How generation intervals shape the relationship between growth rates and reproductive numbers

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Multiple pandemic waves vs multi-period/multi-phasic epidemics: Global shape of the COVID-19 pandemic

The overall course of the COVID-19 pandemic in Western countries has been characterized by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strengthening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasized by the complicated deployment of vaccination campaigns and the onset of virus' variants. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.

Epidemiologic Quantities for Monkeypox Virus Clade I from Historical Data with Implications for Current Outbreaks, Democratic Republic of the Congo

We used published data from outbreak investigations of monkeypox virus clade I in the Democratic Republic of the Congo to estimate the distributions of critical epidemiological parameters. We estimated a mean incubation period of 9.9 days (95% credible interval [CrI] 8.5-11.5 days) and a mean generation time of 17.2 days (95% CrI 14.1-20.9 days) or 11.3 days (95% CrI 9.4-14.0 days), depending on the considered dataset. Presymptomatic transmission was limited. Those estimates suggest generally slower transmission dynamics in clade I than in clade IIb. The time-varying reproduction number for clade I in the Democratic Republic of the Congo was estimated to be below the epidemic threshold in the first half of 2024. However, in the South Kivu Province, where the newly identified subclade Ib has been associated with sustained human-to-human transmission, we estimated an effective reproduction number above the epidemic threshold (95% CrI 0.96-1.27).

Automating COVID-19 epidemiological situation reports based on multiple data sources, the Netherlands, 2020 to 2023

BACKGROUND

During the COVID-19 pandemic, the National Institute for Public Health and the Environment in the Netherlands developed a pipeline of scripts to automate and streamline the production of epidemiological situation reports (epi‑sitrep). The pipeline was developed for the Automation of Data Import, Summarization, and Communication (hereafter called the A-DISC pipeline).

OBJECTIVE

This paper describes the A-DISC pipeline and provides a customizable scripts template that may be useful for other countries wanting to automate their infectious disease surveillance processes.

METHODS

The A-DISC pipeline was developed using the open-source statistical software R. It is organized in four modules: Prepare, Process data, Produce report, and Communicate. The Prepare scripts set the working environment (e.g., load packages). The (data-specific) Process data scripts import, validate, verify, transform, save, analyze, and summarize data as tables and figures and store these data summaries. The Produce report scripts gather summaries from multiple data sources and integrate them into a RMarkdown document - the epi‑sitrep. The Communicate scripts send e-mails to stakeholders with the epi‑sitrep.

RESULTS

As of March 2023, up to ten data sources were automatically summarized into tables and figures by A-DISC. These data summaries were featured in routine extensive COVID-19 epi‑sitreps, shared as open data, plotted on RIVM's website, sent to stakeholders and submitted to European Centre for Disease Prevention and Control via the European Surveillance System -TESSy [38].

DISCUSSION

In the face of an unprecedented high number of cases being reported during the COVID-19 pandemic, the A-DISC pipeline was essential to produce frequent and comprehensive epi‑sitreps. A-DISC's modular and intuitive structure allowed for the integration of data sources of varying complexities, encouraged collaboration among people with various R-scripting capabilities, and improved data lineage. The A-DISC pipeline remains under active development and is currently being used in modified form for the automatization and professionalization of various other disease surveillance processes at the RIVM, with high acceptance from the participant epidemiologists.

CONCLUSION

The A-DISC pipeline is an open-source, robust, and customizable tool for automating epi‑sitreps based on multiple data sources.

Basic Reproduction Number (R0), Doubling Time, and Daily Growth Rate of the COVID-19 Epidemic: An Echological Study

Introduction

In infectious diseases, there are essential indices used to describe the disease state. In this study, we estimated the basic reproduction number, R0, peak level, doubling time, and daily growth rate of COVID-19.

Methods

This ecological study was conducted in 5 provinces of Iran. The daily numbers of new COVID-19 cases from January 17 to February 8, 2020 were used to determine the basic reproduction number (R0), peak date, doubling time, and daily growth rates in all five provinces. A sensitivity analysis was conducted to estimate epidemiological parameters.

Result

The highest and lowest number of deaths were observed in Hamedan (657 deaths) and Chaharmahal and Bakhtiari (54 deaths) provinces, respectively. The doubling time of confirmed cases in Kermanshah and Hamedan ranged widely from 18.59 days (95% confidence interval (CI): 17.38, 20) to 76.66 days (95% CI: 56.36, 119.78). In addition, the highest daily growth rates of confirmed cases were observed in Kermanshah (0.037, 95% CI: 0.034, 0.039) and Sistan and Baluchestan (0.032, 95% CI: 0.030, 0.034) provinces.

Conclusion

In light of our findings, it is imperative to tailor containment strategies to the unique epidemiological profiles of each region in order to effectively mitigate the spread and impact of COVID-19. The wide variation in doubling times underscores the importance of flexibility in public health responses. By adapting measures to local conditions, we can better address the evolving dynamics of the pandemic and safeguard the well-being of communities.

A retrospective assessment of forecasting the peak of the SARS-CoV-2 Omicron BA.1 wave in England

We discuss the invasion of the Omicron BA.1 variant into England as a paradigm for real-time model fitting and projection. Here we use a mixture of simple SIR-type models, analysis of the early data and a more complex age-structure model fit to the outbreak to understand the dynamics. In particular, we highlight that early data shows that the invading Omicron variant had a substantial growth advantage over the resident Delta variant. However, early data does not allow us to reliably infer other key epidemiological parameters-such as generation time and severity-which influence the expected peak hospital numbers. With more complete epidemic data from January 2022 are we able to capture the true scale of the epidemic in terms of both infections and hospital admissions, driven by different infection characteristics of Omicron compared to Delta and a substantial shift in estimated precautionary behaviour during December. This work highlights the challenges of real time forecasting, in a rapidly changing environment with limited information on the variant's epidemiological characteristics.

Bayesian estimation of the time-varying reproduction number for pulmonary tuberculosis in Iran: A registry-based study from 2018 to 2022 using new smear-positive cases

Introduction

Tuberculosis (TB) is one of the most prevalent infectious diseases in the world, causing major public health problems in developing countries. The rate of TB incidence in Iran was estimated to be 13 per 100,000 in 2021. This study aimed to estimate the reproduction number and serial interval for pulmonary tuberculosis in Iran.

