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Rastegar M, Nazar E, Nasehi M, Sharafi S, Fakoor V, Shakeri MT. 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. Infect Dis Model 2024; 9:963-974. [PMID: 38873589 PMCID: PMC11169078 DOI: 10.1016/j.idm.2024.05.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Revised: 04/09/2024] [Accepted: 05/07/2024] [Indexed: 06/15/2024] Open
Abstract
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.
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Affiliation(s)
- Maryam Rastegar
- Department of Biostatistics, School of Health, Mashhad University of Medical Sciences, Mashhad, Iran
| | - Eisa Nazar
- Orthopedic Research Center, Mazandaran University of Medical Sciences, Sari, Iran
| | - Mahshid Nasehi
- Centre for Communicable Diseases Control, Ministry of Health and Medical Education, Tehran, Iran
| | - Saeed Sharafi
- Centre for Communicable Diseases Control, Ministry of Health and Medical Education, Tehran, Iran
| | - Vahid Fakoor
- Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
| | - Mohammad Taghi Shakeri
- Department of Biostatistics, School of Health, Mashhad University of Medical Sciences, Mashhad, Iran
- Social Determinants of Health Research Center, Mashhad University of Medical Sciences, Mashhad, Iran
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2
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Bizzotto A, Guzzetta G, Marziano V, Del Manso M, Mateo Urdiales A, Petrone D, Cannone A, Sacco C, Poletti P, Manica M, Zardini A, Trentini F, Fabiani M, Bella A, Riccardo F, Pezzotti P, Ajelli M, Merler S. Increasing situational awareness through nowcasting of the reproduction number. Front Public Health 2024; 12:1430920. [PMID: 39234082 PMCID: PMC11371679 DOI: 10.3389/fpubh.2024.1430920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2024] [Accepted: 08/05/2024] [Indexed: 09/06/2024] Open
Abstract
Background The time-varying reproduction number R is a critical variable for situational awareness during infectious disease outbreaks; however, delays between infection and reporting of cases hinder its accurate estimation in real-time. A number of nowcasting methods, leveraging available information on data consolidation delays, have been proposed to mitigate this problem. Methods In this work, we retrospectively validate the use of a nowcasting algorithm during 18 months of the COVID-19 pandemic in Italy by quantitatively assessing its performance against standard methods for the estimation of R. Results Nowcasting significantly reduced the median lag in the estimation of R from 13 to 8 days, while concurrently enhancing accuracy. Furthermore, it allowed the detection of periods of epidemic growth with a lead of between 6 and 23 days. Conclusions Nowcasting augments epidemic awareness, empowering better informed public health responses.
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Affiliation(s)
- Andrea Bizzotto
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
- Department of Mathematics, University of Trento, Trento, Italy
| | - Giorgio Guzzetta
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
| | | | - Martina Del Manso
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | | | - Daniele Petrone
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Andrea Cannone
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Chiara Sacco
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Piero Poletti
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
| | - Mattia Manica
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
| | - Agnese Zardini
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
| | - Filippo Trentini
- Covid Crisis Lab, Bocconi University, Milan, Italy
- Department of Social and Political Sciences, Bocconi University, Milan, Italy
| | - Massimo Fabiani
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Antonino Bella
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Flavia Riccardo
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Patrizio Pezzotti
- Department of Infectious Diseases, Istituto Superiore di Sanità, Rome, Italy
| | - Marco Ajelli
- Laboratory for Computational Epidemiology and Public Health, Department of Epidemiology and Biostatistics, Indiana University School of Public Health, Bloomington, IN, United States
| | - Stefano Merler
- Center for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
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3
