The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants.

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

Testing and Isolation Efficacy: Insights from a Simple Epidemic Model.

Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The effect of testing processes on epidemic dynamics depends on factors underlying implementation, particularly testing intensity and on whom testing is focused. Here, we use a simple model to explore how the individual-level effects of testing might directly impact population-level spread. Our model development was motivated by the COVID-19 epidemic, but has generic epidemiological and testing structures. To the classic SIR framework we have added a per capita testing intensity, and compartment-specific testing weights, which can be adjusted to reflect different testing emphases-surveillance, diagnosis, or control. We derive an analytic expression for the relative reduction in the basic reproductive number due to testing, test-reporting and related isolation behaviours. Intensive testing and fast test reporting are expected to be beneficial at the community level because they can provide a rapid assessment of the situation, identify hot spots, and may enable rapid contact-tracing. Direct effects of fast testing at the individual level are less clear, and may depend on how individuals' behaviour is affected by testing information. Our simple model shows that under some circumstances both increased testing intensity and faster test reporting can reduce the effectiveness of control, and allows us to explore the conditions under which this occurs. Conversely, we find that focusing testing on infected individuals always acts to increase effectiveness of control.

Age-dependence of healthcare interventions for COVID-19 in Ontario, Canada.

BACKGROUND: Patient age is one of the most salient clinical indicators of risk from COVID-19. Age-specific distributions of known SARS-CoV-2 infections and COVID-19-related deaths are available for many regions. Less attention has been given to the age distributions of serious medical interventions administered to COVID-19 patients, which could reveal sources of potential pressure on the healthcare system should SARS-CoV-2 prevalence increase, and could inform mass vaccination strategies. The aim of this study is to quantify the relationship between COVID-19 patient age and serious outcomes of the disease, beyond fatalities alone. METHODS: We analysed 277,555 known SARS-CoV-2 infection records for Ontario, Canada, from 23 January 2020 to 16 February 2021 and estimated the age distributions of hospitalizations, Intensive Care Unit admissions, intubations, and ventilations. We quantified the probability of hospitalization given known SARS-CoV-2 infection, and of survival given COVID-19-related hospitalization. RESULTS: The distribution of hospitalizations peaks with a wide plateau covering ages 60-90, whereas deaths are concentrated in ages 80+. The estimated probability of hospitalization given known infection reaches a maximum of 27.8% at age 80 (95% CI 26.0%-29.7%). The probability of survival given hospitalization is nearly 100% for adults younger than 40, but declines substantially after this age; for example, a hospitalized 54-year-old patient has a 91.7% chance of surviving COVID-19 (95% CI 88.3%-94.4%). CONCLUSIONS: Our study demonstrates a significant need for hospitalization in middle-aged individuals and young seniors. This need is not captured by the distribution of deaths, which is heavily concentrated in very old ages. The probability of survival given hospitalization for COVID-19 is lower than is generally perceived for patients over 40. If acute care capacity is exceeded due to an increase in COVID-19 prevalence, the distribution of deaths could expand toward younger ages. These results suggest that vaccine programs should aim to prevent infection not only in old seniors, but also in young seniors and middle-aged individuals, to protect them from serious illness and to limit stress on the healthcare system.

Forward-looking serial intervals correctly link epidemic growth to reproduction numbers.

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

Acceleration of plague outbreaks in the second pandemic.

Historical records reveal the temporal patterns of a sequence of plague epidemics in London, United Kingdom, from the 14th to 17th centuries. Analysis of these records shows that later epidemics spread significantly faster ("accelerated"). Between the Black Death of 1348 and the later epidemics that culminated with the Great Plague of 1665, we estimate that the epidemic growth rate increased fourfold. Currently available data do not provide enough information to infer the mode of plague transmission in any given epidemic; nevertheless, order-of-magnitude estimates of epidemic parameters suggest that the observed slow growth rates in the 14th century are inconsistent with direct (pneumonic) transmission. We discuss the potential roles of demographic and ecological factors, such as climate change or human or rat population density, in driving the observed acceleration.

Reconciling early-outbreak estimates of the basic reproductive number and its uncertainty: framework and applications to the novel coronavirus (SARS-CoV-2) outbreak.

A novel coronavirus (SARS-CoV-2) emerged as a global threat in December 2019. As the epidemic progresses, disease modellers continue to focus on estimating the basic reproductive number [Formula: see text]-the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modelling approaches and resulting estimates of [Formula: see text] during the beginning of the outbreak vary widely, despite relying on similar data sources. Here, we present a statistical framework for comparing and combining different estimates of [Formula: see text] across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate, the mean generation interval and the generation-interval dispersion. We apply our framework to early estimates of [Formula: see text] for the SARS-CoV-2 outbreak, showing that many [Formula: see text] estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of [Formula: see text], including the shape of the generation-interval distribution, in efforts to estimate [Formula: see text] at the outset of an epidemic.