Material and methods

The present national historical cohort study was conducted from March 2018 to March 2022 based on data from the National Tuberculosis and Leprosy Registration Center of Iran's Ministry of Health and Medical Education (MOHME). The study included 30,762 tuberculosis cases and 16,165 new smear-positive pulmonary tuberculosis patients in Iran. We estimated the reproduction number of pulmonary tuberculosis in a Bayesian framework, which can incorporate uncertainty in estimating it. Statistical analyses were accomplished in R software.

Results

The mean age at diagnosis of patients was 52.3 ± 21.2 years, and most patients were in the 35-63 age group (37.1%). Among the data, 9121 (56.4%) cases were males, and 7044 (43.6%) were females. Among patients, 7459 (46.1%) had a delayed diagnosis between 1 and 3 months. Additionally, 3039 (18.8%) cases were non-Iranians, and 2978 (98%) were Afghans. The time-varying reproduction number for pulmonary tuberculosis disease was calculated at an average of 1.06 ± 0.05 (95% Crl 0.96-1.15).

Conclusions

In this study, the incidence and the time-varying reproduction number of pulmonary tuberculosis showed the same pattern. The mean of the time-varying reproduction number indicated that each infected person is causing at least one new infection over time, and the chain of transmission is not being disrupted.

Epidemiological feature analysis of SVEIR model with control strategy and variant evolution

The complex interactions were performed among non-pharmaceutical interventions, vaccinations, and hosts for all epidemics in mainland China during the spread of COVID-19. Specially, the small-scale epidemic in the city described by SVEIR model was less found in the current studies. The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures. In this study, the total population (N) of Jinzhou City was divided into five compartments: the susceptible (S), the vaccinated (V), the exposed (E), the infected (I), and the recovered (R). By surveillance data and the SVEIR model, three methods (maximum likelihood method, exponential growth rate method, next generation matrix method) were governed to estimate basic reproduction number, and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1. Meanwhile, the effective reproduction number for two epidemics were investigated by surveillance data, and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later, and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later. Moreover, the impacts of non-pharmaceutical interventions (awareness delay, peak delay, control intensity) were discussed extensively, the variations of infection scales for Omicron variant and EG.5 variant were also discussed. Furthermore, the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control. The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control, which provided a possible perspective on variant evolution in the future.

Challenges in the case-based surveillance of infectious diseases

To effectively inform infectious disease control strategies, accurate knowledge of the pathogen's transmission dynamics is required. Since the timings of infections are rarely known, estimates of the infection incidence, which is crucial for understanding the transmission dynamics, often rely on measurements of other quantities amenable to surveillance. Case-based surveillance, in which infected individuals are identified by a positive test, is the predominant form of surveillance for many pathogens, and was used extensively during the COVID-19 pandemic. However, there can be many biases present in case-based surveillance indicators due to, for example test sensitivity, changing testing behaviours and the co-circulation of pathogens with similar symptom profiles. Here, we develop a mathematical description of case-based surveillance of infectious diseases. By considering realistic epidemiological parameters and situations, we demonstrate many of the potential biases in common surveillance indicators based on case-based surveillance data. Crucially, we find that many of these common surveillance indicators (e.g. case numbers, test-positive proportion) are heavily biased by circulating pathogens with similar symptom profiles. Future surveillance strategies could be designed to minimize these sources of bias and uncertainty, providing more accurate estimates of a pathogen's transmission dynamics and, ultimately, more targeted application of public health measures.

Fitting Epidemic Models to Data: A Tutorial in Memory of Fred Brauer

Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.

SpatialWavePredict: a tutorial-based primer and toolbox for forecasting growth trajectories using the ensemble spatial wave sub-epidemic modeling framework

BACKGROUND

Dynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox, SpatialWavePredict, to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US.

RESULTS

This tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score.

CONCLUSIONS

We have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.

SubEpiPredict: A tutorial-based primer and toolbox for fitting and forecasting growth trajectories using the ensemble n-sub-epidemic modeling framework

An ensemble n-sub-epidemic modeling framework that integrates sub-epidemics to capture complex temporal dynamics has demonstrated powerful forecasting capability in previous works. This modeling framework can characterize complex epidemic patterns, including plateaus, epidemic resurgences, and epidemic waves characterized by multiple peaks of different sizes. In this tutorial paper, we introduce and illustrate SubEpiPredict, a user-friendly MATLAB toolbox for fitting and forecasting time series data using an ensemble n-sub-epidemic modeling framework. The toolbox can be used for model fitting, forecasting, and evaluation of model performance of the calibration and forecasting periods using metrics such as the weighted interval score (WIS). We also provide a detailed description of these methods including the concept of the n-sub-epidemic model, constructing ensemble forecasts from the top-ranking models, etc. For the illustration of the toolbox, we utilize publicly available daily COVID-19 death data at the national level for the United States. The MATLAB toolbox introduced in this paper can be very useful for a wider group of audiences, including policymakers, and can be easily utilized by those without extensive coding and modeling backgrounds.

Assessing the impact of interventions on the major Omicron BA.2 outbreak in spring 2022 in Shanghai

Background

Shanghai experienced a significant surge in Omicron BA.2 infections from March to June 2022. In addition to the standard interventions in place at that time, additional interventions were implemented in response to the outbreak. However, the impact of these interventions on BA.2 transmission remains unclear.

Methods

We systematically collected data on the daily number of newly reported infections during this wave and utilized a Bayesian approach to estimate the daily effective reproduction number. Data on public health responses were retrieved from the Oxford COVID-19 Government Response Tracker and served as a proxy for the interventions implemented during this outbreak. Using a log-linear regression model, we assessed the impact of these interventions on the reproduction number. Furthermore, we developed a mathematical model of BA.2 transmission. By combining the estimated effect of the interventions from the regression model and the transmission model, we estimated the number of infections and deaths averted by the implemented interventions.

Results

We found a negative association (-0.0069, 95% CI: 0.0096 to -0.0045) between the level of interventions and the number of infections. If interventions did not ramp up during the outbreak, we estimated that the number of infections and deaths would have increased by 22.6% (95% CI: 22.4-22.8%), leading to a total of 768,576 (95% CI: 768,021-769,107) infections and 722 (95% CI: 722-723) deaths. If no interventions were deployed during the outbreak, we estimated that the number of infections and deaths would have increased by 46.0% (95% CI: 45.8-46.2%), leading to a total of 915,099 (95% CI: 914,639-915,518) infections and 860 (95% CI: 860-861) deaths.

Conclusion

Our findings suggest that the interventions adopted during the Omicron BA.2 outbreak in spring 2022 in Shanghai were effective in reducing SARS-CoV-2 transmission and disease burden. Our findings emphasize the importance of non-pharmacological interventions in controlling quick surges of cases during epidemic outbreaks.

A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

Inferring community transmission of SARS-CoV-2 in the United Kingdom using the ONS COVID-19 Infection Survey

Key epidemiological parameters, including the effective reproduction number, R ( t ) , and the instantaneous growth rate, r ( t ) , generated from an ensemble of models, have been informing public health policy throughout the COVID-19 pandemic in the four nations of the United Kingdom of Great Britain and Northern Ireland (UK). However, estimation of these quantities became challenging with the scaling down of surveillance systems as part of the transition from the "emergency" to "endemic" phase of the pandemic. The Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) provided an opportunity to continue estimating these parameters in the absence of other data streams. We used a penalised spline model fitted to the publicly-available ONS CIS test positivity estimates to produce a smoothed estimate of the prevalence of SARS-CoV-2 positivity over time. The resulting fitted curve was used to estimate the "ONS-based" R ( t ) and r ( t ) across the four nations of the UK. Estimates produced under this model are compared to government-published estimates with particular consideration given to the contribution that this single data stream can offer in the estimation of these parameters. Depending on the nation and parameter, we found that up to 77% of the variance in the government-published estimates can be explained by the ONS-based estimates, demonstrating the value of this singular data stream to track the epidemic in each of the four nations. We additionally find that the ONS-based estimates uncover epidemic trends earlier than the corresponding government-published estimates. Our work shows that the ONS CIS can be used to generate key COVID-19 epidemiological parameters across the four UK nations, further underlining the enormous value of such population-level studies of infection. This is not intended as an alternative to ensemble modelling, rather it is intended as a potential solution to the aforementioned challenge faced by public health officials in the UK in early 2022.

Time Scales of Human Mpox Transmission in The Netherlands

Mpox has spread rapidly to many countries in nonendemic regions. After reviewing detailed exposure histories of 109 pairs of mpox cases in the Netherlands, we identified 34 pairs where transmission was likely and the infectee reported a single potential infector with a mean serial interval of 10.1 days (95% credible interval, 6.6-14.7 days). Further investigation into pairs from 1 regional public health service revealed that presymptomatic transmission may have occurred in 5 of 18 pairs. These findings emphasize that precaution remains key, regardless of the presence of recognizable symptoms of mpox.

Drivers and impact of the early silent invasion of SARS-CoV-2 Alpha

SARS-CoV-2 variants of concern (VOCs) circulated cryptically before being identified as a threat, delaying interventions. Here we studied the drivers of such silent spread and its epidemic impact to inform future response planning. We focused on Alpha spread out of the UK. We integrated spatio-temporal records of international mobility, local epidemic growth and genomic surveillance into a Bayesian framework to reconstruct the first three months after Alpha emergence. We found that silent circulation lasted from days to months and decreased with the logarithm of sequencing coverage. Social restrictions in some countries likely delayed the establishment of local transmission, mitigating the negative consequences of late detection. Revisiting the initial spread of Alpha supports local mitigation at the destination in case of emerging events.

Counterfactual analysis of the 2023 Omicron XBB wave in China

Background

China has experienced a COVID-19 wave caused by Omicron XBB variant starting in April 2023. Our aim is to conduct a retrospective analysis exploring the dynamics of the outbreak under counterfactual scenarios that combine the use of vaccines, antiviral drugs, and nonpharmaceutical interventions.

Methods

We developed a mathematical model of XBB transmission in China, which has been calibrated using SARS-CoV-2 positive rates per week. Intrinsic age-specific infection-hospitalization risk, infection-ICU risk, and infection-fatality risk were used to estimate disease burdens, characterized as number of hospital admissions, ICU admissions, and deaths.

Results

We estimated that in absence of behavioral change, the XBB outbreak in spring 2023 would have resulted in 0.86 billion infections (∼61% of the total population). Our counterfactual analysis shows that the synergetic effect of vaccination (70% vaccination coverage), antiviral treatment (20% receiving antiviral treatment), and moderate nonpharmaceutical interventions (20% isolation and L1 PHSMs) could reduce the number of deaths to levels close to seasonal influenza (1.17 vs. 0.65 per 10,000 individuals and 5.85 vs. 3.85 per 10,000 individuals aged 60+, respectively). The maximum peak prevalence of hospital and ICU admissions are estimated to be lower than the corresponding capacities (8.6 vs. 10.4 per 10,000 individuals and 1.2 vs. 2.1 per 10,000 individuals, respectively).

Conclusion

Our findings suggest that the capacity of the Chinese healthcare system was adequate to face the Omicron XBB wave in spring 2023 but, at the same time, supports the importance of administering highly effective vaccine with long-lasting immune response, and the use of antiviral treatments.

SARS-CoV-2 incidence monitoring and statistical estimation of the basic and time-varying reproduction number at the early onset of the pandemic in 45 sub-Saharan African countries

The world battled to defeat a novel coronavirus 2019 (SARS-CoV-2 or COVID-19), a respiratory illness that is transmitted from person to person through contacts with droplets from infected persons. Despite efforts to disseminate preventable messages and adoption of mitigation strategies by governments and the World Health Organization (WHO), transmission spread globally. An accurate assessment of the transmissibility of the coronavirus remained a public health priority for many countries across the world to fight this pandemic, especially at the early onset. In this paper, we estimated the transmission potential of COVID-19 across 45 countries in sub-Saharan Africa using three approaches, namely, [Formula: see text] based on (i) an exponential growth model (ii) maximum likelihood (ML) estimation and (iii) a time-varying basic reproduction number at the early onset of the pandemic. Using data from March 14, 2020, to May 10, 2020, sub-Saharan African countries were still grappling with COVID-19 at that point in the pandemic. The region's basic reproduction number ([Formula: see text]) was 1.89 (95% CI: 1.767 to 2.026) using the growth model and 1.513 (95% CI: 1.491 to 1.535) with the maximum likelihood method, indicating that, on average, infected individuals transmitted the virus to less than two secondary persons. Several countries, including Sudan ([Formula: see text]: 2.03), Ghana ([Formula: see text]: 1.87), and Somalia ([Formula: see text]: 1.85), exhibited high transmission rates. These findings highlighted the need for continued vigilance and the implementation of effective control measures to combat the pandemic in the region. It is anticipated that the findings in this study would not only function as a historical record of reproduction numbers during the COVID-19 pandemic in African countries, but can serve as a blueprint for addressing future pandemics of a similar nature.

Within-host evolution of SARS-CoV-2: how often are de novo mutations transmitted from symptomatic infections?

Despite a relatively low mutation rate, the large number of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections has allowed for substantial genetic change, leading to a multitude of emerging variants. Using a recently determined mutation rate (per site replication), as well as within-host parameter estimates for symptomatic SARS-CoV-2 infection, we apply a stochastic transmission-bottleneck model to describe the survival probability of de novo SARS-CoV-2 mutations as a function of bottleneck size and selection coefficient. For narrow bottlenecks, we find that mutations affecting per-target-cell attachment rate (with phenotypes associated with fusogenicity and ACE2 binding) have similar transmission probabilities to mutations affecting viral load clearance (with phenotypes associated with humoral evasion). We further find that mutations affecting the eclipse rate (with phenotypes associated with reorganization of cellular metabolic processes and synthesis of viral budding precursor material) are highly favoured relative to all other traits examined. We find that mutations leading to reduced removal rates of infected cells (with phenotypes associated with innate immune evasion) have limited transmission advantage relative to mutations leading to humoral evasion. Predicted transmission probabilities, however, for mutations affecting innate immune evasion are more consistent with the range of clinically estimated household transmission probabilities for de novo mutations. This result suggests that although mutations affecting humoral evasion are more easily transmitted when they occur, mutations affecting innate immune evasion may occur more readily. We examine our predictions in the context of a number of previously characterized mutations in circulating strains of SARS-CoV-2. Our work offers both a null model for SARS-CoV-2 mutation rates and predicts which aspects of viral life history are most likely to successfully evolve, despite low mutation rates and repeated transmission bottlenecks.

Transmission potential of mpox in mainland China, June-July 2023: estimating reproduction number during the initial phase of the epidemic

Despite reporting very few mpox cases in early 2023, mainland China observed a surge of over 500 cases during the summer. Amid ambiguous prevention strategies and stigma surrounding mpox transmission, the epidemic silently escalated. This study aims to quantify the scale of the mpox epidemic and assess the transmission dynamics of the virus by estimating the effective reproduction number (Re) during its early phase. Publicly available data were aggregated to obtain daily mpox case counts in mainland China, and the Re value was estimated using an exponential growth model. The mean Re value was found to be 1.57 (95% credible interval [1.38-1.78]), suggesting a case doubling time of approximately 2 weeks. This estimate was compared with Re values from 16 other countries' national outbreaks in 2022 that had cumulative case count exceeding 700 symptomatic cases by the end of that year. The Re estimates for these outbreaks ranged from 1.13 for Portugal to 2.31 for Colombia. The pooled mean Re was 1.49 (95% credible interval [1.32-1.67]), which aligns closely with the Re for mainland China. These findings underscore the need for immediate and effective control measures including targeted vaccination campaigns to mitigate the further spread and impact of the epidemic.

Key Challenges for Respiratory Virus Surveillance while Transitioning out of Acute Phase of COVID-19 Pandemic

To support the ongoing management of viral respiratory diseases while transitioning out of the acute phase of the COVID-19 pandemic, many countries are moving toward an integrated model of surveillance for SARS-CoV-2, influenza virus, and other respiratory pathogens. Although many surveillance approaches catalyzed by the COVID-19 pandemic provide novel epidemiologic insight, continuing them as implemented during the pandemic is unlikely to be feasible for nonemergency surveillance, and many have already been scaled back. Furthermore, given anticipated cocirculation of SARS-CoV-2 and influenza virus, surveillance activities in place before the pandemic require review and adjustment to ensure their ongoing value for public health. In this report, we highlight key challenges for the development of integrated models of surveillance. We discuss the relative strengths and limitations of different surveillance practices and studies as well as their contribution to epidemiologic assessment, forecasting, and public health decision-making.

Exact confidence intervals for population growth rate, longevity and generation time

By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for r, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

The role of absolute humidity in influenza transmission in Beijing, China: risk assessment and attributable fraction identification

To assess the impact of absolute humidity on influenza transmission in Beijing from 2014 to 2019, we estimated the influenza transmissibility via the instantaneous reproduction number (Rt), and evaluated its nonlinear exposure-response association and delayed effects with absolute humidity by using the distributed lag nonlinear model (DLNM). Attributable fraction (AF) of Rt due to absolute humidity was calculated. The result showed a significant M-shaped relationship between Rt and absolute humidity. Compared with the effect of high absolute humidity, the low absolute humidity effect was more immediate with the most significant effect observed at lag 6 days. AFs were relatively high for the group aged 15-24 years, and was the lowest for the group aged 0-4 years with low absolute humidity. Therefore, we concluded that the component attributed to the low absolute humidity effect is greater. Young and middle-aged people are more sensitive to low absolute humidity than children and elderly.

GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software ( https://github.com/gchowell/forecasting_growthmodels ), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Impact of different nucleic acid testing scenarios on COVID-19 transmission

In the past three years, waves of COVID-19 infections have emerged one after another, and may enter a small-scale wave-like recurrent epidemic pattern in the future. When COVID-19 infections occur in small-scale, how to efficiently detect and prevent the disease has become the main problem. In this study, based on the characteristics of the Omicron variant and China's pandemic prevention and control strategies, the following three nucleic acid testing scenarios were simulated: scenario 1 (baseline scenario) included conducting nucleic acid testing at administrative region; scenario 2 included conducting nucleic acid testing at the community; and scenario 3 included conducting nucleic acid testing at the health facility closest to households. The model calibration showed that the baseline scenario was consistent with the actual transmission scenario of the disease. The simulation results revealed that compared with scenario 1, the cumulative cases in scenarios 2 and 3 were reduced by 9.52 % and 46.83 %, respectively. Compared with scenario 2, the cumulative cases in scenario 3 were reduced by 41.23 %. Thus, adopting nucleic acid testing measures at the household level can effectively limit the spread of COVID-19 and should be given a priority when local emergency occurs in the future.

Transmission chains of the first local outbreak cause by Delta VariantB.1.617.2 COVID-19 in Guangzhou, Southern China

BACKGROUND

The first local outbreak of Delta Variant B.1.617.2 COVID-19 of China occurred in Guangzhou city, south China, in May 2021. This study analyzed the transmission chains and local cluster characteristics of this outbreak, intended to provide information support for the development and adjustment of local prevention and control strategies.

METHODS

The transmission chains and local cluster characteristics of 161 local cases in the outbreak were described and analyzed. Incubation period, serial interval and generation time were calculated using the exact time of exposure and symptom onset date of the cases. The daily number of reported cases and the estimated generation time were used to estimate the effective reproduction number (Rt).

RESULTS

We identified 7 superspreading events who had more than 5 next generation cases and their infected cases infected 70.81%(114/161) of all the cases transmission. Dining and family exposure were the main transmission routes in the outbreak, with 29.19% exposed through dining and 32.30% exposed through family places. Through further analysis of the outbreak, the estimated mean incubation period was 4.22 (95%CI: 3.66-4.94) days, the estimated mean generation time was 2.60 (95%CI: 1.96-3.11) days, and the estimated Rt was 3.29 (95%CI: 2.25-5.07).

CONCLUSIONS

Classification and dynamically adjusted prevention and control measures had been carried out according to analysis of transmission chains and epidemical risk levels, including promoting nucleic acid screening at different regions and different risk levels, dividing closed-off area, controlled area according to the risk of infection, raising the requirements of leaving Guangzhou. By the above control measures, Guangzhou effectively control the outbreak within 28 days without implementing a large-scale lockdown policy.

A Bayesian hierarchical approach to account for evidence and uncertainty in the modeling of infectious diseases: An application to COVID-19

Infectious disease models can serve as critical tools to predict the development of cases and associated healthcare demand and to determine the set of nonpharmaceutical interventions (NPIs) that is most effective in slowing the spread of an infectious agent. Current approaches to estimate NPI effects typically focus on relatively short time periods and either on the number of reported cases, deaths, intensive care occupancy, or hospital occupancy as a single indicator of disease transmission. In this work, we propose a Bayesian hierarchical model that integrates multiple outcomes and complementary sources of information in the estimation of the true and unknown number of infections while accounting for time-varying underreporting and weekday-specific delays in reported cases and deaths, allowing us to estimate the number of infections on a daily basis rather than having to smooth the data. To address dynamic changes occurring over long periods of time, we account for the spread of new variants, seasonality, and time-varying differences in host susceptibility. We implement a Markov chain Monte Carlo algorithm to conduct Bayesian inference and illustrate the proposed approach with data on COVID-19 from 20 European countries. The approach shows good performance on simulated data and produces posterior predictions that show a good fit to reported cases, deaths, hospital, and intensive care occupancy.

Early underdetected dissemination across countries followed by extensive local transmission propelled the 2022 mpox epidemic

The World Health Organization declared mpox a public health emergency of international concern in July 2022. To investigate global mpox transmission and population-level changes associated with controlling spread, we built phylogeographic and phylodynamic models to analyze MPXV genomes from five global regions together with air traffic and epidemiological data. Our models reveal community transmission prior to detection, changes in case-reporting throughout the epidemic, and a large degree of transmission heterogeneity. We find that viral introductions played a limited role in prolonging spread after initial dissemination, suggesting that travel bans would have had only a minor impact. We find that mpox transmission in North America began declining before more than 10% of high-risk individuals in the USA had vaccine-induced immunity. Our findings highlight the importance of broader routine specimen screening surveillance for emerging infectious diseases and of joint integration of genomic and epidemiological information for early outbreak control.

Real-time estimation of the effective reproduction number of COVID-19 from behavioral data

Monitoring the effective reproduction number [Formula: see text] of a rapidly unfolding pandemic in real-time is key to successful mitigation and prevention strategies. However, existing methods based on case numbers, hospital admissions or fatalities suffer from multiple measurement biases and temporal lags due to high test positivity rates or delays in symptom development or administrative reporting. Alternative methods such as web search and social media tracking are less directly indicating epidemic prevalence over time. We instead record age-stratified anonymous contact matrices at a daily resolution using a longitudinal online-offline survey in Hungary during the first two waves of the COVID-19 pandemic. This approach is innovative, cheap, and provides information in near real-time for estimating [Formula: see text] at a daily resolution. Moreover, it allows to complement traditional surveillance systems by signaling periods when official monitoring infrastructures are unreliable due to observational biases.

Estimating the potential impact and diagnostic requirements for SARS-CoV-2 test-and-treat programs

Oral antivirals have the potential to reduce the public health burden of COVID-19. However, now that we have exited the emergency-phase of the COVID-19 pandemic, declining SARS-CoV-2 clinical testing rates (average testing rates = [Formula: see text]10 tests/100,000 people/day in low-and-middle income countries; <100 tests/100,000 people/day in high-income countries; September 2023) make the development of effective test-and-treat programs challenging. We used an agent-based model to investigate how testing rates and strategies affect the use and effectiveness of oral antiviral test-to-treat programs in four country archetypes of different income levels and demographies. We find that in the post-emergency-phase of the pandemic, in countries where low testing rates are driven by limited testing capacity, significant population-level impact of test-and-treat programs can only be achieved by both increasing testing rates and prioritizing individuals with greater risk of severe disease. However, for all countries, significant reductions in severe cases with antivirals are only possible if testing rates were substantially increased with high willingness of people to seek testing. Comparing the potential population-level reductions in severe disease outcomes of test-to-treat programs and vaccination shows that test-and-treat strategies are likely substantially more resource intensive requiring very high levels of testing (≫100 tests/100,000 people/day) and antiviral use suggesting that vaccination should be a higher priority.