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Hulland EN, Charpignon ML, El Hayek GY, Zhao L, Desai AN, Majumder MS. Estimating time-varying cholera transmission and oral cholera vaccine effectiveness in Haiti and Cameroon, 2021-2023. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2024:2024.06.12.24308792. [PMID: 39185512 PMCID: PMC11343247 DOI: 10.1101/2024.06.12.24308792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 08/27/2024]
Abstract
In 2023, cholera affected approximately 1 million people and caused more than 5000 deaths globally, predominantly in low-income and conflict settings. In recent years, the number of new cholera outbreaks has grown rapidly. Further, ongoing cholera outbreaks have been exacerbated by conflict, climate change, and poor infrastructure, resulting in prolonged crises. As a result, the demand for treatment and intervention is quickly outpacing existing resource availability. Prior to improved water and sanitation systems, cholera, a disease primarily transmitted via contaminated water sources, also routinely ravaged high-income countries. Crumbling infrastructure and climate change are now putting new locations at risk - even in high-income countries. Thus, understanding the transmission and prevention of cholera is critical. Combating cholera requires multiple interventions, the two most common being behavioral education and water treatment. Two-dose oral cholera vaccination (OCV) is often used as a complement to these interventions. Due to limited supply, countries have recently switched to single-dose vaccines (OCV1). One challenge lies in understanding where to allocate OCV1 in a timely manner, especially in settings lacking well-resourced public health surveillance systems. As cholera occurs and propagates in such locations, timely, accurate, and openly accessible outbreak data are typically inaccessible for disease modeling and subsequent decision-making. In this study, we demonstrated the value of open-access data to rapidly estimate cholera transmission and vaccine effectiveness. Specifically, we obtained non-machine readable (NMR) epidemic curves for recent cholera outbreaks in two countries, Haiti and Cameroon, from figures published in situation and disease outbreak news reports. We used computational digitization techniques to derive weekly counts of cholera cases, resulting in nominal differences when compared against the reported cumulative case counts (i.e., a relative error rate of 5.67% in Haiti and 0.54% in Cameroon). Given these digitized time series, we leveraged EpiEstim-an open-source modeling platform-to derive rapid estimates of time-varying disease transmission via the effective reproduction number (R t ). To compare OCV1 effectiveness in the two considered countries, we additionally used VaxEstim, a recent extension of EpiEstim that facilitates the estimation of vaccine effectiveness via the relation among three inputs: the basic reproduction number (R 0 ),R t , and vaccine coverage. Here, with Haiti and Cameroon as case studies, we demonstrated the first implementation of VaxEstim in low-resource settings. Importantly, we are the first to use VaxEstim with digitized data rather than traditional epidemic surveillance data. In the initial phase of the outbreak, weekly rolling average estimates ofR t were elevated in both countries: 2.60 in Haiti [95% credible interval: 2.42-2.79] and 1.90 in Cameroon [1.14-2.95]. These values are largely consistent with previous estimates ofR 0 in Haiti, where average values have ranged from 1.06 to 3.72, and in Cameroon, where average values have ranged from 1.10 to 3.50. In both Haiti and Cameroon, this initial period of high transmission preceded a longer period during whichR t oscillated around the critical threshold of 1. Our results derived from VaxEstim suggest that Haiti had higher OCV1 effectiveness than Cameroon (75.32% effective [54.00-86.39%] vs. 54.88% [18.94-84.90%]). These estimates of OCV1 effectiveness are generally aligned with those derived from field studies conducted in other countries. Thus, our case study reinforces the validity of VaxEstim as an alternative to costly, time-consuming field studies of OCV1 effectiveness. Indeed, prior work in South Sudan, Bangladesh, and the Democratic Republic of the Congo reported OCV1 effectiveness ranging from approximately 40% to 80%. This work underscores the value of combining NMR sources of outbreak case data with computational techniques and the utility of VaxEstim for rapid, inexpensive estimation of vaccine effectiveness in data-poor outbreak settings.
