. Transmission chains for TB are notoriously difficult to ascertain, but mathematical modelling approaches, combined with whole-genome sequencing data, have strong potential to contribute to transmission analyses. Using such data, we aimed to reconstruct transmission histories for the outbreak using a Bayesian approach, and to use machine-learning techniques with patient-level data to identify the key covariates associated with transmission. By using our transmission reconstruction method that accounts for phylogenetic uncertainty, we are able to identify 21 transmission events with reasonable confidence, 9 of which have zero SNP distance, and a maximum distance of 3. Patient age, alcohol abuse and history of homelessness were found to be the most important predictors of being credible TB transmitters.

Evidence for transmission of COVID-19 prior to symptom onset.

We collated contact tracing data from COVID-19 clusters in Singapore and Tianjin, China and estimated the extent of pre-symptomatic transmission by estimating incubation periods and serial intervals. The mean incubation periods accounting for intermediate cases were 4.91 days (95%CI 4.35, 5.69) and 7.54 (95%CI 6.76, 8.56) days for Singapore and Tianjin, respectively. The mean serial interval was 4.17 (95%CI 2.44, 5.89) and 4.31 (95%CI 2.91, 5.72) days (Singapore, Tianjin). The serial intervals are shorter than incubation periods, suggesting that pre-symptomatic transmission may occur in a large proportion of transmission events (0.4-0.5 in Singapore and 0.6-0.8 in Tianjin, in our analysis with intermediate cases, and more without intermediates). Given the evidence for pre-symptomatic transmission, it is vital that even individuals who appear healthy abide by public health measures to control COVID-19.

The first cases of COVID-19 were identified in Wuhan, a city in Central China, in December 2019. The virus quickly spread within the country and then across the globe. By the third week in January, the first cases were confirmed in Tianjin, a city in Northern China, and in Singapore, a city country in Southeast Asia. By late February, Tianjin had 135 cases and Singapore had 93 cases. In both cities, public health officials immediately began identifying and quarantining the contacts of infected people. The information collected in Tianjin and Singapore about COVID-19 is very useful for scientists. It makes it possible to determine the disease's incubation period, which is how long it takes to develop symptoms after virus exposure. It can also show how many days pass between an infected person developing symptoms and a person they infect developing symptoms. This period is called the serial interval. Scientists use this information to determine whether individuals infect others before showing symptoms themselves and how often this occurs. Using data from Tianjin and Singapore, Tindale, Stockdale et al. now estimate the incubation period for COVID-19 is between five and eight days and the serial interval is about four days. About 40% to 80% of the novel coronavirus transmission occurs two to four days before an infected person has symptoms. This transmission from apparently healthy individuals means that staying home when symptomatic is not enough to control the spread of COVID-19. Instead, broad-scale social distancing measures are necessary. Understanding how COVID-19 spreads can help public health officials determine how to best contain the virus and stop the outbreak. The new data suggest that public health measures aimed at preventing asymptomatic transmission are essential. This means that even people who appear healthy need to comply with preventive measures like mask use and social distancing.

Modelling and Bayesian analysis of the Abakaliki smallpox data.

The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. The only previous analysis of the full data set relied on approximation methods to derive a likelihood and did not assess model adequacy. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian statistical analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations and which yield a wider range of results than previous analyses. We also carry out model assessment using simulation-based methods. Our findings suggest that the outbreak was largely driven by the interaction structure of the population, and that the introduction of control measures was not the sole reason for the end of the epidemic. We also obtain quantitative estimates of key quantities including reproduction numbers.