The impact of household structure on disease-induced herd immunity

The disease-induced herd immunity level [Formula: see text] is the fraction of the population that must be infected by an epidemic to ensure that a new epidemic among the remaining susceptible population is not supercritical. For a homogeneously mixing population [Formula: see text] equals the classical herd immunity level [Formula: see text], which is the fraction of the population that must be vaccinated in advance of an epidemic so that the epidemic is not supercritical. For most forms of heterogeneous mixing [Formula: see text], sometimes dramatically so. For an SEIR (susceptible [Formula: see text] exposed [Formula: see text] infective [Formula: see text] recovered) model of an epidemic among a population that is partitioned into households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate in the population at large, we show that [Formula: see text] unless variability in the household size distribution is sufficiently large. Thus, introducing household structure into a model typically has the opposite effect on disease-induced herd immunity than most other forms of population heterogeneity. We reach this conclusion by considering an approximation [Formula: see text] of [Formula: see text], supported by numerical studies using real-world household size distributions. For [Formula: see text], we prove that [Formula: see text] when all households have size n, and conjecture that this inequality holds for any common household size n. We prove results comparing [Formula: see text] and [Formula: see text] for epidemics which are highly infectious within households, and also for epidemics which are weakly infectious within households.

Characterizing the role of human behavior in the effectiveness of contact-tracing applications

Introduction

Although numerous countries relied on contact-tracing (CT) applications as an epidemic control measure against the COVID-19 pandemic, the debate around their effectiveness is still open. Most studies indicate that very high levels of adoption are required to stop disease progression, placing the main interest of policymakers in promoting app adherence. However, other factors of human behavior, like delays in adherence or heterogeneous compliance, are often disregarded.

Methods

To characterize the impact of human behavior on the effectiveness of CT apps we propose a multilayer network model reflecting the co-evolution of an epidemic outbreak and the app adoption dynamics over a synthetic population generated from survey data. The model was initialized to produce epidemic outbreaks resembling the first wave of the COVID-19 pandemic and was used to explore the impact of different changes in behavioral features in peak incidence and maximal prevalence.

Results

The results corroborate the relevance of the number of users for the effectiveness of CT apps but also highlight the need for early adoption and, at least, moderate levels of compliance, which are factors often not considered by most policymakers.

Discussion

The insight obtained was used to identify a bottleneck in the implementation of several apps, such as the Spanish CT app, where we hypothesize that a simplification of the reporting system could result in increased effectiveness through a rise in the levels of compliance.

Using a Bayesian hierarchical approach to study the association between non-pharmaceutical interventions and the spread of Covid-19 in Germany

Non-Pharmaceutical Interventions (NPIs) are community mitigation strategies, aimed at reducing the spread of illnesses like the coronavirus pandemic, without relying on pharmaceutical drug treatments. This study aims to evaluate the effectiveness of different NPIs across sixteen states of Germany, for a time period of 21 months of the pandemic. We used a Bayesian hierarchical approach that combines different sub-models and merges information from complementary sources, to estimate the true and unknown number of infections. In this framework, we used data on reported cases, hospitalizations, intensive care unit occupancy, and deaths to estimate the effect of NPIs. The list of NPIs includes: "contact restriction (up to 5 people)", "strict contact restriction", "curfew", "events permitted up to 100 people", "mask requirement in shopping malls", "restaurant closure", "restaurants permitted only with test", "school closure" and "general behavioral changes". We found a considerable reduction in the instantaneous reproduction number by "general behavioral changes", "strict contact restriction", "restaurants permitted only with test", "contact restriction (up to 5 people)", "restaurant closure" and "curfew". No association with school closures could be found. This study suggests that some public health measures, including general behavioral changes, strict contact restrictions, and restaurants permitted only with tests are associated with containing the Covid-19 pandemic. Future research is needed to better understand the effectiveness of NPIs in the context of Covid-19 vaccination.

Spatio-temporal surveillance and early detection of SARS-CoV-2 variants of concern: a retrospective analysis

The SARS-CoV-2 pandemic has been characterized by the repeated emergence of genetically distinct virus variants of increased transmissibility and immune evasion compared to pre-existing lineages. In many countries, their containment required the intervention of public health authorities and the imposition of control measures. While the primary role of testing is to identify infection, target treatment, and limit spread (through isolation and contact tracing), a secondary benefit is in terms of surveillance and the early detection of new variants. Here we study the spatial invasion and early spread of the Alpha, Delta and Omicron (BA.1 and BA.2) variants in England from September 2020 to February 2022 using the random neighbourhood covering (RaNCover) method. This is a statistical technique for the detection of aberrations in spatial point processes, which we tailored here to community PCR (polymerase-chain-reaction) test data where the TaqPath kit provides a proxy measure of the switch between variants. Retrospectively, RaNCover detected the earliest signals associated with the four novel variants that led to large infection waves in England. With suitable data our method therefore has the potential to rapidly detect outbreaks of future SARS-CoV-2 variants, thus helping to inform targeted public health interventions.

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.

Rapid prototyping of models for COVID-19 outbreak detection in workplaces

Early case detection is critical to preventing onward transmission of COVID-19 by enabling prompt isolation of index infections, and identification and quarantining of contacts. Timeliness and completeness of ascertainment depend on the surveillance strategy employed. This paper presents modelling used to inform workplace testing strategies for the Australian government in early 2021. We use rapid prototype modelling to quickly investigate the effectiveness of testing strategies to aid decision making. Models are developed with a focus on providing relevant results to policy makers, and these models are continually updated and improved as new questions are posed. Developed to support the implementation of testing strategies in high risk workplace settings in Australia, our modelling explores the effects of test frequency and sensitivity on outbreak detection. We start with an exponential growth model, which demonstrates how outbreak detection changes depending on growth rate, test frequency and sensitivity. From the exponential model, we learn that low sensitivity tests can produce high probabilities of detection when testing occurs frequently. We then develop a more complex Agent Based Model, which was used to test the robustness of the results from the exponential model, and extend it to include intermittent workplace scheduling. These models help our fundamental understanding of disease detectability through routine surveillance in workplaces and evaluate the impact of testing strategies and workplace characteristics on the effectiveness of surveillance. This analysis highlights the risks of particular work patterns while also identifying key testing strategies to best improve outbreak detection in high risk workplaces.

Assessing changes in incubation period, serial interval, and generation time of SARS-CoV-2 variants of concern: a systematic review and meta-analysis

BACKGROUND

After the first COVID-19 wave caused by the ancestral lineage, the pandemic has been fueled from the continuous emergence of new SARS-CoV-2 variants. Understanding key time-to-event periods for each emerging variant of concern is critical as it can provide insights into the future trajectory of the virus and help inform outbreak preparedness and response planning. Here, we aim to examine how the incubation period, serial interval, and generation time have changed from the ancestral SARS-CoV-2 lineage to different variants of concern.

METHODS

We conducted a systematic review and meta-analysis that synthesized the estimates of incubation period, serial interval, and generation time (both realized and intrinsic) for the ancestral lineage, Alpha, Beta, and Omicron variants of SARS-CoV-2.

RESULTS

Our study included 280 records obtained from 147 household studies, contact tracing studies, or studies where epidemiological links were known. With each emerging variant, we found a progressive shortening of each of the analyzed key time-to-event periods, although we did not find statistically significant differences between the Omicron subvariants. We found that Omicron BA.1 had the shortest pooled estimates for the incubation period (3.49 days, 95% CI: 3.13-4.86 days), Omicron BA.5 for the serial interval (2.37 days, 95% CI: 1.71-3.04 days), and Omicron BA.1 for the realized generation time (2.99 days, 95% CI: 2.48-3.49 days). Only one estimate for the intrinsic generation time was available for Omicron subvariants: 6.84 days (95% CrI: 5.72-8.60 days) for Omicron BA.1. The ancestral lineage had the highest pooled estimates for each investigated key time-to-event period. We also observed shorter pooled estimates for the serial interval compared to the incubation period across the virus lineages. When pooling the estimates across different virus lineages, we found considerable heterogeneities (I2 > 80%; I2 refers to the percentage of total variation across studies that is due to heterogeneity rather than chance), possibly resulting from heterogeneities between the different study populations (e.g., deployed interventions, social behavior, demographic characteristics).

CONCLUSIONS

Our study supports the importance of conducting contact tracing and epidemiological investigations to monitor changes in SARS-CoV-2 transmission patterns. Our findings highlight a progressive shortening of the incubation period, serial interval, and generation time, which can lead to epidemics that spread faster, with larger peak incidence, and harder to control. We also consistently found a shorter serial interval than incubation period, suggesting that a key feature of SARS-CoV-2 is the potential for pre-symptomatic transmission. These observations are instrumental to plan for future COVID-19 waves.

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.

Replicating superspreader dynamics with compartmental models

Infectious disease outbreaks often exhibit superspreader dynamics, where most infected people generate no, or few secondary cases, and only a small fraction of individuals are responsible for a large proportion of transmission. Although capturing this heterogeneity is critical for estimating outbreak risk and the effectiveness of group-specific interventions, it is typically neglected in compartmental models of infectious disease transmission-which constitute the most common transmission dynamic modeling framework. In this study we propose different classes of compartmental epidemic models that incorporate transmission heterogeneity, fit them to a number of real outbreak datasets, and benchmark their performance against the canonical superspreader model (i.e., the negative binomial branching process model). We find that properly constructed compartmental models can capably reproduce observed superspreader dynamics and we provide the pathogen-specific parameter settings required to do so. As a consequence, we also show that compartmental models parameterized according to a binary clinical classification have limited support.

Data-driven estimation of the instantaneous reproduction number and growth rates for the 2022 monkeypox outbreak in Europe

OBJECTIVE

To estimate the instantaneous reproduction number Rt and the epidemic growth rates for the 2022 monkeypox outbreaks in the European region.

METHODS

We gathered daily laboratory-confirmed monkeypox cases in the most affected European countries from the beginning of the outbreak to September 23, 2022. A data-driven estimation of the instantaneous reproduction number is obtained using a novel filtering type Bayesian inference. A phenomenological growth model coupled with a Bayesian sequential approach to update forecasts over time is used to obtain time-dependent growth rates in several countries.

RESULTS

The instantaneous reproduction number Rt for the laboratory-confirmed monkeypox cases in Spain, France, Germany, the UK, the Netherlands, Portugal, and Italy. At the early phase of the outbreak, our estimation for Rt, which can be used as a proxy for the basic reproduction number R0, was 2.06 (95% CI 1.63 - 2.54) for Spain, 2.62 (95% CI 2.23 - 3.17) for France, 2.81 (95% CI 2.51 - 3.09) for Germany, 1.82 (95% CI 1.52 - 2.18) for the UK, 2.84 (95% CI 2.07 - 3.91) for the Netherlands, 1.13 (95% CI 0.99 - 1.32) for Portugal, 3.06 (95% CI 2.48 - 3.62) for Italy. Cumulative cases for these countries present subexponential rather than exponential growth dynamics.

CONCLUSIONS

Our findings suggest that the current monkeypox outbreaks present limited transmission chains of human-to-human secondary infection so the possibility of a huge pandemic is very low. Confirmed monkeypox cases are decreasing significantly in the European region, the decline might be attributed to public health interventions and behavioral changes in the population due to increased risk perception. Nevertheless, further strategies toward elimination are essential to avoid the subsequent evolution of the monkeypox virus that can result in new outbreaks.

A novel queue-based stochastic epidemic model with adaptive stabilising control

The main objective of this paper is to propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a setup under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate comprise the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly more straightforward and tractable than semi-Markov models with a similar level of generality. Based on stochastic stability, we derive a sufficient condition for a shrinking epidemic regarding the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil, and assess the effect of different stabilising strategies in the latter setting. Results suggest that the proposed approach can curb the epidemic with various occupation rate levels if the mitigation is timely.

Scoring epidemiological forecasts on transformed scales

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most appropriate due to the exponential nature of epidemic processes and the varying magnitudes of observed values across space and time. In this paper, we argue that transforming counts before applying scores such as the CRPS or WIS can effectively mitigate these difficulties and yield epidemiologically meaningful and easily interpretable results. Using the CRPS on log-transformed values as an example, we list three attractive properties: Firstly, it can be interpreted as a probabilistic version of a relative error. Secondly, it reflects how well models predicted the time-varying epidemic growth rate. And lastly, using arguments on variance-stabilizing transformations, it can be shown that under the assumption of a quadratic mean-variance relationship, the logarithmic transformation leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. Applying a transformation of log(x + 1) to data and forecasts from the European COVID-19 Forecast Hub, we find that it changes model rankings regardless of stratification by forecast date, location or target types. Situations in which models missed the beginning of upward swings are more strongly emphasised while failing to predict a downturn following a peak is less severely penalised when scoring transformed forecasts as opposed to untransformed ones. We conclude that appropriate transformations, of which the natural logarithm is only one particularly attractive option, should be considered when assessing the performance of different models in the context of infectious disease incidence.

Estimating the epidemic reproduction number from temporally aggregated incidence data: A statistical modelling approach and software tool

The time-varying reproduction number (Rt) is an important measure of epidemic transmissibility that directly informs policy decisions and the optimisation of control measures. EpiEstim is a widely used opensource software tool that uses case incidence and the serial interval (SI, time between symptoms in a case and their infector) to estimate Rt in real-time. The incidence and the SI distribution must be provided at the same temporal resolution, which can limit the applicability of EpiEstim and other similar methods, e.g. for contexts where the time window of incidence reporting is longer than the mean SI. In the EpiEstim R package, we implement an expectation-maximisation algorithm to reconstruct daily incidence from temporally aggregated data, from which Rt can then be estimated. We assess the validity of our method using an extensive simulation study and apply it to COVID-19 and influenza data. For all datasets, the influence of intra-weekly variability in reported data was mitigated by using aggregated weekly data. Rt estimated on weekly sliding windows using incidence reconstructed from weekly data was strongly correlated with estimates from the original daily data. The simulation study revealed that Rt was well estimated in all scenarios and regardless of the temporal aggregation of the data. In the presence of weekend effects, Rt estimates from reconstructed data were more successful at recovering the true value of Rt than those obtained from reported daily data. These results show that this novel method allows Rt to be successfully recovered from aggregated data using a simple approach with very few data requirements. Additionally, by removing administrative noise when daily incidence data are reconstructed, the accuracy of Rt estimates can be improved.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .

The daily updated Dutch national database on COVID-19 epidemiology, vaccination and sewage surveillance

The Dutch national open database on COVID-19 has been incrementally expanded since its start on 30 April 2020 and now includes datasets on symptoms, tests performed, individual-level positive cases and deaths, cases and deaths among vulnerable populations, settings of transmission, hospital and ICU admissions, SARS-CoV-2 variants, viral loads in sewage, vaccinations and the effective reproduction number. This data is collected by municipal health services, laboratories, hospitals, sewage treatment plants, vaccination providers and citizens and is cleaned, analysed and published, mostly daily, by the National Institute for Public Health and the Environment (RIVM) in the Netherlands, using automated scripts. Because these datasets cover the key aspects of the pandemic and are available at detailed geographical level, they are essential to gain a thorough understanding of the past and current COVID-19 epidemiology in the Netherlands. Future purposes of these datasets include country-level comparative analysis on the effect of non-pharmaceutical interventions against COVID-19 in different contexts, such as different cultural values or levels of socio-economic disparity, and studies on COVID-19 and weather factors.

Epidemic thresholds and human mobility

A comprehensive view of disease epidemics demands a deep understanding of the complex interplay between human behaviour and infectious diseases. Here, we propose a flexible modelling framework that brings conclusions about the influence of human mobility and disease transmission on early epidemic growth, with applicability in outbreak preparedness. We use random matrix theory to compute an epidemic threshold, equivalent to the basic reproduction number [Formula: see text], for a SIR metapopulation model. The model includes both systematic and random features of human mobility. Variations in disease transmission rates, mobility modes (i.e. commuting and migration), and connectivity strengths determine the threshold value and whether or not a disease may potentially establish in the population, as well as the local incidence distribution.

Generalized epidemic model incorporating non-Markovian infection processes and waning immunity

The Markovian approach, which assumes exponentially distributed interinfection times, is dominant in epidemic modeling. However, this assumption is unrealistic as an individual's infectiousness depends on its viral load and varies over time. In this paper, we present a Susceptible-Infected-Recovered-Vaccinated-Susceptible epidemic model incorporating non-Markovian infection processes. The model can be easily adapted to accurately capture the generation time distributions of emerging infectious diseases, which is essential for accurate epidemic prediction. We observe noticeable variations in the transient behavior under different infectiousness profiles and the same basic reproduction number R_{0}. The theoretical analyses show that only R_{0} and the mean immunity period of the vaccinated individuals have an impact on the critical vaccination rate needed to achieve herd immunity. A vaccination level at the critical vaccination rate can ensure a very low incidence among the population in the case of future epidemics, regardless of the infectiousness profiles.

Relative role of community transmission and campus contagion in driving the spread of SARS-CoV-2: Lessons from Princeton University

Mathematical models have played a crucial role in exploring and guiding pandemic responses. University campuses present a particularly well-documented case for institutional outbreaks, thereby providing a unique opportunity to understand detailed patterns of pathogen spread. Here, we present descriptive and modeling analyses of SARS-CoV-2 transmission on the Princeton University (PU) campus-this model was used throughout the pandemic to inform policy decisions and operational guidelines for the university campus. Epidemic patterns between the university campus and surrounding communities exhibit strong spatiotemporal correlations. Mathematical modeling analysis further suggests that the amount of on-campus transmission was likely limited during much of the wider pandemic until the end of 2021. Finally, we find that a superspreading event likely played a major role in driving the Omicron variant outbreak on the PU campus during the spring semester of the 2021-2022 academic year. Despite large numbers of cases on campus in this period, case levels in surrounding communities remained low, suggesting that there was little spillover transmission from campus to the local community.