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Affiliation(s)
- Erin N Hulland
- Computational Health Informatics Program, Boston Children's Hospital & Harvard Medical School, Boston, MA, United States
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
| | - Marie-Laure Charpignon
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA, United States
| | - Ghinwa Y El Hayek
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
| | - Lihong Zhao
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
- Department of Mathematics, Virginia Tech, Blacksburg, VA, United States
| | - Angel N Desai
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
- Department of Internal Medicine, Division of Infectious Diseases, University of California, Davis Health Medical Center, Sacramento, CA, United States
| | - Maimuna S Majumder
- Computational Health Informatics Program, Boston Children's Hospital & Harvard Medical School, Boston, MA, United States
- Comp Epi Dispersed Volunteer Research Network, Boston, MA, United States
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4
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Eales O, McCaw JM, Shearer FM. Challenges in the case-based surveillance of infectious diseases. ROYAL SOCIETY OPEN SCIENCE 2024; 11:240202. [PMID: 39205993 PMCID: PMC11349437 DOI: 10.1098/rsos.240202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 05/01/2024] [Accepted: 06/14/2024] [Indexed: 09/04/2024]
Abstract
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.
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Affiliation(s)
- Oliver Eales
- Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
| | - James M. McCaw
- Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
- School of Mathematics and Statistics, The University of Melbourne, Parkville, Australia
| | - Freya M. Shearer
- Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Parkville, Australia
- Infectious Disease Ecology and Modelling, Telethon Kids Institute, Perth, Australia
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5
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Ogi-Gittins I, Hart WS, Song J, Nash RK, Polonsky J, Cori A, Hill EM, Thompson RN. A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. Epidemics 2024; 47:100773. [PMID: 38781911 DOI: 10.1016/j.epidem.2024.100773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Revised: 02/29/2024] [Accepted: 05/13/2024] [Indexed: 05/25/2024] Open
Abstract
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.
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Affiliation(s)
- I Ogi-Gittins
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Coventry CV4 7AL, UK
| | - W S Hart
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - J Song
- Communicable Disease Surveillance Centre, Health Protection Division, Public Health Wales, Cardiff CF10 4BZ, UK
| | - R K Nash
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College, London W2 1PG, UK
| | - J Polonsky
- Geneva Centre of Humanitarian Studies, University of Geneva, Geneva 1205, Switzerland
| | - A Cori
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College, London W2 1PG, UK
| | - E M Hill
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Coventry CV4 7AL, UK
| | - R N Thompson
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.
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6
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Charniga K, Madewell ZJ, Masters NB, Asher J, Nakazawa Y, Spicknall IH. Nowcasting and forecasting the 2022 U.S. mpox outbreak: Support for public health decision making and lessons learned. Epidemics 2024; 47:100755. [PMID: 38452454 DOI: 10.1016/j.epidem.2024.100755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 01/14/2024] [Accepted: 02/26/2024] [Indexed: 03/09/2024] Open
Abstract
In June of 2022, the U.S. Centers for Disease Control and Prevention (CDC) Mpox Response wanted timely answers to important epidemiological questions which can now be answered more effectively through infectious disease modeling. Infectious disease models have shown to be valuable tools for decision making during outbreaks; however, model complexity often makes communicating the results and limitations of models to decision makers difficult. We performed nowcasting and forecasting for the 2022 mpox outbreak in the United States using the R package EpiNow2. We generated nowcasts/forecasts at the national level, by Census region, and for jurisdictions reporting the greatest number of mpox cases. Modeling results were shared for situational awareness within the CDC Mpox Response and publicly on the CDC website. We retrospectively evaluated forecast predictions at four key phases (early, exponential growth, peak, and decline) during the outbreak using three metrics, the weighted interval score, mean absolute error, and prediction interval coverage. We compared the performance of EpiNow2 with a naïve Bayesian generalized linear model (GLM). The EpiNow2 model had less probabilistic error than the GLM during every outbreak phase except for the early phase. We share our experiences with an existing tool for nowcasting/forecasting and highlight areas of improvement for the development of future tools. We also reflect on lessons learned regarding data quality issues and adapting modeling results for different audiences.
