Improved inference of time-varying reproduction numbers during infectious disease outbreaks

Data-driven mathematical modeling approaches for COVID-19: A survey

In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

rtestim: Time-varying reproduction number estimation with trend filtering

To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.

Prioritising older individuals for COVID-19 booster vaccination leads to optimal public health outcomes in a range of socio-economic settings

The rapid development of vaccines against SARS-CoV-2 altered the course of the COVID-19 pandemic. In most countries, vaccinations were initially targeted at high-risk populations, including older individuals and healthcare workers. Now, despite substantial infection- and vaccine-induced immunity in host populations worldwide, waning immunity and the emergence of novel variants continue to cause significant waves of infection and disease. Policy makers must determine how to deploy booster vaccinations, particularly when constraints in vaccine supply, delivery and cost mean that booster vaccines cannot be administered to everyone. A key question is therefore whether older individuals should again be prioritised for vaccination, or whether alternative strategies (e.g. offering booster vaccines to the individuals who have most contacts with others and therefore drive infection) can instead offer indirect protection to older individuals. Here, we use mathematical modelling to address this question, considering SARS-CoV-2 transmission in a range of countries with different socio-economic backgrounds. We show that the population structures of different countries can have a pronounced effect on the impact of booster vaccination, even when identical booster vaccination targeting strategies are adopted. However, under the assumed transmission model, prioritising older individuals for booster vaccination consistently leads to the most favourable public health outcomes in every setting considered. This remains true for a range of assumptions about booster vaccine supply and timing, and for different assumed policy objectives of booster vaccination.

Jointly estimating epidemiological dynamics of Covid-19 from case and wastewater data in Aotearoa New Zealand

BACKGROUND

Timely and informed public health responses to infectious diseases such as COVID-19 necessitate reliable information about infection dynamics. The case ascertainment rate (CAR), the proportion of infections that are reported as cases, is typically much less than one and varies with testing practices and behaviours, making reported cases unreliable as the sole source of data. The concentration of viral RNA in wastewater samples provides an alternate measure of infection prevalence that is not affected by clinical testing, healthcare-seeking behaviour or access to care.

METHODS

We construct a state-space model with observed data of levels of SARS-CoV-2 in wastewater and reported case incidence and estimate the hidden states of the effective reproduction number, R, and CAR using sequential Monte Carlo methods.

RESULTS

We analyse data from 1 January 2022 to 31 March 2023 from Aotearoa New Zealand. Our model estimates that R peaks at 2.76 (95% CrI 2.20, 3.83) around 18 February 2022 and the CAR peaks around 12 March 2022. We calculate that New Zealand's second Omicron wave in July 2022 is similar in size to the first, despite fewer reported cases. We estimate that the CAR in the BA.5 Omicron wave in July 2022 is approximately 50% lower than in the BA.1/BA.2 Omicron wave in March 2022.

CONCLUSIONS

Estimating R, CAR, and cumulative number of infections provides useful information for planning public health responses and understanding the state of immunity in the population. This model is a useful disease surveillance tool, improving situational awareness of infectious disease dynamics in real-time.

Using real-time modelling to inform the 2017 Ebola outbreak response in DR Congo

Important policy questions during infections disease outbreaks include: i) How effective are particular interventions?; ii) When can resource-intensive interventions be removed? We used mathematical modelling to address these questions during the 2017 Ebola outbreak in Likati Health Zone, Democratic Republic of the Congo (DRC). Eight cases occurred before 15 May 2017, when the Ebola Response Team (ERT; co-ordinated by the World Health Organisation and DRC Ministry of Health) was deployed to reduce transmission. We used a branching process model to estimate that, pre-ERT arrival, the reproduction number was R = 1.49 (95% credible interval ( 0.67, 2.81 ) ). The risk of further cases occurring without the ERT was estimated to be 0.97 (97%). However, no cases materialised, suggesting that the ERT's measures were effective. We also estimated the risk of withdrawing the ERT in real-time. By the actual ERT withdrawal date (2 July 2017), the risk of future cases without the ERT was only 0.01, indicating that the ERT withdrawal decision was safe. We evaluated the sensitivity of our results to the estimated R value and considered different criteria for determining the ERT withdrawal date. This research provides an extensible modelling framework that can be used to guide decisions about when to relax interventions during future outbreaks.

Analysis of the impact of COVID-19 variants and vaccination on the time-varying reproduction number: statistical methods

Introduction

The COVID-19 pandemic has profoundly impacted global health systems, requiring the monitoring of infection waves and strategies to control transmission. Estimating the time-varying reproduction number is crucial for understanding the epidemic and guiding interventions.

Methods

Probability distributions of serial interval are estimated for Pre-Delta and Delta periods. We conducted a comparative analysis of time-varying reproduction numbers, taking into account population immunity and variant differences. We incorporated the regional heterogeneity and age distribution of the population, as well as the evolving variants and vaccination rates over time. COVID-19 transmission dynamics were analyzed with variants and vaccination.

Results

The reproduction number is computed with and without considering variant-based immunity. In addition, values of reproduction number significantly differed by variants, emphasizing immunity's importance. Enhanced vaccination efforts and stringent control measures were effective in reducing the transmission of the Delta variant. Conversely, Pre-Delta variant appeared less influenced by immunity levels, due to lower vaccination rates. Furthermore, during the Pre-Delta period, there was a significant difference between the region-specific and the non-region-specific reproduction numbers, with particularly distinct pattern differences observed in Gangwon, Gyeongbuk, and Jeju in Korea.

Discussion

This research elucidates the dynamics of COVID-19 transmission concerning the dominance of the Delta variant, the efficacy of vaccinations, and the influence of immunity levels. It highlights the necessity for targeted interventions and extensive vaccination coverage. This study makes a significant contribution to the understanding of disease transmission mechanisms and informs public health strategies.

Uncovering COVID-19 transmission tree: identifying traced and untraced infections in an infection network

Introduction

This paper presents a comprehensive analysis of COVID-19 transmission dynamics using an infection network derived from epidemiological data in South Korea, covering the period from January 3, 2020, to July 11, 2021. The network illustrates infector-infectee relationships and provides invaluable insights for managing and mitigating the spread of the disease. However, significant missing data hinder conventional analysis of such networks from epidemiological surveillance.

Methods

To address this challenge, this article suggests a novel approach for categorizing individuals into four distinct groups, based on the classification of their infector or infectee status as either traced or untraced cases among all confirmed cases. The study analyzes the changes in the infection networks among untraced and traced cases across five distinct periods.

Results

The four types of cases emphasize the impact of various factors, such as the implementation of public health strategies and the emergence of novel COVID-19 variants, which contribute to the propagation of COVID-19 transmission. One of the key findings is the identification of notable transmission patterns in specific age groups, particularly in those aged 20-29, 40-69, and 0-9, based on the four type classifications. Furthermore, we develop a novel real-time indicator to assess the potential for infectious disease transmission more effectively. By analyzing the lengths of connected components, this indicator facilitates improved predictions and enables policymakers to proactively respond, thereby helping to mitigate the effects of the pandemic on global communities.

