Estimation Of Reproduction Number Research Articles

Reliability of Early Estimates of the Basic Reproduction Number of COVID-19: A Systematic Review and Meta-Analysis.

Objective: This systematic review estimated the pooled for early COVID-19 outbreaks and identified the impact of study-related factors such as methods, study location and study period on the estimated . Methods: We searched electronic databases for human studies published in English between 1 December 2019 and 30 September 2020 with no restriction on country/region. Two investigators independently performed the data extraction of the studies selected for inclusion during full-text screening. The primary outcome, , was analysed by random-effects meta-analysis using the restricted maximum likelihood method. Results: We identified 26,425 studies through our search and included 151 articles in the systematic review, among which 81 were included in the meta-analysis. The estimates of from studies included in the meta-analysis ranged from 0.4 to 12.58. The pooled for COVID-19 was estimated to be 2.66 (95% CI, 2.41–2.94). The results showed heterogeneity among studies and strong evidence of a small-study effect. Conclusions: The high heterogeneity in studies makes the use of the for basic epidemic planning difficult and presents a huge problem for risk assessment and data synthesis. Consensus on the use of for outbreak assessment is needed, and its use for assessing epidemic risk is not recommended.

Filtering and improved Uncertainty Quantification in the dynamic estimation of effective reproduction numbers

The effective reproduction number Rt measures an infectious disease’s transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches do not quantify the uncertainty correctly in estimating Rt, as expected by the observed variability in contagion patterns. We elaborate on the Bayesian estimation of Rt by improving on the Poisson sampling model of Cori et al. (2013). By adding an autoregressive latent process, we build a Dynamic Linear Model on the log of observed Rts, resulting in a filtering type Bayesian inference. We use a conjugate analysis, and all calculations are explicit. Results show an improved uncertainty quantification on the estimation of Rt’s, with a reliable method that could safely be used by non-experts and within other forecasting systems. We illustrate our approach with recent data from the current COVID19 epidemic in Mexico.

Estimation of local time-varying reproduction numbers in noisy surveillance data.

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia.This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

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

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

Estimation of the basic reproduction number of COVID-19 from the incubation period distribution.

The estimates of the future course of spreading of the SARS-CoV-2 virus are frequently based on Markovian models in which the duration of residence in any compartment is exponentially distributed. Accordingly, the basic reproduction number R_0 is also determined from formulae where it is related to the parameters of such models. The observations show that the start of infectivity of an individual appears nearly at the same time as the onset of symptoms, while the distribution of the incubation period is not an exponential. Therefore, we propose a method for estimation of R_0 for COVID-19 based on the empirical incubation period distribution and assumed very short infectivity period that lasts only few days around the onset of symptoms. We illustrate this venerable approach to estimate R_0 for six major European countries in the first wave of the epidemic. The calculations show that even if the infectivity starts 2 days before the onset of symptoms and stops instantly when they appear (immediate isolation), the value of R_0 is larger than that from the classical, SIR model. For more realistic cases, when only individuals with mild symptoms spread the virus for few days after onset of symptoms, the respective values are even larger. This implies that calculations of R_0 and other characteristics of spreading of COVID-19 based on the classical, Markovian approaches should be taken very cautiously.

Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2.

The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.

Modeling COVID-19 Transmissions and Evaluation of Large Scale Social Restriction in Jakarta, Indonesia

This paper presents mathematical modeling and quantitative evaluation of Large Scale Social Restriction (LSSR) in Jakarta between 10 April and 4 June 2020. The special capital region of Jakarta is the only province among 34 provinces in Indonesia with an average Testing Positivity Rate (TPR) below 5% recommended by the World Health Organization (WHO). The transmission model is based on a discrete-time compartmental epidemiological model incorporating suspected cases. The quantitative evaluation is measured based on the estimation of the time-varying effective reproduction number (Rt). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by Rt < 1. However, once the LSSR was relaxed, the effective reproduction number increased significantly. The model is further used for short-term forecasting to mitigate the course of the pandemic.

An assessment of transmission dynamics via time-varying reproduction number of the second wave of the COVID-19 epidemic in Fiji.