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Affiliation(s)
- Kelly Charniga
- Division of High-Consequence Pathogens and Pathology, National Center for Emerging and Zoonotic Infectious Diseases, CDC, USA.
| | | | | | - Jason Asher
- Center for Forecasting and Outbreak Analytics, CDC, USA
| | - Yoshinori Nakazawa
- Division of High-Consequence Pathogens and Pathology, National Center for Emerging and Zoonotic Infectious Diseases, CDC, USA
| | - Ian H Spicknall
- Division of Sexually Transmitted Disease Prevention, National Center for HIV, Viral Hepatitis, STD, & TB Prevention, CDC, USA
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7
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Goldstein IH, Wakefield J, Minin VM. Incorporating testing volume into estimation of effective reproduction number dynamics. JOURNAL OF THE ROYAL STATISTICAL SOCIETY. SERIES A, (STATISTICS IN SOCIETY) 2024; 187:436-453. [PMID: 38617598 PMCID: PMC11009926 DOI: 10.1093/jrsssa/qnad128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 09/04/2023] [Accepted: 09/10/2023] [Indexed: 04/16/2024]
Abstract
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.
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Affiliation(s)
| | - Jon Wakefield
- Departments of Biostatistics and Statistics, University of Washington, Seattle, WA, USA
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8
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Eales O, Riley S. Differences between the true reproduction number and the apparent reproduction number of an epidemic time series. Epidemics 2024; 46:100742. [PMID: 38227994 DOI: 10.1016/j.epidem.2024.100742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 12/21/2023] [Accepted: 01/11/2024] [Indexed: 01/18/2024] Open
Abstract
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.
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Affiliation(s)
- Oliver Eales
- Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia; School of Public Health, Imperial College London, London, United Kingdom; MRC Centre for Global infectious Disease Analysis, Imperial College London, London, United Kingdom; Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, United Kingdom.
| | - Steven Riley
- School of Public Health, Imperial College London, London, United Kingdom; MRC Centre for Global infectious Disease Analysis, Imperial College London, London, United Kingdom; Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, United Kingdom.
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9
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Bonaldi C, Fouillet A, Sommen C, Lévy-Bruhl D, Paireau J. Monitoring the reproductive number of COVID-19 in France: Comparative estimates from three datasets. PLoS One 2023; 18:e0293585. [PMID: 37906577 PMCID: PMC10617725 DOI: 10.1371/journal.pone.0293585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 10/17/2023] [Indexed: 11/02/2023] Open
Abstract
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.
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Affiliation(s)
- Christophe Bonaldi
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Anne Fouillet
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Cécile Sommen
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Daniel Lévy-Bruhl
- Infectious Diseases Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Juliette Paireau
- Infectious Diseases Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
- Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Université de Paris Cité, CNRS UMR 2000, Paris, France
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10
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Li K, Wang J, Xie J, Rui J, Abudunaibi B, Wei H, Liu H, Zhang S, Li Q, Niu Y, Chen T. Advancements in Defining and Estimating the Reproduction Number in Infectious Disease Epidemiology. China CDC Wkly 2023; 5:829-834. [PMID: 37814634 PMCID: PMC10560332 DOI: 10.46234/ccdcw2023.158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/11/2023] [Indexed: 10/11/2023] Open
Affiliation(s)
- Kangguo Li
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayi Wang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayuan Xie
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jia Rui
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Buasiyamu Abudunaibi
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hongjie Wei
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hong Liu
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Shuo Zhang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Qun Li
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Yan Niu
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Tianmu Chen
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
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11
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Scire J, Huisman JS, Grosu A, Angst DC, Lison A, Li J, Maathuis MH, Bonhoeffer S, Stadler T. estimateR: an R package to estimate and monitor the effective reproductive number. BMC Bioinformatics 2023; 24:310. [PMID: 37568078 PMCID: PMC10416499 DOI: 10.1186/s12859-023-05428-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 07/24/2023] [Indexed: 08/13/2023] Open
Abstract
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].
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Affiliation(s)
- Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland.
- Swiss Institute of Bioinformatics, Lausanne, Switzerland.
| | - Jana S Huisman
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
- Department of Physics, Massachusetts Institute of Technology, Cambridge, USA
| | - Ana Grosu
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Daniel C Angst
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Adrian Lison
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Jinzhou Li
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Marloes H Maathuis
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Sebastian Bonhoeffer
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland.
- Swiss Institute of Bioinformatics, Lausanne, Switzerland.
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12
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Nash RK, Bhatt S, Cori A, Nouvellet P. Estimating the epidemic reproduction number from temporally aggregated incidence data: A statistical modelling approach and software tool. PLoS Comput Biol 2023; 19:e1011439. [PMID: 37639484 PMCID: PMC10491397 DOI: 10.1371/journal.pcbi.1011439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 09/08/2023] [Accepted: 08/18/2023] [Indexed: 08/31/2023] Open
Abstract
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.
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Affiliation(s)
- Rebecca K. Nash
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
| | - Samir Bhatt
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
- Section of Epidemiology, Department of Public Health, University of Copenhagen, Copenhagen, Denmark
| | - Anne Cori
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
| | - Pierre Nouvellet
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
- School of Life Sciences, University of Sussex, Brighton, United Kingdom
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13
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Sebastiani G, Spassiani I. New Insights into the Estimation of Reproduction Numbers during an Epidemic. Vaccines (Basel) 2022; 10:1788. [PMID: 36366299 PMCID: PMC9694736 DOI: 10.3390/vaccines10111788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 10/18/2022] [Accepted: 10/18/2022] [Indexed: 09/10/2024] Open
Abstract
In this paper, we deal with the problem of estimating the reproduction number Rt during an epidemic, as it represents one of the most used indicators to study and control this phenomenon. In particular, we focus on two issues. First, to estimate Rt, we consider the use of positive test case data as an alternative to the first symptoms data, which are typically used. We both theoretically and empirically study the relationship between the two approaches. Second, we modify a method for estimating Rt during an epidemic that is widely used by public institutions in several countries worldwide. Our procedure is not affected by the problems deriving from the hypothesis of Rt local constancy, which is assumed in the standard approach. We illustrate the results obtained by applying the proposed methodologies to real and simulated SARS-CoV-2 datasets. In both cases, we also apply some specific methods to reduce systematic and random errors affecting the data. Our results show that the Rt during an epidemic can be estimated by using the positive test data, and that our estimator outperforms the standard estimator that makes use of the first symptoms data. It is hoped that the techniques proposed here could help in the study and control of epidemics, particularly the current SARS-CoV-2 pandemic.
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Affiliation(s)
- Giovanni Sebastiani
- Istituto per le Applicazioni del Calcolo Mauro Picone, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Rome, Italy
- Mathematics Department “Guido Castelnuovo”, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Department of Mathematics and Statistics, University of Tromsø, H. Hansens veg 18, 9019 Tromsø, Norway
- Istituto Nazionale di Geofisica e Vulcanologia (INGV), Via di Vigna Murata 605, 00143 Rome, Italy
| | - Ilaria Spassiani
- Istituto Nazionale di Geofisica e Vulcanologia (INGV), Via di Vigna Murata 605, 00143 Rome, Italy
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14
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Gressani O, Wallinga J, Althaus CL, Hens N, Faes C. EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number. PLoS Comput Biol 2022; 18:e1010618. [PMID: 36215319 PMCID: PMC9584461 DOI: 10.1371/journal.pcbi.1010618] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 10/20/2022] [Accepted: 09/30/2022] [Indexed: 11/17/2022] Open
Abstract
In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t. It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of [Formula: see text] by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of [Formula: see text] in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a "plug-in'' estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of [Formula: see text] as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.
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Affiliation(s)
- Oswaldo Gressani
- Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
| | - Jacco Wallinga
- Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, The Netherlands
| | - Christian L. Althaus
- Institute of Social and Preventive Medicine, University of Bern, Bern, Switzerland
| | - Niel Hens
- Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
- Centre for Health Economics Research and Modelling Infectious Diseases, Vaxinfectio, University of Antwerp, Antwerp, Belgium
| | - Christel Faes
- Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
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