Are epidemic growth rates more informative than reproduction numbers?

Genomic epidemiology reveals 2022 mpox epidemic in New York City governed by heavy-tailed sexual contact networks

The global mpox epidemic in 2022 was likely caused by transmission of mpox virus (MPXV) through sexual contact networks, with New York City (NYC) experiencing the first and largest outbreak in the United States. By performing a phylogeographic and epidemiological analysis of MPXV, we identify at least 200 introductions of MPXV into NYC and 84 leading to onward transmission. Through a comparative analysis with human immunodeficiency virus (HIV) in NYC, we find that both MPXV and HIV genomic cluster sizes are best fit by scale-free distributions and that people in MPXV clusters are more likely to have previously received an HIV diagnosis (odds ratio=1.58; p=0.012) and be a member of a recently growing HIV transmission cluster, indicating overlapping sexual contact networks. We then model the transmission of MPXV through sexual contact networks and show that highly connected individuals would be disproportionately infected at the start of an epidemic, thereby likely resulting in the exhaustion of the most densely connected parts of the sexual network. This dynamic explains the rapid expansion and decline of the NYC outbreak, as well as the estimated cumulative incidence of less than 2% within high-risk populations. By synthesizing the genomic epidemiology of MPXV and HIV with epidemic modeling, we demonstrate that MPXV transmission dynamics can be understood by general principles of sexually transmitted pathogens.

Global patterns of rebound to normal RSV dynamics following COVID-19 suppression

BACKGROUND

Annual epidemics of respiratory syncytial virus (RSV) had consistent timing and intensity between seasons prior to the SARS-CoV-2 pandemic (COVID-19). However, starting in April 2020, RSV seasonal activity declined due to COVID-19 non-pharmaceutical interventions (NPIs) before re-emerging after relaxation of NPIs. We described the unusual patterns of RSV epidemics that occurred in multiple subsequent waves following COVID-19 in different countries and explored factors associated with these patterns.

METHODS

Weekly cases of RSV from twenty-eight countries were obtained from the World Health Organisation and combined with data on country-level characteristics and the stringency of the COVID-19 response. Dynamic time warping and regression were used to cluster time series patterns and describe epidemic characteristics before and after COVID-19 pandemic, and identify related factors.

RESULTS

While the first wave of RSV epidemics following pandemic suppression exhibited unusual patterns, the second and third waves more closely resembled typical RSV patterns in many countries. Post-pandemic RSV patterns differed in their intensity and/or timing, with several broad patterns across the countries. The onset and peak timings of the first and second waves of RSV epidemics following COVID-19 suppression were earlier in the Southern than Northern Hemisphere. The second wave of RSV epidemics was also earlier with higher population density, and delayed if the intensity of the first wave was higher. More stringent NPIs were associated with lower RSV growth rate and intensity and a shorter gap between the first and second waves.

CONCLUSION

Patterns of RSV activity have largely returned to normal following successive waves in the post-pandemic era. Onset and peak timings of future epidemics following disruption of normal RSV dynamics need close monitoring to inform the delivery of preventive and control measures.

Differences between the true reproduction number and the apparent reproduction number of an epidemic time series

The time-varying reproduction number R(t) measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating R(t) from an epidemic time series, is that R(t) has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, RA(t), the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between RA(t) and R(t) depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of R(t), and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics.

The basic reproduction number (R0) of ebola virus disease: A systematic review and meta-analysis

BACKGROUND

Ebola virus disease (Ebola) is highly pathogenic, transmissible, and often deadly, with debilitating consequences. Superspreading within a cluster is also possible. In this study, we aim to document Ebola basic reproduction number (R0): the average number of new cases associated with an Ebola case in a completely susceptible population.

METHODS

We undertook a systematic review and meta-analysis. We searched PubMed, EMBASE, and Web of Science for studies published between 1976 and February 27, 2023. We also manually searched the reference lists of the reviewed studies to identify additional studies. We included studies that reported R0 during Ebola outbreaks in Africa. We excluded studies that reported only the effective reproduction number (Rt). Abstracting data from included studies was performed using a pilot-tested standard form. Two investigators reviewed the studies, extracted the data, and assessed quality. The pooled R0 was determined by a random-effects meta-analysis. R0 was stratified by country. We also estimated the theoretically required immunization coverage to reach herd-immunity using the formula of (1-1/R0) × 100 %.

RESULTS

The search yielded 2042 studies. We included 53 studies from six African countries in the systematic review providing 97 Ebola mean R0 estimates. 27 (with 46 data points) studies were included in the meta-analysis. The overall pooled mean Ebola R0 was 1.95 (95 % CI 1.74-2.15), with high heterogeneity (I2 = 99.99 %; τ2 = 0.38; and p < 0.001) and evidence of small-study effects (Egger's statistics: Z = 4.67; p < 0.001). Mean Ebola R0 values ranged from 1.2 to 10.0 in Nigeria, 1.1 to 7 in Guinea, 1.14 to 8.33 in Sierra Leone, 1.13 to 5 in Liberia, 1.2 to 5.2 in DR Congo, 1.34 to 2.7 in Uganda, and from 1.40 to 2.55 for all West African countries combined. Pooled mean Ebola R0 was 9.38 (95 % CI 4.16-14.59) in Nigeria, 3.31 (95 % CI 2.30-4.32) in DR Congo, 2.0 (95 % CI 1.25-2.76) in Uganda, 1.83 (95 % CI 1.61-2.05) in Liberia, 1.73 (95 % CI 1.47-2.0) in Sierra Leonne, and 1.44 (95 % CI 1.29-1.60) in Guinea. In theory, 50 % of the population needs to be vaccinated to achieve herd immunity, assuming that Ebola vaccine would be 100 % effective.

CONCLUSIONS

Ebola R0 varies widely across countries. Ebola has a much wider R0 range than is often claimed (1.3-2.0). It is possible for an Ebola index case to infect more than two susceptible individuals.

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.

Instantaneous reproduction number and epidemic growth rate for predicting COVID-19 waves: the first 2 years of the pandemic in Spain

Introduction

Several indicators were employed to manage the COVID-19 pandemic. In this study, our objective was to compare the instantaneous reproductive number and the epidemic growth rate in the Spanish population.

Methods

Data on daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained. The four "pandemic state indicators", which are daily numbers of cases, admissions into hospitals, admissions into ICUs, and deaths due to COVID-19 in Spain from March 2020 to March 2022 were obtained from the Instituto de Salud Carlos III. The epidemic growth rate was estimated as the derivative of the natural logarithm of daily cases with respect to time. Both the reproductive number and the growth rate, as "pandemic trend indicators," were evaluated according to their capacity to anticipate waves as "pandemic state indicators."

Results

Using both the reproductive number and the epidemic growth rate, we were able to anticipate most COVID-19 waves. In most waves, the more severe the presentation of COVID-19, the more effective the pandemic trend indicators would be.

Conclusion

Besides daily number of cases or other measures of disease frequency, the epidemic growth rate and the reproductive number have different roles in measuring the trend of an epidemic. Naïve interpretations and the use of any indicator as a unique value to make decisions should be discouraged.

Heterogeneity is a key factor describing the initial outbreak of COVID-19

Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous.

Effectiveness assessment of non-pharmaceutical interventions: lessons learned from the COVID-19 pandemic

Effectiveness of non-pharmaceutical interventions (NPIs), such as school closures and stay-at-home orders, during the COVID-19 pandemic has been assessed in many studies. Such assessments can inform public health policies and contribute to evidence-based choices of NPIs during subsequent waves or future epidemics. However, methodological issues and no standardised assessment practices have restricted the practical value of the existing evidence. Here, we present and discuss lessons learned from the COVID-19 pandemic and make recommendations for standardising and improving assessment, data collection, and modelling. These recommendations could contribute to reliable and policy-relevant assessments of the effectiveness of NPIs during future epidemics.

Impact of spatiotemporal heterogeneity in COVID-19 disease surveillance on epidemiological parameters and case growth rates

SARS-CoV-2 case data are primary sources for estimating epidemiological parameters and for modelling the dynamics of outbreaks. Understanding biases within case-based data sources used in epidemiological analyses is important as they can detract from the value of these rich datasets. This raises questions of how variations in surveillance can affect the estimation of epidemiological parameters such as the case growth rates. We use standardised line list data of COVID-19 from Argentina, Brazil, Mexico and Colombia to estimate delay distributions of symptom-onset-to-confirmation, -hospitalisation and -death as well as hospitalisation-to-death at high spatial resolutions and throughout time. Using these estimates, we model the biases introduced by the delay from symptom-onset-to-confirmation on national and state level case growth rates (rt) using an adaptation of the Richardson-Lucy deconvolution algorithm. We find significant heterogeneities in the estimation of delay distributions through time and space with delay difference of up to 19 days between epochs at the state level. Further, we find that by changing the spatial scale, estimates of case growth rate can vary by up to 0.13 d^-1. Lastly, we find that states with a high variance and/or mean delay in symptom-onset-to-diagnosis also have the largest difference between the rt estimated from raw and deconvolved case counts at the state level. We highlight the importance of high-resolution case-based data in understanding biases in disease reporting and how these biases can be avoided by adjusting case numbers based on empirical delay distributions. Code and openly accessible data to reproduce analyses presented here are available.

Responses to COVID-19 with probabilistic programming

The COVID-19 pandemic left its unique mark on the twenty-first century as one of the most significant disasters in history, triggering governments all over the world to respond with a wide range of interventions. However, these restrictions come with a substantial price tag. It is crucial for governments to form anti-virus strategies that balance the trade-off between protecting public health and minimizing the economic cost. This work proposes a probabilistic programming method to quantify the efficiency of major initial non-pharmaceutical interventions. We present a generative simulation model that accounts for the economic and human capital cost of adopting such strategies, and provide an end-to-end pipeline to simulate the virus spread and the incurred loss of various policy combinations. By investigating the national response in 10 countries covering four continents, we found that social distancing coupled with contact tracing is the most successful policy, reducing the virus transmission rate by 96% along with a 98% reduction in economic and human capital loss. Together with experimental results, we open-sourced a framework to test the efficacy of each policy combination.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges

The reproduction numberR has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations ofR , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulatingR becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Using multiple sampling strategies to estimate SARS-CoV-2 epidemiological parameters from genomic sequencing data

The choice of viral sequences used in genetic and epidemiological analysis is important as it can induce biases that detract from the value of these rich datasets. This raises questions about how a set of sequences should be chosen for analysis. We provide insights on these largely understudied problems using SARS-CoV-2 genomic sequences from Hong Kong, China, and the Amazonas State, Brazil. We consider multiple sampling schemes which were used to estimate Rt and rt as well as related R0 and date of origin parameters. We find that both Rt and rt are sensitive to changes in sampling whilst R0 and the date of origin are relatively robust. Moreover, we find that analysis using unsampled datasets result in the most biased Rt and rt estimates for both our Hong Kong and Amazonas case studies. We highlight that sampling strategy choices may be an influential yet neglected component of sequencing analysis pipelines.

On the use of the reproduction number for SARS-CoV-2: Estimation, misinterpretations and relationships with other ecological measures

The basic reproduction number, R 0, and its real-time analogue, Rt , are summary measures that reflect the ability of an infectious disease to spread through a population. Estimation methods for Rt  have a long history, have been widely developed and are now enhanced by application to the COVID-19 pandemic. While retrospective analyses of Rt have provided insight into epidemic dynamics and the effects of control strategies in prior outbreaks, misconceptions around the interpretation of Rt have arisen with broader recognition and near real-time monitoring of this parameter alongside reported case data during the COVID-19 pandemic. Here, we discuss some widespread misunderstandings regarding the use of Rt  as a barometer for population risk and its related use as an 'on/off' switch for policy decisions regarding relaxation of non-pharmaceutical interventions. Computation of Rt  from downstream data (e.g. hospitalizations) when infection counts are unreliable exacerbates lags between when transmission happens and when events are recorded. We also discuss analyses that have shown various relationships between Rt  and measures of mobility, vaccination coverage and a test-trace-isolation intervention in different settings.