Conclusion

This study offers a novel approach to categorizing COVID-19 cases, provides insights into transmission patterns, and introduces a real-time indicator for better assessment and management of the disease transmission, thereby supporting more effective public health interventions.

A novel approach to model the role of mobility suppression and vaccinations in containing epidemics in a network of cities

This paper presents a comprehensive agent-based model for the spread of an infection in a network of cities. Directional mobility is defined between each two cities and can take different values. The work examines the role that such mobility levels play in containing the infection with various vaccination coverage and age distributions. The results indicate that mobility reduction is sufficient to control the disease under all circumstances and full lockdowns are not a necessity. It has to be reduced to different ratios depending on the vaccination level and age distribution. A key finding is that increasing vaccination coverage above a certain level does not affect the mobility suppression level required to control the infection anymore for the cases of young population and heterogeneous age distributions. By investigating several migration and commuting patterns, it is found that shutting mobility in a few local places is favored against reducing mobility over the entire country network. In addition, commuting -and not migration-influences the spread level of the infection. The work offers an exclusive combined network-based and agent-based model that makes use of randomly generated mobility matrices.

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.

The influence of cross-border mobility on the COVID-19 epidemic in Nordic countries

Restrictions of cross-border mobility are typically used to prevent an emerging disease from entering a country in order to slow down its spread. However, such interventions can come with a significant societal cost and should thus be based on careful analysis and quantitative understanding on their effects. To this end, we model the influence of cross-border mobility on the spread of COVID-19 during 2020 in the neighbouring Nordic countries of Denmark, Finland, Norway and Sweden. We investigate the immediate impact of cross-border travel on disease spread and employ counterfactual scenarios to explore the cumulative effects of introducing additional infected individuals into a population during the ongoing epidemic. Our results indicate that the effect of inter-country mobility on epidemic growth is non-negligible essentially when there is sizeable mobility from a high prevalence country or countries to a low prevalence one. Our findings underscore the critical importance of accurate data and models on both epidemic progression and travel patterns in informing decisions related to inter-country mobility restrictions.

A novel indicator in epidemic monitoring through a case study of Ebola in West Africa (2014-2016)

The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014-2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (Rt) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when Rt approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when Rt is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and Rt = 1 while examining the E/S ratio across various values of S(0).

SARS-CoV-2 Transmission in Alberta, British Columbia, and Ontario, Canada, January 2020-January 2022

We estimated COVID-19 transmission potential and case burden by variant type in Alberta, British Columbia, and Ontario, Canada, during January 23, 2020-January 27, 2022; we also estimated the effectiveness of public health interventions to reduce transmission. We estimated time-varying reproduction number (Rt) over 7-day sliding windows and nonoverlapping time-windows determined by timing of policy changes. We calculated incidence rate ratios (IRRs) for each variant and compared rates to determine differences in burden among provinces. Rt corresponding with emergence of the Delta variant increased in all 3 provinces; British Columbia had the largest increase, 43.85% (95% credible interval [CrI] 40.71%-46.84%). Across the study period, IRR was highest for Omicron (8.74 [95% CrI 8.71-8.77]) and burden highest in Alberta (IRR 1.80 [95% CrI 1.79-1.81]). Initiating public health interventions was associated with lower Rt and relaxing restrictions and emergence of new variants associated with increases in Rt.

Incorporating testing volume into estimation of effective reproduction number dynamics

Branching process inspired models are widely used to estimate the effective reproduction number-a useful summary statistic describing an infectious disease outbreak-using counts of new cases. Case data is a real-time indicator of changes in the reproduction number, but is challenging to work with because cases fluctuate due to factors unrelated to the number of new infections. We develop a new model that incorporates the number of diagnostic tests as a surveillance model covariate. Using simulated data and data from the SARS-CoV-2 pandemic in California, we demonstrate that incorporating tests leads to improved performance over the state of the art.

An Intense Out-of-Season Rebound of Influenza Activity After the Relaxation of Coronavirus Disease 2019 Restrictions in Beijing, China

Background

The aim of this study was to investigate the changes of epidemic characteristics of influenza activity pre- and post-coronavirus disease 2019 (COVID-19) in Beijing, China.

Methods

Epidemiologic data were collected from the influenza surveillance system in Beijing. We compared epidemic intensity, epidemic onset and duration, and influenza transmissibility during the 2022-2023 season with pre-COVID-19 seasons from 2014 to 2020.

Results

The overall incidence rate of influenza in the 2022-2023 season was significantly higher than that of the pre-COVID-19 period, with the record-high level of epidemic intensity in Beijing. The onset and duration of the influenza epidemic period in 2022-2023 season was notably later and shorter than that of the 2014-2020 seasons. Maximum daily instantaneous reproduction number (Rt) of the 2022-2023 season (Rt = 2.31) was much higher than that of the pre-COVID-19 period (Rt = 1.49). The incidence of influenza A(H1N1) and A(H3N2) were the highest among children aged 0-4 years and 5-14 years, respectively, in the 2022-2023 season.

Conclusions

A late, intense, and short-term peak influenza activity was observed in the 2022-2023 season in Beijing. Children <15 years old were impacted the most by the interruption of influenza circulation during the COVID-19 pandemic. Maintaining continuous surveillance and developing targeted public health strategies of influenza is necessary.

Transmission dynamics of Zika virus with multiple infection routes and a case study in Brazil

The Zika virus (ZIKV) is a serious global public health crisis. A major control challenge is its multiple transmission modes. This paper aims to simulate the transmission patterns of ZIKV using a dynamic process-based epidemiological model written in ordinary differential equations, which incorporates the human-to-mosquito infection by bites and sewage, mosquito-to-human infection by bites, and human-to-human infection by sex. Mathematical analyses are carried out to calculate the basic reproduction number and backward bifurcation, and prove the existence and stability of the equilibria. The model is validated with infection data by applying it to the 2015-2016 ZIKV epidemic in Brazil. The results indicate that the reproduction number is estimated to be 2.13, in which the contributions by mosquito bite, sex and sewage account for 85.7%, 3.5% and 10.8%, respectively. This number and the morbidity rate are most sensitive to parameters related to mosquito ecology, rather than asymptomatic or human-to-human transmission. Multiple transmission routes and suitable temperature exacerbate ZIKV infection in Brazil, and the vast majority of human infection cases were prevented by the intervention implemented. These findings may provide new insights to improve the risk assessment of ZIKV infection.

Variability in the serial interval of COVID-19 in South Korea: a comprehensive analysis of age and regional influences

Introduction

Quantifying the transmissibility over time, particularly by region and age, using parameters such as serial interval and time-varying reproduction number, helps in formulating targeted interventions. Moreover, considering the impact of geographical factors on transmission provides valuable insights into the effectiveness of control measures.

