Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

ern: An [Formula: see text] package to estimate the effective reproduction number using clinical and wastewater surveillance data

The effective reproduction number, [Formula: see text], is an important epidemiological metric used to assess the state of an epidemic, as well as the effectiveness of public health interventions undertaken in response. When [Formula: see text] is above one, it indicates that new infections are increasing, and thus the epidemic is growing, while an [Formula: see text] is below one indicates that new infections are decreasing, and so the epidemic is under control. There are several established software packages that are readily available to statistically estimate [Formula: see text] using clinical surveillance data. However, there are comparatively few accessible tools for estimating [Formula: see text] from pathogen wastewater concentration, a surveillance data stream that cemented its utility during the COVID-19 pandemic. We present the [Formula: see text] package ern that aims to perform the estimation of the effective reproduction number from real-world wastewater or aggregated clinical surveillance data in a user-friendly way.

Unravelling the effect of New Year's Eve celebrations on SARS-CoV-2 transmission

Public holidays have been associated with SARS-CoV-2 incidence surges, although a firm link remains to be established. This association is sometimes attributed to events where transmissions occur at a disproportionately high rate, known as superspreading events. Here, we describe a sudden surge in new cases with the Omicron BA.1 strain amongst higher education students in Belgium. Contact tracers classed most of these cases as likely or possibly infected on New Year's Eve, indicating a direct trigger by New Year celebrations. Using a combination of contact tracing and phylogenetic data, we show the limited role of superspreading events in this surge. Finally, the numerous simultaneous transmissions allowed a unique opportunity to determine the distribution of incubation periods of the Omicron strain. Overall, our results indicate that, even under social restrictions, a surge in transmissibility of SARS-CoV-2 can occur when holiday celebrations result in small social gatherings attended simultaneously and communitywide.

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Increased population susceptibility to seasonal influenza during the COVID-19 pandemic in China and the United States

To the best of our knowledge, no previous study has quantitatively estimated the dynamics and cumulative susceptibility to influenza infections after the widespread lifting of COVID-19 public health measures. We constructed an imitated stochastic susceptible-infected-removed model using particle-filtered Markov Chain Monte Carlo sampling to estimate the time-dependent reproduction number of influenza based on influenza surveillance data in southern China, northern China, and the United States during the 2022-2023 season. We compared these estimates to those from 2011 to 2019 seasons without strong social distancing interventions to determine cumulative susceptibility during COVID-19 restrictions. Compared to the 2011-2019 seasons without a strong intervention with social measures, the 2022-2023 influenza season length was 45.0%, 47.1%, and 57.1% shorter in southern China, northern China, and the United States, respectively, corresponding to an 140.1%, 74.8%, and 50.9% increase in scale of influenza infections, and a 60.3%, 72.9%, and 45.1% increase in population susceptibility to influenza. Large and high-intensity influenza epidemics occurred in China and the United States in 2022-2023. Population susceptibility increased in 2019-2022, especially in China. We recommend promoting influenza vaccination, taking personal prevention actions on at-risk populations, and monitoring changes in the dynamic levels of influenza and other respiratory infections to prevent potential outbreaks in the coming influenza season.

Using spectral characterization to identify healthcare-associated infection (HAI) patients for clinical contact precaution

Healthcare-associated infections (HAIs) are a major problem in hospital infection control. Although HAIs can be suppressed using contact precautions, such precautions are expensive, and we can only apply them to a small fraction of patients (i.e., a limited budget). In this work, we focus on two clinical problems arising from the limited budget: (a) choosing the best patients to be placed under precaution given a limited budget to minimize the spread (the isolation problem), and (b) choosing the best patients to release when limited budget requires some of the patients to be cleared from precaution (the clearance problem). A critical challenge in addressing them is that HAIs have multiple transmission pathways such that locations can also accumulate 'load' and spread the disease. One of the most common practices when placing patients under contact precautions is the regular clearance of pathogen loads. However, standard propagation models like independent cascade (IC)/susceptible-infectious-susceptible (SIS) cannot capture such mechanisms directly. Hence to account for this challenge, using non-linear system theory, we develop a novel spectral characterization of a recently proposed pathogen load based model, 2-MODE-SIS model, on people/location networks to capture spread dynamics of HAIs. We formulate the two clinical problems using this spectral characterization and develop effective and efficient algorithms for them. Our experiments show that our methods outperform several natural structural and clinical approaches on real-world hospital testbeds and pick meaningful solutions.