This study involves the estimation of a key epidemiological parameter for evaluating and monitoring the transmissibility of a disease. The time-varying reproduction number is the index for quantifying the transmissibility of infectious diseases. Accurate and timely estimation of the time-varying reproduction number is essential for optimizing non-pharmacological interventions and movement control orders during epidemics. The time-varying reproduction number for the second wave of the pandemic in Fiji is estimated using the popular EpiEstim R package and the publicly available COVID-19 data from 19 April 2021 to 1 December 2021. Our findings show that the non-pharmacological interventions and movement control orders introduced and enforced by the Fijian Government had a significant impact in preventing the spread of COVID-19. Moreover, the results show that many restrictions were either relaxed or eased when the time-varying reproduction number was below the threshold value of 1. The results have provided some information on the second wave of the COVID-19 pandemic that could be used in the future as a guide for public health policymakers in Fiji. Estimation of time-varying reproduction numbers would be helpful for continuous monitoring of the effectiveness of the current public health policies that are being implemented in Fiji.

Analysis of the Geographic Transmission Differences of COVID-19 in China Caused by Population Movement and Population Density.

The coronavirus disease (COVID-19) has led to a global pandemic and caused huge healthy and economic losses. Non-pharmaceutical interventions, especially contact tracing and social distance restrictions, play a vital role in the control of COVID-19. Understanding the spatial impact is essential for designing such a control policy. Based on epidemic data of the confirmed cases after the Wuhan lockdown, we calculate the invasive reproduction numbers of COVID-19 in the different regions of China. Statistical analysis indicates a significant positive correlation between the reproduction numbers and the population input sizes from Wuhan, which indicates that the large-scale population movement contributed a lot to the geographic spread of COVID-19 in China. Moreover, there is a significant positive correlation between reproduction numbers and local population densities, which shows that the higher population density intensifies the spread of disease. Considering that in the early stage, there were sequential imported cases that affected the estimation of reproduction numbers, we classify the imported cases and local cases through the information of epidemiological data and calculate the net invasive reproduction number to quantify the local spread of the epidemic. The results are applied to the design of border control policy on the basis of vaccination coverage.

Spatio-Temporal Characteristics of Dengue Outbreaks

Based on a data set of dengue cases in the Brazilian city of Fortaleza, collected from 2011 to 2016, we study the spatio-temporal characteristics of dengue outbreaks to characterize epidemic and non-epidemic years. First, we identify regions that show a high incidence of dengue cases and mosquito larvae in different years and analyze their corresponding correlations. We find that the characteristic correlation length of the epidemic is at least of the order of the system size, suggesting that factors such as citizen mobility may play a significant role in driving the spatial spread of the disease. We also find that in epidemic years, spatial correlations are substantially higher with a distribution skewed towards large values than non-epidemic years. Inspired by this observation, we perform a mean-field estimation of the basic reproduction number and find that the estimated values agree well with the values reported for other regions in Brazil and other countries, pointing towards similar underlying spreading mechanisms. These findings provide insights into the spreading characteristics of dengue in densely populated areas and may be relevant for improving disease containment strategies.

Measuring Basic Reproduction Number to Assess Effects of Nonpharmaceutical Interventions on Nosocomial SARS-CoV-2 Transmission.

Outbreaks of SARS-CoV-2 infection frequently occur in hospitals. Preventing nosocomial infection requires insight into hospital transmission. However, estimates of the basic reproduction number (R0) in care facilities are lacking. Analyzing a closely monitored SARS-CoV-2 outbreak in a hospital in early 2020, we estimated the patient-to-patient transmission rate and R0. We developed a model for SARS-CoV-2 nosocomial transmission that accounts for stochastic effects and undetected infections and fit it to patient test results. The model formalizes changes in testing capacity over time, and accounts for evolving PCR sensitivity at different stages of infection. R0 estimates varied considerably across wards, ranging from 3 to 15 in different wards. During the outbreak, the hospital introduced a contact precautions policy. Our results strongly support a reduction in the hospital-level R0 after this policy was implemented, from 8.7 to 1.3, corresponding to a policy efficacy of 85% and demonstrating the effectiveness of nonpharmaceutical interventions.

Estimation of Reproduction Number for Covid-19 with Statistical Correction of Notifications Delay

The pandemic of Covid-19 began in Brazil in February 2020. To evaluate the evolution of pandemics some metrics can be estimated, such as the reproduction number, Rt, and the basic reproduction number, R0. Due to the delay in the notifications, these estimates may present a bias. Taking the reported data, besides a sample of individuals who reported the day of symptoms onset, it is possible to estimate delay probabilities and to perform a deconvolution to correct the notifications' delay. In this work, it was performed a corrected estimate of Rt. This estimate is done based on the curve of notifications corrected through deconvolution. The approach is applied in three country cities and in the capital of Minas Gerais state. The behavior of Rt concerning the Minas Consciente program was evaluated. It was observed that the corrected Rt was more suitable to measure the effect of the program when compared to the raw Rt. When it was determined a more rigid mobility and activities regime by the program, it was observed a decrease in the median of the variation of the Rt of the cities studied.

Preliminary Estimation of the Basic Reproduction Number of SARS-CoV-2 in the Middle East

Up to April 9, 2020, 142490 cases have been confirmed as COVID-19 infection including 5705 associated deaths in the Middle East. Most of the countries, such as Qatar, Bahrain, Iraq, Kuwait, United Arab Emirates (UAE), Oman, Lebanon, and Saudi Arabia have imported COVID-19 cases from Iran. Using the available data from WHO webpage, up to 9 April 2020, we traced epidemic curves and estimated the basic reproduction number ( ) of COVID-19 through the susceptible-infectious-recovered (SIR) model for the Middle East countries. Epidemic curves for Middle East countries and territory show similar trend as Iran, with a couple of weeks’ delay in time. In SIR model, ranged between 7.41 as in Turkey to lowest as 2.60 for Oman whereas basic reproduction number for Iran, Kuwait, Bahrain, Qatar, Saudi Arabia, United Arab Emirates (UAE), Oman, Jordan, Egypt, Lebanon, Syria, Israel, West Bank and Gaza Strip territory, and Cyprus were 4.13, 2.71, 3.39, 4.18, 4.45, 2.75, 2.60, 3.52, 3.35, 3.16, 4.99, 4.08, 2.89, and 4.05, respectively. This study indicates an important trend on an early outbreak of COVID-19 based on estimated for the Middle East countries, mean 3.76 for COVID-19, with median and interquartile range (IQR) in the Middle East.

Real-time estimation of the epidemic reproduction number: Scoping review of the applications and challenges.

The time-varying reproduction number (Rt) is an important measure of transmissibility during outbreaks. Estimating whether and how rapidly an outbreak is growing (Rt > 1) or declining (Rt < 1) can inform the design, monitoring and adjustment of control measures in real-time. We use a popular R package for Rt estimation, EpiEstim, as a case study to evaluate the contexts in which Rt estimation methods have been used and identify unmet needs which would enable broader applicability of these methods in real-time. A scoping review, complemented by a small EpiEstim user survey, highlight issues with the current approaches, including the quality of input incidence data, the inability to account for geographical factors, and other methodological issues. We summarise the methods and software developed to tackle the problems identified, but conclude that significant gaps remain which should be addressed to enable easier, more robust and applicable estimation of Rt during epidemics.

Appropriately smoothing prevalence data to inform estimates of growth rate and reproduction number

The time-varying reproduction number (Rt) can change rapidly over the course of a pandemic due to changing restrictions, behaviours, and levels of population immunity. Many methods exist that allow the estimation of Rt from case data. However, these are not easily adapted to point prevalence data nor can they infer Rt across periods of missing data. We developed a Bayesian P-spline model suitable for fitting to a wide range of epidemic time-series, including point-prevalence data. We demonstrate the utility of the model by fitting to periodic daily SARS-CoV-2 swab-positivity data in England from the first 7 rounds (May 2020–December 2020) of the REal-time Assessment of Community Transmission-1 (REACT-1) study. Estimates of Rt over the period of two subsequent rounds (6–8 weeks) and single rounds (2–3 weeks) inferred using the Bayesian P-spline model were broadly consistent with estimates from a simple exponential model, with overlapping credible intervals. However, there were sometimes substantial differences in point estimates. The Bayesian P-spline model was further able to infer changes in Rt over shorter periods tracking a temporary increase above one during late-May 2020, a gradual increase in Rt over the summer of 2020 as restrictions were eased, and a reduction in Rt during England’s second national lockdown followed by an increase as the Alpha variant surged. The model is robust against both under-fitting and over-fitting and is able to interpolate between periods of available data; it is a particularly versatile model when growth rate can change over small timescales, as in the current SARS-CoV-2 pandemic. This work highlights the importance of pairing robust methods with representative samples to track pandemics.

Modelling preventive measures and their effect on generation times in emerging epidemics.

We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.

Pandemic Times-A Helping Hand Against COVID

Abstract: The novel coronavirus (COVID-19) that was first reported at the end of 2019 has impacted almost every aspect of life as we know it. This paper focuses on the incidence of the disease in India and Maharashtra—two of the most affected Landmasses. Using one simple machine learning algorithms, we model the daily and cumulative incidence of COVID-19 in India and Maharashtra during the early stage of the outbreak, and compute estimates for basic measures of the infectiousness of the disease including the basic reproduction number, growth rate, and doubling time. Estimates of the basic reproduction number were found to be larger than 1 in both cases, with values taking a huge leap every months as they double their mutation rate. Estimates were also computed for the more dynamic effective reproduction number, which showed that since the first cases were confirmed in the respective countries the severity has generally been decreasing. The predictive ability of the machine learning algorithms was found to give a better fit and simple estimates of the daily incidence for the affected places. The following website gives us a particular idea about the entire covid situation in Maharashtra.

Estimation of the basic reproduction number of Alpha and Delta variants of COVID-19 pandemic in Iran.

Estimating the basic reproduction number of a pandemic and the changes that appear on this value over time provide a good understanding of the contagious nature of the virus and efficiency of the controlling strategies. In this paper, we focus on studying the basic reproduction number (R0) for two important variants of COVID-19 pandemic in Iran: Alpha and Delta variants. We use four different methods, three statistical models and one mathematical model, to compute R0: Exponential Growth Rate (EGR), Maximum Likelihood (ML), Sequential Bayesian (SB), and time-dependent SIR model. Alpha variant of COVID-19 was active in Iran from March 10, 2021 until June 10, 2021. Our computations indicate that total R0 of this variant according to EGR, ML, SB, and SIR model is respectively 0.9999 (95% CI: 0.9994-1), 1.046 (95% CI: 1.044-1.049), 1.06 (95% CI: 1.03-1.08), and 2.79 (95% CI: 2.77-2.81) in the whole active time interval. Moreover, during the time interval from April 3, 2021 to April 9, 2021 in which this variant was in its exponential growth in Iran, R0 of Alpha variant in Iran according to SB, EGR, ML, and SIR model is respectively 2.26 (95% CI: 2.04-2.49), 2.64 (95% CI: 2.58-2.7), 11.38 (95% CI: 11.28-11.48), and 12.13 (95% CI: 12.12-12.14). Delta variant was active in Iran during the time interval from June 22, 2021 until September 22, 2021. Our computations show that during the time interval from July 3, 2021 to July 8, 2021 in which this variant was in its exponential growth in Iran, R0 of Delta variant in Iran according to SB, EGR, ML, and SIR model is respectively 3 (95% CI: 2.34-3.66), 3.1 (95% CI: 3.02-3.17), 12 (95% CI: 11.89-12.12), and 23.3 (95% CI: 23.19-23.41). Further, total R0 of Delta variant in Iran in the whole active time interval according to EGR, ML, SB, and SIR model is respectively 1.042 (95% CI: 1.04-1.043), 1.053 (95% CI: 1.051-1.055), 0.79 (95% CI: 0.63-0.95), and 5.65 (95% CI: 5.6-5.7). As the results show Delta variant was more severe than Alpha variant in Iran. Chasing the changes in R0 during each variant shows that the controlling strategies applied were effective in controlling the virus spread.

Assortative mixing among vaccination groups and biased estimation of reproduction numbers

Assortative mixing among vaccination groups and biased estimation of reproduction numbers

Source code and secondary data of the stochastic process based COVID-19 simulation model.

The novel coronavirus disease (COVID-19) culminated in a pandemic with many countries affected in varying stages. We aimed to develop a simulation environment for COVID-19 spread, taking environmental and social factors into account. This program consists of three main components; a stochastic process-based model for simulating epidemics, a basic reproduction number estimation unit and a graphics generator. The model can take a variety of environmental factors as input and simulate expected behaviours of the infection spread, enabling policymakers and the scientific community to test the effects of different mitigation strategies in a sandbox.