Methods

Drawing on a comprehensive dataset of COVID-19 cases in South Korea, we analyzed transmission dynamics with a focus on age and regional variations. The dataset, compiled through the efforts of dedicated epidemiologists, includes information on symptom onset dates, enabling detailed investigations. The pandemic was divided into distinct phases, aligning with changes in policies, emergence of variants, and vaccination efforts. We analyzed various interventions such as social distancing, vaccination rates, school closures, and population density. Key parameters like serial interval, heatmaps, and time-varying reproduction numbers were used to quantify age and region-specific transmission trends.

Results

Analysis of transmission pairs within age groups highlighted the significant impact of school closure policies on the spread among individuals aged 0-19. This analysis also shed light on transmission dynamics within familial and educational settings. Changes in confirmed cases over time revealed a decrease in spread among individuals aged 65 and older, attributed to higher vaccination rates. Conversely, densely populated metropolitan areas experienced an increase in confirmed cases. Examination of time-varying reproduction numbers by region uncovered heterogeneity in transmission patterns, with regions implementing strict social distancing measures showing both increased confirmed cases and delayed spread, indicating the effectiveness of these policies.

Discussion

Our findings underscore the importance of evaluating and tailoring epidemic control policies based on key COVID-19 parameters. The analysis of social distancing measures, school closures, and vaccine impact provides valuable insights into controlling transmission. By quantifying the impact of these interventions on different age groups and regions, we contribute to the ongoing efforts to combat the COVID-19 pandemic effectively.

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

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

Impact of public health policy and mobility change on transmission potential of severe acute respiratory syndrome coronavirus 2 in Rhode Island, March 2020 - November 2021

To study the SARS-CoV-2 transmission potential in Rhode Island (RI) and its association with policy changes and mobility changes, the time-varying reproduction number, Rt, was estimated. The daily incident case counts (16 March 2020, through 30 November 2021) were bootstrapped within a 15-day sliding window and multiplied by Poisson-distributed multipliers (λ = 4, sensitivity analysis: 11) to generate 1000 estimated infection counts, to which EpiEstim was applied to generate Rt time series. The median Rt percentage change when policies changed was estimated. The time lag correlations were assessed between the 7-day moving average of the relative changes in Google mobility data in the first 90 days, and Rt and estimated infection count, respectively. There were three major pandemic waves in RI in 2020-2021: spring 2020, winter 2020-2021 and fall-winter 2021. The median Rt fluctuated within the range of 0.5-2 from April 2020 to November 2021. Mask mandate (18 April 2020) was associated with a decrease in Rt (-25.99%, 95% CrI: -37.42%, -14.30%). Termination of mask mandates on 6 July 2021 was associated with an increase in Rt (36.74%, 95% CrI: 27.20%, 49.13%). Positive correlations were found between changes in grocery and pharmacy, Rt retail and recreation, transit, and workplace visits, for both Rt and estimated infection count, respectively. Negative correlations were found between changes in residential area visits for both Rt and estimated infection count, respectively. Public health policies enacted in RI were associated with changes in the pandemic trajectory. This ecological study provides further evidence of how non-pharmaceutical interventions and vaccination slowed COVID-19 transmission in RI.

Comparing the Performance of Three Computational Methods for Estimating the Effective Reproduction Number

The effective reproduction number ( R t ) is one of the most important epidemiological parameters, providing suggestions for monitoring the development trend of diseases and also for adjusting the prevention and control policies. However, a few studies have focused on the performance of some common computational methods for Rt. The purpose of this article is to compare the performance of three computational methods for Rt: the time-dependent (TD) method, the new time-varying (NT) method, and the sequential Bayesian (SB) method. Four evaluation methods-accuracy, correlation coefficient, similarity based on trend, and dynamic time warping distance-were used to compare the effectiveness of three computational methods for Rt under different time lags and time windows. The results showed that the NT method was a better choice for real-time monitoring and analysis of the epidemic in the middle and late stages of the infectious disease. The TD method could reflect the change of the number of cases stably and accurately, and was more suitable for monitoring the change of Rt during the whole process of the epidemic outbreak. When the data were relatively stable, the SB method could also provide a reliable estimate for Rt, while the error would increase when the fluctuation in the number of cases increased. The results would provide suggestions for selecting appropriate Rt estimation methods and making policy adjustments more timely and effectively according to the change of Rt.

Wastewater-based reproduction numbers and projections of COVID-19 cases in three areas in Japan, November 2021 to December 2022

BackgroundWastewater surveillance has expanded globally as a means to monitor spread of infectious diseases. An inherent challenge is substantial noise and bias in wastewater data because of the sampling and quantification process, limiting the applicability of wastewater surveillance as a monitoring tool.AimTo present an analytical framework for capturing the growth trend of circulating infections from wastewater data and conducting scenario analyses to guide policy decisions.MethodsWe developed a mathematical model for translating the observed SARS-CoV-2 viral load in wastewater into effective reproduction numbers. We used an extended Kalman filter to infer underlying transmissions by smoothing out observational noise. We also illustrated the impact of different countermeasures such as expanded vaccinations and non-pharmaceutical interventions on the projected number of cases using three study areas in Japan during 2021-22 as an example.ResultsObserved notified cases were matched with the range of cases estimated by our approach with wastewater data only, across different study areas and virus quantification methods, especially when the disease prevalence was high. Estimated reproduction numbers derived from wastewater data were consistent with notification-based reproduction numbers. Our projections showed that a 10-20% increase in vaccination coverage or a 10% reduction in contact rate may suffice to initiate a declining trend in study areas.ConclusionOur study demonstrates how wastewater data can be used to track reproduction numbers and perform scenario modelling to inform policy decisions. The proposed framework complements conventional clinical surveillance, especially when reliable and timely epidemiological data are not available.

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.

Estimating SARS-CoV-2 transmission parameters between coinciding outbreaks in a university population and the surrounding community

Prior studies suggest that population heterogeneity in SARS-CoV-2 (COVID-19) transmission plays an important role in epidemic dynamics. During the fall of 2020, many US universities and the surrounding communities experienced an increase in reported incidence of SARS-CoV-2 infections, with a high disease burden among students. We explore the transmission dynamics of an outbreak of SARS-CoV-2 among university students, how it impacted the non-student population via cross-transmission, and how it could influence pandemic planning and response. Using surveillance data of reported SARS-CoV-2 cases, we developed a two-population SEIR model to estimate transmission parameters and evaluate how these subpopulations interacted during the 2020 Fall semester. We estimated the transmission rate among the university students (βU) and community residents (βC), as well as the rate of cross-transmission between the two subpopulations (βM) using particle Markov Chain Monte Carlo (pMCMC) simulation-based methods. We found that both populations were more likely to interact with others in their population and that cross-transmission was minimal. The cross-transmission estimate (βM) was considerably smaller [0.04 × 10-5 (95% CI: 0.00 × 10-5, 0.15 × 10-5)] compared to the community estimate (βC) at 2.09 × 10-5 (95% CI: 1.12 × 10-5, 2.90 × 10-5) and university estimate (βU) at 27.92 × 10-5 (95% CI: 19.97 × 10-5, 39.15 × 10-5). The higher within population transmission rates among the university and the community (698 and 52 times higher, respectively) when compared to the cross-transmission rate, suggests that these two populations did not transmit between each other heavily, despite their geographic overlap. During the first wave of the pandemic, two distinct epidemics occurred among two subpopulations within a relatively small US county population where university students accounted for roughly 41% of the total population. Transmission parameter estimates varied substantially with minimal or no cross-transmission between the subpopulations. Assumptions that county-level and other small populations are well-mixed during a respiratory viral pandemic should be reconsidered. More granular models reflecting overlapping subpopulations may assist with better-targeted interventions for local public health and healthcare facilities.

Near-term forecasting of Covid-19 cases and hospitalisations in Aotearoa New Zealand

Near-term forecasting of infectious disease incidence and consequent demand for acute healthcare services can support capacity planning and public health responses. Despite well-developed scenario modelling to support the Covid-19 response, Aotearoa New Zealand lacks advanced infectious disease forecasting capacity. We develop a model using Aotearoa New Zealand's unique Covid-19 data streams to predict reported Covid-19 cases, hospital admissions and hospital occupancy. The method combines a semi-mechanistic model for disease transmission to predict cases with Gaussian process regression models to predict the fraction of reported cases that will require hospital treatment. We evaluate forecast performance against out-of-sample data over the period from 2 October 2022 to 23 July 2023. Our results show that forecast performance is reasonably good over a 1-3 week time horizon, although generally deteriorates as the time horizon is lengthened. The model has been operationalised to provide weekly national and regional forecasts in real-time. This study is an important step towards development of more sophisticated situational awareness and infectious disease forecasting tools in Aotearoa New Zealand.

Explaining transmission rate variations and forecasting epidemic spread in multiple regions with a semiparametric mixed effects SIR model

The transmission rate is a central parameter in mathematical models of infectious disease. Its pivotal role in outbreak dynamics makes estimating the current transmission rate and uncovering its dependence on relevant covariates a core challenge in epidemiological research as well as public health policy evaluation. Here, we develop a method for flexibly inferring a time-varying transmission rate parameter, modeled as a function of covariates and a smooth Gaussian process (GP). The transmission rate model is further embedded in a hierarchy to allow information borrowing across parallel streams of regional incidence data. Crucially, the method makes use of optional vaccination data as a first step toward modeling of endemic infectious diseases. Computational techniques borrowed from the Bayesian spatial analysis literature enable fast and reliable posterior computation. Simulation studies reveal that the method recovers true covariate effects at nominal coverage levels. We analyze data from the COVID-19 pandemic and validate forecast intervals on held-out data. User-friendly software is provided to enable practitioners to easily deploy the method in public health research.

Estimating effective reproduction number revisited

Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks. In this study, we improve the estimation of the effective reproduction number through two main approaches. First, we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework. We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme. By doing so, we enhance the accuracy of approximating the underlying epidemic process compared to previous methods, even when the counting period is similar to the mean generation time of an infectious disease. Second, we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion. Specifically, given that observed incidence counts follow a negative binomial distribution, the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution. With this formulation, we establish posterior uncertainty bounds for the effective reproduction number. Finally, we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.

Monitoring the reproductive number of COVID-19 in France: Comparative estimates from three datasets

BACKGROUND

The effective reproduction number (Rt) quantifies the average number of secondary cases caused by one person with an infectious disease. Near-real-time monitoring of Rt during an outbreak is a major indicator used to monitor changes in disease transmission and assess the effectiveness of interventions. The estimation of Rt usually requires the identification of infected cases in the population, which can prove challenging with the available data, especially when asymptomatic people or with mild symptoms are not usually screened. The purpose of this study was to perform sensitivity analysis of Rt estimates for COVID-19 surveillance in France based on three data sources with different sensitivities and specificities for identifying infected cases.

METHODS

We applied a statistical method developed by Cori et al. to estimate Rt using (1) confirmed cases identified from positive virological tests in the population, (2) suspected cases recorded by a national network of emergency departments, and (3) COVID-19 hospital admissions recorded by a national administrative system to manage hospital organization.

RESULTS

Rt estimates in France from May 27, 2020, to August 12, 2022, showed similar temporal trends regardless of the dataset. Estimates based on the daily number of confirmed cases provided an earlier signal than the two other sources, with an average lag of 3 and 6 days for estimates based on emergency department visits and hospital admissions, respectively.

CONCLUSION

The COVID-19 experience confirmed that monitoring temporal changes in Rt was a key indicator to help the public health authorities control the outbreak in real time. However, gaining access to data on all infected people in the population in order to estimate Rt is not straightforward in practice. As this analysis has shown, the opportunity to use more readily available data to estimate Rt trends, provided that it is highly correlated with the spread of infection, provides a practical solution for monitoring the COVID-19 pandemic and indeed any other epidemic.

Data-driven models for the risk of infection and hospitalization during a pandemic: Case study on COVID-19 in Nepal

The newly emerging pandemic disease often poses unexpected troubles and hazards to the global health system, particularly in low and middle-income countries like Nepal. In this study, we developed mathematical models to estimate the risk of infection and the risk of hospitalization during a pandemic which are critical for allocating resources and planning health policies. We used our models in Nepal's unique data set to explore national and provincial-level risks of infection and risk of hospitalization during the Delta and Omicron surges. Furthermore, we used our model to identify the effectiveness of non-pharmaceutical interventions (NPIs) to mitigate COVID-19 in various groups of people in Nepal. Our analysis shows no significant difference in reproduction numbers in provinces between the Delta and Omicron surge periods, but noticeable inter-provincial disparities in the risk of infection (for example, during Delta (Omicron) surges, the risk of infection of Bagmati province is: ∼ 98.94 (89.62); Madhesh province: ∼ 12.16 (5.1); Karnali province ∼31.16 (3) per hundred thousands). Our estimates show a significantly low level of hospitalization risk during the Omicron surge compared to the Delta surge (hospitalization risk is: ∼10% in Delta and ∼2.5% in Omicron). We also found significant inter-provincial disparities in the hospitalization rate (for example, ∼ 6% in Madhesh province and ∼ 21% in Sudur Paschim) during the Delta surge. Moreover, our results show that closing only schools, colleges, and workplaces reduces the risk of infection by one-third, while a complete lockdown reduces the infections by two-thirds. Our study provides a framework for the computation of the risk of infection and the risk of hospitalization and offers helpful information for controlling the pandemic.