Improved time-varying reproduction numbers using the generation interval for COVID-19

Estimating key epidemiological parameters, such as incubation period, serial interval (SI), generation interval (GI) and latent period, is essential to quantify the transmissibility and effects of various interventions of COVID-19. These key parameters play a critical role in quantifying the basic reproduction number. With the hard work of epidemiological investigators in South Korea, estimating these key parameters has become possible based on infector-infectee surveillance data of COVID-19 between February 2020 and April 2021. Herein, the mean incubation period was estimated to be 4.9 days (95% CI: 4.2, 5.7) and the mean generation interval was estimated to be 4.3 days (95% CI: 4.2, 4.4). The mean serial interval was estimated to be 4.3, with a standard deviation of 4.2. It is also revealed that the proportion of presymptomatic transmission was ~57%, which indicates the potential risk of transmission before the disease onset. We compared the time-varying reproduction number based on GI and SI and found that the time-varying reproduction number based on GI may result in a larger estimation of Rt, which refers to the COVID-19 transmission potential around the rapid increase of cases. This highlights the importance of considering presymptomatic transmission and generation intervals when estimating the time-varying reproduction number.

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible-Infectious-Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months. The results demonstrate the applicability of the method in simulating the dynamics of the epidemic and reveal an interesting relationship between the number of currently infectious individuals and the effective reproduction number, which is a useful tool for predicting the epidemic dynamics. For all conducted experiments, the results show that the local maximum (and minimum) values of the time-dependent effective reproduction number occur approximately three weeks before the local maximum (and minimum) values of the number of currently infectious individuals. This work provides a novel and efficient approach for the identification of time-dependent epidemics parameters.

Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic

BACKGROUND

The age of infection plays an important role in assessing an individual's daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article's main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model.

RESULTS

We present some results of the parameters' identification of the model when all the eigenvalues are known. This method was applied to Japan's third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month.

CONCLUSION

We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.

Is the virus-laden standing water change the transmission intensity of SARS-CoV-2 after precipitation? A framework for empirical studies

Understanding the relationship between precipitation and SARS-CoV-2 is significant for combating COVID-19 in the wet season. However, the causes for the variation of SARS-CoV-2 transmission intensity after precipitation is unclear. Starting from "the Zhengzhou event," we found that the virus-laden standing water formed after precipitation might trigger some additional routes for SARS-CoV-2 transmission and thus change the transmission intensity of SARS-CoV-2. Then, we developed an interdisciplinary framework to examine whether the health risk related to the virus-laden standing water needs to be a concern. The framework enables the comparison of the instant and lag effects of precipitation on the transmission intensity of SARS-CoV-2 between city clusters with different formation risks of the virus-laden standing water. Based on the city-level data of China between January 01, 2020, and December 31, 2021, we conducted an empirical study. The result showed that in the cities with a high formation risk of the virus-laden standing water, heavy rain increased the instant transmission intensity of SARS-CoV-2 by 6.2% (95%CI: 4.85-10.2%), while in the other cities, precipitation was uninfluential to SARS-CoV-2 transmission, revealing that the health risk of the virus-laden standing water should not be underestimated during the COVID-19 pandemic. To reduce the relevant risk, virus-laden water control and proper disinfection are feasible response strategies.

EpiRegress: A Method to Estimate and Predict the Time-Varying Effective Reproduction Number

The time-varying reproduction (Rt) provides a real-time estimate of pathogen transmissibility and may be influenced by exogenous factors such as mobility and mitigation measures which are not directly related to epidemiology parameters and observations. Meanwhile, evaluating the impacts of these factors is vital for policy makers to propose and adjust containment strategies. Here, we developed a Bayesian regression framework, EpiRegress, to provide Rt estimates and assess impacts of diverse factors on virus transmission, utilising daily case counts, mobility, and policy data. To demonstrate the method’s utility, we used simulations as well as data in four regions from the Western Pacific with periods of low COVID-19 incidence, namely: New South Wales, Australia; New Zealand; Singapore; and Taiwan, China. We found that imported cases had a limited contribution on the overall epidemic dynamics but may degrade the quality of the Rt estimate if not explicitly accounted for. We additionally demonstrated EpiRegress’s capability in nowcasting disease transmissibility before contemporaneous cases diagnosis. The approach was proved flexible enough to respond to periods of atypical local transmission during epidemic lulls and to periods of mass community transmission. Furthermore, in epidemics where travel restrictions are present, it is able to distinguish the influence of imported cases.

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

Simple Summary

In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise.

Abstract

The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve.