Fundamental limits on inferring epidemic resurgence in real time using effective reproduction numbers

Evaluating a Public Health Assessment and Response Framework: SARS-CoV-2 Spread Under the Controlled Distancing Model of Rio Grande do Sul, Brazil

In early 2020, to halt the spread of SARS-CoV-2, the state government of Rio Grande do Sul in Brazil established a public health assessment and response framework known as a "controlled distancing model." Using this framework, the government divided the state into 21 regions and evaluated them against a composite index of disease transmission and health service capacity. Regions were assessed using a color-coded scale of flags that was updated on a weekly basis and used to guide the adoption of nonpharmaceutical interventions. In this study, we aimed to evaluate the extent to which the controlled distancing model accurately assessed transmission and the effectiveness of its responses throughout 2020. We estimated the weekly effective reproduction number (Rt) of SARS-CoV-2 for each region using a renewal equation-based statistical model of notified COVID-19 deaths. Using Rt estimates, we explored whether flag colors assigned by the controlled distancing model either reflected or affected SARS-CoV-2 transmission. Results showed that flag assignments did reflect variations in Rt to a limited extent, but we found no evidence that they affected Rt in the short term. Medium-term effects were apparent in only 4 regions after 8 or more weeks of red flag assignment. Analysis of Google movement metrics showed no evidence that people moved differently under different flags. The dissociation between flag colors and the propagation of SARS-CoV-2 does not call into question the effectiveness of nonpharmaceutical interventions. Our results show, however, that decisions made under the controlled distancing model framework were ineffective both at influencing the movement of people and halting the spread of the virus.

Angular reproduction numbers improve estimates of transmissibility when disease generation times are misspecified or time-varying

We introduce the angular reproduction number Ω, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number R, and generation time distribution w. Predominant approaches for tracking pathogen spread infer either R or the epidemic growth rate r. However, R is biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. R and r may also disagree on the relative transmissibility of epidemics or variants (i.e. rA > rB does not imply RA > RB for variants A and B). We find that Ω responds meaningfully to mismatches and time-variations in w while mostly maintaining the interpretability of R. We prove that Ω > 1 implies R > 1 and that Ω agrees with r on the relative transmissibility of pathogens. Estimating Ω is no more difficult than inferring R, uses existing software, and requires no generation time measurements. These advantages come at the expense of selecting one free parameter. We propose Ω as complementary statistic to R and r that improves transmissibility estimates when w is misspecified or time-varying and better reflects the impact of interventions, when those interventions concurrently change R and w or alter the relative risk of co-circulating pathogens.

Risk averse reproduction numbers improve resurgence detection

The effective reproduction number R is a prominent statistic for inferring the transmissibility of infectious diseases and effectiveness of interventions. R purportedly provides an easy-to-interpret threshold for deducing whether an epidemic will grow (R>1) or decline (R<1). We posit that this interpretation can be misleading and statistically overconfident when applied to infections accumulated from groups featuring heterogeneous dynamics. These groups may be delineated by geography, infectiousness or sociodemographic factors. In these settings, R implicitly weights the dynamics of the groups by their number of circulating infections. We find that this weighting can cause delayed detection of outbreak resurgence and premature signalling of epidemic control because it underrepresents the risks from highly transmissible groups. Applying E-optimal experimental design theory, we develop a weighting algorithm to minimise these issues, yielding the risk averse reproduction number E. Using simulations, analytic approaches and real-world COVID-19 data stratified at the city and district level, we show that E meaningfully summarises transmission dynamics across groups, balancing bias from the averaging underlying R with variance from directly using local group estimates. An E>1generates timely resurgence signals (upweighting risky groups), while an E<1ensures local outbreaks are under control. We propose E as an alternative to R for informing policy and assessing transmissibility at large scales (e.g., state-wide or nationally), where R is commonly computed but well-mixed or homogeneity assumptions break down.

A Bayesian nonparametric method for detecting rapid changes in disease transmission

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, R_t. Real-time or retrospective identification of changes in R_t following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in R_t within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume that R_t is piecewise-constant, and the incidence data and priors determine when or whether R_t should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in R_t and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the R_t profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Using digital traces to build prospective and real-time county-level early warning systems to anticipate COVID-19 outbreaks in the United States

Coronavirus disease 2019 (COVID-19) continues to affect the world, and the design of strategies to curb disease outbreaks requires close monitoring of their trajectories. We present machine learning methods that leverage internet-based digital traces to anticipate sharp increases in COVID-19 activity in U.S. counties. In a complementary direction to the efforts led by the Centers for Disease Control and Prevention (CDC), our models are designed to detect the time when an uptrend in COVID-19 activity will occur. Motivated by the need for finer spatial resolution epidemiological insights, we build upon previous efforts conceived at the state level. Our methods-tested in an out-of-sample manner, as events were unfolding, in 97 counties representative of multiple population sizes across the United States-frequently anticipated increases in COVID-19 activity 1 to 6 weeks before local outbreaks, defined when the effective reproduction number Rt becomes larger than 1 for a period of 2 weeks.

Quantifying the information in noisy epidemic curves

Reliably estimating the dynamics of transmissible diseases from noisy surveillance data is an enduring problem in modern epidemiology. Key parameters are often inferred from incident time series, with the aim of informing policy-makers on the growth rate of outbreaks or testing hypotheses about the effectiveness of public health interventions. However, the reliability of these inferences depends critically on reporting errors and latencies innate to the time series. Here, we develop an analytical framework to quantify the uncertainty induced by under-reporting and delays in reporting infections, as well as a metric for ranking surveillance data informativeness. We apply this metric to two primary data sources for inferring the instantaneous reproduction number: epidemic case and death curves. We find that the assumption of death curves as more reliable, commonly made for acute infectious diseases such as COVID-19 and influenza, is not obvious and possibly untrue in many settings. Our framework clarifies and quantifies how actionable information about pathogen transmissibility is lost due to surveillance limitations.

Anticipating infectious disease re-emergence and elimination: a test of early warning signals using empirically based models

Timely forecasts of the emergence, re-emergence and elimination of human infectious diseases allow for proactive, rather than reactive, decisions that save lives. Recent theory suggests that a generic feature of dynamical systems approaching a tipping point-early warning signals (EWS) due to critical slowing down (CSD)-can anticipate disease emergence and elimination. Empirical studies documenting CSD in observed disease dynamics are scarce, but such demonstration of concept is essential to the further development of model-independent outbreak detection systems. Here, we use fitted, mechanistic models of measles transmission in four cities in Niger to detect CSD through statistical EWS. We find that several EWS accurately anticipate measles re-emergence and elimination, suggesting that CSD should be detectable before disease transmission systems cross key tipping points. These findings support the idea that statistical signals based on CSD, coupled with decision-support algorithms and expert judgement, could provide the basis for early warning systems of disease outbreaks.