Estimating the time-varying reproduction number for COVID-19 in South Africa during the first four waves using multiple measures of incidence for public and private sectors across four waves

OBJECTIVES

The aim of this study was to quantify transmission trends in South Africa during the first four waves of the COVID-19 pandemic using estimates of the time-varying reproduction number (R) and to compare the robustness of R estimates based on three different data sources, and using data from public and private sector service providers.

METHODS

R was estimated from March 2020 through April 2022, nationally and by province, based on time series of rt-PCR-confirmed cases, hospitalisations, and hospital-associated deaths, using a method that models daily incidence as a weighted sum of past incidence, as implemented in the R package EpiEstim. R was also estimated separately using public and private sector data.

RESULTS

Nationally, the maximum case-based R following the introduction of lockdown measures was 1.55 (CI: 1.43-1.66), 1.56 (CI: 1.47-1.64), 1.46 (CI: 1.38-1.53) and 3.33 (CI: 2.84-3.97) during the first (Wuhan-Hu), second (Beta), third (Delta), and fourth (Omicron) waves, respectively. Estimates based on the three data sources (cases, hospitalisations, deaths) were generally similar during the first three waves, but higher during the fourth wave for case-based estimates. Public and private sector R estimates were generally similar except during the initial lockdowns and in case-based estimates during the fourth wave.

CONCLUSION

Agreement between R estimates using different data sources during the first three waves suggests that data from any of these sources could be used in the early stages of a future pandemic. The high R estimates for Omicron relative to earlier waves are interesting given a high level of exposure pre-Omicron. The agreement between public and private sector R estimates highlights that clients of the public and private sectors did not experience two separate epidemics, except perhaps to a limited extent during the strictest lockdowns in the first wave.

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.

The effective reproductive number: Modeling and prediction with application to the multi-wave Covid-19 pandemic

Classical compartmental models of infectious disease assume that spread occurs through a homogeneous population. This produces poor fits to real data, because individuals vary in their number of epidemiologically-relevant contacts, and hence in their ability to transmit disease. In particular, network theory suggests that super-spreading events tend to happen more often at the beginning of an epidemic, which is inconsistent with the homogeneity assumption. In this paper we argue that a flexible decay shape for the effective reproductive number (Rt) indexed by the susceptible fraction (St) is a theory-informed modeling choice, which better captures the progression of disease incidence over human populations. This, in turn, produces better retrospective fits, as well as more accurate prospective predictions of observed epidemic curves. We extend this framework to fit multi-wave epidemics, and to accommodate public health restrictions on mobility. We demonstrate the performance of this model by doing a prediction study over two years of the SARS-CoV2 pandemic.

Extending EpiEstim to estimate the transmission advantage of pathogen variants in real-time: SARS-CoV-2 as a case-study

The evolution of SARS-CoV-2 has demonstrated that emerging variants can set back the global COVID-19 response. The ability to rapidly assess the threat of new variants is critical for timely optimisation of control strategies. We present a novel method to estimate the effective transmission advantage of a new variant compared to a reference variant combining information across multiple locations and over time. Through an extensive simulation study designed to mimic real-time epidemic contexts, we show that our method performs well across a range of scenarios and provide guidance on its optimal use and interpretation of results. We also provide an open-source software implementation of our method. The computational speed of our tool enables users to rapidly explore spatial and temporal variations in the estimated transmission advantage. We estimate that the SARS-CoV-2 Alpha variant is 1.46 (95% Credible Interval 1.44-1.47) and 1.29 (95% CrI 1.29-1.30) times more transmissible than the wild type, using data from England and France respectively. We further estimate that Delta is 1.77 (95% CrI 1.69-1.85) times more transmissible than Alpha (England data). Our approach can be used as an important first step towards quantifying the threat of emerging or co-circulating variants of infectious pathogens in real-time.

A DNA Nanodevice-Based Platform with Diverse Capabilities

Social biotic colonies often perform intricate tasks by interindividual communication and cooperation. Inspired by these biotic behaviors, a DNA nanodevice community is proposed as a universal and scalable platform. The modular nanodevice as the infrastructure of platform contains a DNA origami triangular prism framework and a hairpin-swing arm machinery core. By coding and decoding a signal domain on the shuttled output strand in different nanodevices, an orthogonal inter-nanodevice communication network is established to connect multi-nanodevices into a functional platform. The nanodevice platform enables implementation of diverse tasks, including signal cascading and feedback, molecular input recording, distributed logic computing, and modeling of simulation for virus transmission. The nanodevice platform with powerful compatibility and programmability presents an elegant example of the combination of the distributed operation of multiple devices and the complicated interdevice communication network, and may become a new generation of intelligent DNA nanosystems.

Impact of vaccine measures on the transmission dynamics of COVID-19

In many nations, efforts to prevent and control COVID-19 have been significantly impeded by the SARS-CoV-2 virus ongoing mutation. The Omicron strain, a more recent and prevalent strain, has had more significant detrimental effects in countries worldwide. To investigate the impact of the Omicron BA.2 strain on vaccine efficacy, we proposed a model with vaccination and immunological decline in this research. Then, we fitted our model based on the number of daily new instances reported by the government in Jilin and Shanghai, China. We estimated the effective reproduction number Re = 4.71 for the Jilin and Re = 3.32 for Shanghai. Additionally, we do sensitivity analysis to identify the critical factors affecting the effective reproduction number Re. It was found that vaccination rate, effectiveness rate, and declining rate had a significant effect on Re. Further, we investigate the relevant parameter thresholds that make Re lower than unity. Finally, rich numerical experiments were then carried out. We observed that even when vaccine efficiency was not high, increasing vaccination rates had a significant effect on early disease transmission, that limiting social distance was the most economical and rational measure to control the spread of disease, and that for a short period, reducing immune decline was not significant in curbing disease transmission.

estimateR: an R package to estimate and monitor the effective reproductive number

BACKGROUND

Accurate estimation of the effective reproductive number ([Formula: see text]) of epidemic outbreaks is of central relevance to public health policy and decision making. We present estimateR, an R package for the estimation of the reproductive number through time from delayed observations of infection events. Such delayed observations include confirmed cases, hospitalizations or deaths. The package implements the methodology of Huisman et al. but modularizes the [Formula: see text] estimation procedure to allow easy implementation of new alternatives to the currently available methods. Users can tailor their analyses according to their particular use case by choosing among implemented options.

RESULTS

The estimateR R package allows users to estimate the effective reproductive number of an epidemic outbreak based on observed cases, hospitalization, death or any other type of event documenting past infections, in a fast and timely fashion. We validated the implementation with a simulation study: estimateR yielded estimates comparable to alternative publicly available methods while being around two orders of magnitude faster. We then applied estimateR to empirical case-confirmation incidence data for COVID-19 in nine countries and for dengue fever in Brazil; in parallel, estimateR is already being applied (i) to SARS-CoV-2 measurements in wastewater data and (ii) to study influenza transmission based on wastewater and clinical data in other studies. In summary, this R package provides a fast and flexible implementation to estimate the effective reproductive number for various diseases and datasets.

CONCLUSIONS

The estimateR R package is a modular and extendable tool designed for outbreak surveillance and retrospective outbreak investigation. It extends the method developed for COVID-19 by Huisman et al. and makes it available for a variety of pathogens, outbreak scenarios, and observation types. Estimates obtained with estimateR can be interpreted directly or used to inform more complex epidemic models (e.g. for forecasting) on the value of [Formula: see text].

Estimating SARS-CoV-2 infections and associated changes in COVID-19 severity and fatality

Background

The difficulty in identifying SARS-CoV-2 infections has not only been the major obstacle to control the COVID-19 pandemic but also to quantify changes in the proportion of infections resulting in hospitalization, intensive care unit (ICU) admission, or death.

Methods

We developed a model of SARS-CoV-2 transmission and vaccination informed by official estimates of the time-varying reproduction number to estimate infections that occurred in Italy between February 2020 and 2022. Model outcomes were compared with the Italian National surveillance data to estimate changes in the SARS-CoV-2 infection ascertainment ratio (IAR), infection hospitalization ratio (IHR), infection ICU ratio (IIR), and infection fatality ratio (IFR) in five different sub-periods associated with the dominance of the ancestral lineages and Alpha, Delta, and Omicron BA.1 variants.

Results

We estimate that, over the first 2 years of pandemic, the IAR ranged between 15% and 40% (range of 95%CI: 11%-61%), with a peak value in the second half of 2020. The IHR, IIR, and IFR consistently decreased throughout the pandemic with 22-44-fold reductions between the initial phase and the Omicron period. At the end of the study period, we estimate an IHR of 0.24% (95%CI: 0.17-0.36), IIR of 0.015% (95%CI: 0.011-0.023), and IFR of 0.05% (95%CI: 0.04-0.08).

Conclusions

Since 2021, changes in the dominant SARS-CoV-2 variant, vaccination rollout, and the shift of infection to younger ages have reduced SARS-CoV-2 infection ascertainment. The same factors, combined with the improvement of patient management and care, contributed to a massive reduction in the severity and fatality of COVID-19.

COVID-19 Pandemic: Did Strict Mobility Restrictions Save Lives and Healthcare Costs in Maharashtra, India?

INTRODUCTION

Maharashtra, India, remained a hotspot during the COVID-19 pandemic. After the initial complete lockdown, the state slowly relaxed restrictions. We aim to estimate the lockdown's impact on COVID-19 cases and associated healthcare costs.

METHODS

Using daily case data for 84 days (9 March-31 May 2020), we modeled the epidemic's trajectory and predicted new cases for different phases of lockdown. We fitted log-linear models to estimate the growth rate, basic (R₀), daily reproduction number (R_e), and case doubling time. Based on pre-restriction and Phase 1 R₀, we predicted new cases for the rest of the restriction phases, and we compared them with the actual number of cases during each phase. Furthermore, using the published and gray literature, we estimated the costs and savings of implementing these restrictions for the projected period, and we performed a sensitivity analysis.

RESULTS

The estimated median R₀ during the different phases was 1.14 (95% CI: 0.85, 1.45) for pre-lockdown, 1.67 (95% CI: 1.50, 1.82) for phase 1 (strict mobility restrictions), 1.24 (95% CI: 1.12, 1.35) for phase 2 (extension of phase 1 with no restrictions on agricultural and essential services), 1.12 (95% CI: 1.01, 1.23) for phase 3 (extension of phase 2 with mobility relaxations in areas with few infections), and 1.05 (95% CI: 0.99, 1.123) for phase 4 (implementation of localized lockdowns in high-case-load areas with fewer restrictions on other areas), respectively. The corresponding doubling time rate for cases (in days) was 17.78 (95% CI: 5.61, -15.19), 3.87 (95% CI: 3.15, 5.00), 10.37 (95% CI: 7.10, 19.30), 20.31 (95% CI: 10.70, 212.50), and 45.56 (95% CI: 20.50, -204.52). For the projected period, the cases could have reached 631,819 without the lockdown, as the actual reported number of cases was 64,975. From a healthcare perspective, the estimated total value of averted cases was INR 194.73 billion (USD 2.60 billion), resulting in net cost savings of 84.05%. The Incremental Cost-Effectiveness Ratio (ICER) per Quality Adjusted Life Year (QALY) for implementing the lockdown, rather than observing the natural course of the pandemic, was INR 33,812.15 (USD 450.83).

CONCLUSION

Maharashtra's early public health response delayed the pandemic and averted new cases and deaths during the first wave of the pandemic. However, we recommend that such restrictions be carefully used while considering the local socio-economic realities in countries like India.

Analysis of metapopulation models of the transmission of SARS-CoV-2 in the United States

During the COVID-19 pandemic, renewal equation estimates of time-varying effective reproduction numbers were useful to policymakers in evaluating the need for and impact of mitigation measures. Our objective here is to illustrate the utility of mechanistic expressions for the basic and effective (or intrinsic and realized) reproduction numbers, [Formula: see text] and related quantities derived from a Susceptible-Exposed-Infectious-Removed (SEIR) model including features of COVID-19 that might affect transmission of SARS-CoV-2, including asymptomatic, pre-symptomatic, and symptomatic infections, with which people may be hospitalized. Expressions from homogeneous host population models can be analyzed to determine the effort needed to reduce [Formula: see text] from [Formula: see text] to 1 and contributions of modeled mitigation measures. Our model is stratified by age, 0-4, 5-9, …, 75+ years, and location, the 50 states plus District of Columbia. Expressions from such heterogeneous host population models include subpopulation reproduction numbers, contributions from the above-mentioned infectious states, metapopulation numbers, subpopulation contributions, and equilibrium prevalence. While the population-immunity at which [Formula: see text] has captured the popular imagination, the metapopulation [Formula: see text] could be attained in an infinite number of ways even if only one intervention (e.g., vaccination) were capable of reducing [Formula: see text] However, gradients of expressions derived from heterogeneous host population models,[Formula: see text] can be evaluated to identify optimal allocations of limited resources among subpopulations. We illustrate the utility of such analytical results by simulating two hypothetical vaccination strategies, one uniform and other indicated by [Formula: see text] as well as the actual program estimated from one of the CDC's nationwide seroprevalence surveys conducted from mid-summer 2020 through the end of 2021.

Association of climatic variables with risk of transmission of influenza in Guangzhou, China, 2005-2021

BACKGROUND

Climatic variables constitute important extrinsic determinants of transmission and seasonality of influenza. Yet quantitative evidence of independent associations of viral transmissibility with climatic factors has thus far been scarce and little is known about the potential effects of interactions between climatic factors on transmission.

OBJECTIVE

This study aimed to examine the associations of key climatic factors with risk of influenza transmission in subtropical Guangzhou.

METHODS

Influenza epidemics were identified over a 17-year period using the moving epidemic method (MEM) from a dataset of N = 295,981 clinically- and laboratory-confirmed cases of influenza in Guangzhou. Data on eight key climatic variables were collected from China Meteorological Data Service Centre. Generalized additive model combined with the distributed lag non-linear model (DLNM) were developed to estimate the exposure-lag-response curve showing the trajectory of instantaneous reproduction number (R_t) across the distribution of each climatic variable after adjusting for depletion of susceptible, inter-epidemic effect and school holidays. The potential interaction effects of temperature, humidity and rainfall on influenza transmission were also examined.

RESULTS

Over the study period (2005-21), 21 distinct influenza epidemics with varying peak timings and durations were identified. Increasing air temperature, sunshine, absolute and relative humidity were significantly associated with lower R_t, while the associations were opposite in the case of ambient pressure, wind speed and rainfall. Rainfall, relative humidity, and ambient temperature were the top three climatic contributors to variance in transmissibility. Interaction models found that the detrimental association between high relative humidity and transmissibility was more pronounced at high temperature and rainfall.

CONCLUSION

Our findings are likely to help understand the complex role of climatic factors in influenza transmission, guiding informed climate-related mitigation and adaptation policies to reduce transmission in high density subtropical cities.

Modeling vaccination coverage during the 2022 central Ohio measles outbreak: a cross-sectional study

Background

Of the eight large (>50 cases) US postelimination outbreaks, the first and last occurred in Ohio. Ohio's vaccination registry is incomplete. Community-level immunity gaps threaten more than two decades of measles elimination in the US. We developed a statistical model, VaxEstim, to rapidly estimate the early-phase vaccination coverage and immunity gap in the exposed population during the 2022 Central Ohio outbreak.

Methods

We used reconstructed daily incidence (from publicly available data) and assumptions about the distribution of the serial interval, or the time between symptom onset in successive measles cases, to estimate the effective reproduction number (i.e., the average number of secondary infections caused by an infected individual in a partially immune population). We estimated early-phase measles vaccination coverage by comparing the effective reproduction number to the basic reproduction number (i.e., the average number of secondary infections caused by an infected individual in a fully susceptible population) while accounting for vaccine effectiveness. Finally, we estimated the early-phase immunity gap as the difference between the estimated critical vaccination threshold and vaccination coverage.

Findings

VaxEstim estimated the early-phase vaccination coverage as 53% (95% credible interval, 21%-77%), the critical vaccination threshold as 93%, and the immunity gap as 42% (95% credible interval, 18%-74%).

Interpretation

This study estimates a significant immunity gap in the exposed population during the early phase of the 2022 Central Ohio measles outbreak, suggesting a robust public health response is needed to identify the susceptible community and develop community-specific strategies to close the immunity gap.

Funding

This work was supported in part by the National Institute of General Medical Sciences, National Institutes of Health; the UK Medical Research Council (MRC); the Foreign, Commonwealth and Development Office; the National Institute for Health Research (NIHR) Health Protection Research Unit in Modelling Methodology; Imperial College London, and the London School of Hygiene & Tropical Medicine, Community Jameel; the EDCTP2 programme, supported by the EU; and the Sergei Brin Foundation.

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.

A Multi-SCALE Community Network-Based SEIQR Model to Evaluate the Dynamic NPIs of COVID-19

Regarding the problem of epidemic outbreak prevention and control, infectious disease dynamics models cannot support urban managers in reducing urban-scale healthcare costs through community-scale control measures, as they usually have difficulty meeting the requirements for simulation at different scales. In this paper, we propose combining contact networks at different spatial scales to study the COVID-19 outbreak in Shanghai from March to July 2022, calculate the initial Rt through the number of cases at the beginning of the outbreak, and evaluate the effectiveness of dynamic non-pharmaceutical interventions (NPIs) adopted at different time periods in Shanghai using our proposed approach. In particular, our proposed contact network is a three-layer multi-scale network that is used to distinguish social interactions occurring in areas of different sizes, as well as to distinguish between intensive and non-intensive population contacts. This susceptible-exposure-infection-quarantine-recovery (SEIQR) epidemic model constructed based on a multi-scale network can more effectively assess the feasibility of small-scale control measures, such as assessing community quarantine measures and mobility restrictions at different moments and phases of an epidemic. Our experimental results show that this model can meet the simulation needs at different scales, and our further discussion and analysis show that the spread of the epidemic in Shanghai from March to July 2022 can be successfully controlled by implementing a strict long-term dynamic NPI strategy.

Optimal Epidemic Control under Uncertainty: Tradeoffs between Information Collection and Other Actions

BACKGROUND

Recent epidemics and measures taken to control them-through vaccination or other actions-have highlighted the role and importance of uncertainty in public health. There is generally a tradeoff between information collection and other uses of resources. Whether this tradeoff is solved explicitly or implicitly, the concept of value of information is central to inform policy makers in an uncertain environment.

METHOD

We use a deterministic SIR (susceptible, infectious, recovered) disease emergence and transmission model with vaccination that can be administered as 1 or 2 doses. The disease parameters and vaccine characteristics are uncertain. We study the tradeoffs between information acquisition and 2 other measures: bringing vaccination forward and acquiring more vaccine doses. To do this, we quantify the expected value of perfect information (EVPI) under different constraints faced by public health authorities (i.e., the time of the vaccination campaign implementation and the number of vaccine doses available).

RESULTS

We discuss the appropriateness of different responses under uncertainty. We show that, in some cases, vaccinating later or with less vaccine doses but more information about the epidemic, and the efficacy of control strategies may bring better results than vaccinating earlier or with more doses and less information, respectively.

CONCLUSION

In the present methodological article, we show in an abstract setting how clearly defining and treating the tradeoff between information acquisition and the relaxation of constraints can improve public health decision making.

HIGHLIGHTS

Uncertainties can seriously hinder epidemic control, but resolving them is costly. Thus, there are tradeoffs between information collection and alternative uses of resources.We use a generic SIR model with vaccination and a value-of-information framework to explore these tradeoffs.We show in which cases vaccinating later with more information about the epidemic and the efficacy of control measures may be better-or not-than vaccinating earlier with less information.We show in which cases vaccinating with fewer vaccine doses and more information about the epidemic and the efficacy of control measures may be better-or not-than vaccinating with more doses and less information.

A new method for the joint estimation of instantaneous reproductive number and serial interval during epidemics

Although some methods for estimating the instantaneous reproductive number during epidemics have been developed, the existing frameworks usually require information on the distribution of the serial interval and/or additional contact tracing data. However, in the case of outbreaks of emerging infectious diseases with an unknown natural history or undetermined characteristics, the serial interval and/or contact tracing data are often not available, resulting in inaccurate estimates for this quantity. In the present study, a new framework was specifically designed for joint estimates of the instantaneous reproductive number and serial interval. Concretely, a likelihood function for the two quantities was first introduced. Then, the instantaneous reproductive number and the serial interval were modeled parametrically as a function of time using the interpolation method and a known traditional distribution, respectively. Using the Bayesian information criterion and the Markov Chain Monte Carlo method, we ultimately obtained their estimates and distribution. The simulation study revealed that our estimates of the two quantities were consistent with the ground truth. Seven data sets of historical epidemics were considered and further verified the robust performance of our method. Therefore, to some extent, even if we know only the daily incidence, our method can accurately estimate the instantaneous reproductive number and serial interval to provide crucial information for policymakers to design appropriate prevention and control interventions during epidemics.

Spatiotemporal reproduction number with Bayesian model selection for evaluation of emerging infectious disease transmissibility: an application to COVID-19 national surveillance data

BACKGROUND

To control emerging diseases, governments often have to make decisions based on limited evidence. The effective or temporal reproductive number is used to estimate the expected number of new cases caused by an infectious person in a partially susceptible population. While the temporal dynamic is captured in the temporal reproduction number, the dominant approach is currently based on modeling that implicitly treats people within a population as geographically well mixed.

METHODS

In this study we aimed to develop a generic and robust methodology for estimating spatiotemporal dynamic measures that can be instantaneously computed for each location and time within a Bayesian model selection and averaging framework. A simulation study was conducted to demonstrate robustness of the method. A case study was provided of a real-world application to COVID-19 national surveillance data in Thailand.

RESULTS

Overall, the proposed method allowed for estimation of different scenarios of reproduction numbers in the simulation study. The model selection chose the true serial interval when included in our study whereas model averaging yielded the weighted outcome which could be less accurate than model selection. In the case study of COVID-19 in Thailand, the best model based on model selection and averaging criteria had a similar trend to real data and was consistent with previously published findings in the country.

CONCLUSIONS

The method yielded robust estimation in several simulated scenarios of force of transmission with computing flexibility and practical benefits. Thus, this development can be suitable and practically useful for surveillance applications especially for newly emerging diseases. As new outbreak waves continue to develop and the risk changes on both local and global scales, our work can facilitate policymaking for timely disease control.

Local travel behaviour under continuing COVID-19 waves- A proxy for pandemic fatigue?

COVID-19 continues to threaten the world. Relaxing local travel behaviours on preventing the spread of COVID-19, may increase the infection risk in subsequent waves of SARS-CoV-2 transmission. In this study, we analysed changes in the travel behaviour of different population groups (adult, child, student, elderly) during four pandemic waves in Hong Kong before January 2021, by 4-billion second-by-second smartcard records of subway. A significant continuous relaxation in human travel behaviour was observed during the four waves of SARS-CoV-2 transmission. Residents sharply reduced their local travel by 51.9%, 50.1%, 27.6%, and 20.5% from the first to fourth pandemic waves, respectively. The population flow in residential areas, workplaces, schools, shopping areas, amusement areas and border areas, decreased on average by 30.3%, 33.5%, 41.9%, 58.1%, 85.4% and 99.6%, respectively, during the pandemic weeks. We also found that many other cities around the world experienced a similar relaxation trend in local travel behaviour, by comparing traffic congestion data during the pandemic with data from the same period in 2019. The quantitative pandemic fatigue in local travel behaviour could help governments partially predicting personal protective behaviours, and thus to suggest more accurate interventions during subsequent waves, especially for highly infectious virus variants such as Omicron.

A note on variable susceptibility, the herd-immunity threshold and modeling of infectious diseases

The unfolding of the COVID-19 pandemic has been very difficult to predict using mathematical models for infectious diseases. While it has been demonstrated that variations in susceptibility have a damping effect on key quantities such as the incidence peak, the herd-immunity threshold and the final size of the pandemic, this complex phenomenon is almost impossible to measure or quantify, and it remains unclear how to incorporate it for modeling and prediction. In this work we show that, from a modeling perspective, variability in susceptibility on an individual level is equivalent with a fraction θ of the population having an "artificial" sterilizing immunity. We also derive novel formulas for the herd-immunity threshold and the final size of the pandemic, and show that these values are substantially lower than predicted by the classical formulas, in the presence of variable susceptibility. In the particular case of SARS-CoV-2, there is by now undoubtedly variable susceptibility due to waning immunity from both vaccines and previous infections, and our findings may be used to greatly simplify models. If such variations were also present prior to the first wave, as indicated by a number of studies, these findings can help explain why the magnitude of the initial waves of SARS-CoV-2 was relatively low, compared to what one may have expected based on standard models.

A Bayesian nonparametric method for detecting rapid changes in disease transmission

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

A modelling approach to estimate the transmissibility of SARS-CoV-2 during periods of high, low, and zero case incidence

Against a backdrop of widespread global transmission, a number of countries have successfully brought large outbreaks of COVID-19 under control and maintained near-elimination status. A key element of epidemic response is the tracking of disease transmissibility in near real-time. During major outbreaks, the effective reproduction number can be estimated from a time-series of case, hospitalisation or death counts. In low or zero incidence settings, knowing the potential for the virus to spread is a response priority. Absence of case data means that this potential cannot be estimated directly. We present a semi-mechanistic modelling framework that draws on time-series of both behavioural data and case data (when disease activity is present) to estimate the transmissibility of SARS-CoV-2 from periods of high to low - or zero - case incidence, with a coherent transition in interpretation across the changing epidemiological situations. Of note, during periods of epidemic activity, our analysis recovers the effective reproduction number, while during periods of low - or zero - case incidence, it provides an estimate of transmission risk. This enables tracking and planning of progress towards the control of large outbreaks, maintenance of virus suppression, and monitoring the risk posed by re-introduction of the virus. We demonstrate the value of our methods by reporting on their use throughout 2020 in Australia, where they have become a central component of the national COVID-19 response.

An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data

In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when estimating epidemiological parameters. The main statistical challenge in models that intrinsically account for a misreporting process lies in the joint estimation of the time-varying reproduction number and the delay/underreporting parameters. Existing Bayesian approaches typically rely on Markov chain Monte Carlo algorithms that are extremely costly from a computational perspective. We propose a much faster alternative based on Laplacian-P-splines (LPS) that combines Bayesian penalized B-splines for flexible and smooth estimation of the instantaneous reproduction number and Laplace approximations to selected posterior distributions for fast computation. Assuming a known generation interval distribution, the incidence at a given calendar time is governed by the epidemic renewal equation and the delay structure is specified through a composite link framework. Laplace approximations to the conditional posterior of the spline vector are obtained from analytical versions of the gradient and Hessian of the log-likelihood, implying a drastic speed-up in the computation of posterior estimates. Furthermore, the proposed LPS approach can be used to obtain point estimates and approximate credible intervals for the delay and reporting probabilities. Simulation of epidemics with different combinations for the underreporting rate and delay structure (one-day, two-day, and weekend delays) show that the proposed LPS methodology delivers fast and accurate estimates outperforming existing methods that do not take into account underreporting and delay patterns. Finally, LPS is illustrated in two real case studies of epidemic outbreaks.