scholarly journals Estimating effective reproduction number using generation time versus serial interval, with application to COVID-19 in the Greater Toronto Area, Canada

2020 ◽  
Author(s):  
Jesse Knight ◽  
Sharmistha Mishra
Keyword(s):  
Time Series ◽  
Generation Time ◽  
Time Distribution ◽  
Reproduction Number ◽  
Reproductive Number ◽  
Transmission Potential ◽  
Greater Toronto Area ◽  
Critical Measure ◽  
Serial Interval ◽  
Interval Distribution

AbstractBackgroundThe effective reproductive number Re(t) is a critical measure of epidemic potential. Re(t) can be calculated in near real time using an incidence time series and the generation time distribution—the time between infection events in an infector-infectee pair. In calculating Re(t), the generation time distribution is often approximated by the serial interval distribution—the time between symptom onset in an infector-infectee pair. However, while generation time must be positive by definition, serial interval can be negative if transmission can occur before symptoms, such as in covid-19, rendering such an approximation improper in some contexts.MethodsWe developed a method to infer the generation time distribution from parametric definitions of the serial interval and incubation period distributions. We then compared estimates of Re(t) for covid-19 in the Greater Toronto Area of Canada using: negative-permitting versus non-negative serial interval distributions, versus the inferred generation time distribution.ResultsWe estimated the generation time of covid-19 to be Gamma-distributed with mean 3.99 and standard deviation 2.96 days. Relative to the generation time distribution, non-negative serial interval distribution caused overestimation of Re(t) due to larger mean, while negative-permitting serial interval distribution caused underestimation of Re(t) due to larger variance.ImplicationsApproximation of the generation time distribution of covid-19 with non-negative or negative-permitting serial interval distributions when calculating Re(t) may result in over or underestimation of transmission potential, respectively.

scholarly journals On the relationship between serial interval, infectiousness profile and generation time

2020 ◽  
Author(s):  
Sonja Lehtinen ◽  
Peter Ashcroft ◽  
Sebastian Bonhoeffer
Keyword(s):  
Symptom Onset ◽  
Generation Time ◽  
Time Distribution ◽  
Contact Tracing ◽  
Time Interval ◽  
Single Individual ◽  
Serial Interval ◽  
The Impact ◽  
The Relationship ◽  
Interval Distribution

The timing of transmission plays a key role in the dynamics and controllability of an epidemic. However, observing the distribution of generation times (time interval between the points of infection of an infector and infectee in a transmission pair) requires data on infection times, which are generally unknown. The timing of symptom onset is more easily observed; the generation time distribution is therefore often estimated based on the serial interval distribution (distribution of time intervals between symptom onset of an infector and an infectee). This estimation follows one of two approaches: i) approximating the generation time distribution by the serial interval distribution; or ii) deriving the generation time distribution from the serial interval and incubation period (time interval between infection and symptom onset in a single individual) distributions. These two approaches make different -- and not always explicitly stated -- assumptions about the relationship between infectiousness and symptoms, resulting in different generation time distributions with the same mean but unequal variances. Here, we clarify the assumptions that each approach makes and show that neither set of assumptions is plausible for most pathogens. However, the variances of the generation time distribution derived under each assumption can reasonably be considered as upper (approximation with serial interval) and lower (derivation from serial interval) bounds. Thus, we suggest a pragmatic solution is to use both approaches and treat these as edge cases in downstream analysis. We discuss the impact of the variance of the generation time distribution on the controllability of an epidemic through strategies based on contact tracing, and we show that underestimating this variance is likely to overestimate controllability.

scholarly journals Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis

2018 ◽  
Vol 146 (12) ◽  
pp. 1478-1494 ◽  
Author(s):  
Y. Ma ◽  
C. R. Horsburgh ◽  
L. F. White ◽  
H. E. Jenkins
Keyword(s):  
Systematic Review ◽  
Parameter Estimation ◽  
The Netherlands ◽  
Cause Of Death ◽  
Reproduction Number ◽  
Reproductive Number ◽  
Interval Estimates ◽  
Transmission Parameters ◽  
Serial Interval ◽  
Number Of Publications

AbstractTuberculosis (TB) is the leading global infectious cause of death. Understanding TB transmission is critical to creating policies and monitoring the disease with the end goal of TB elimination. To our knowledge, there has been no systematic review of key transmission parameters for TB. We carried out a systematic review of the published literature to identify studies estimating either of the two key TB transmission parameters: the serial interval (SI) and the reproductive number. We identified five publications that estimated the SI and 56 publications that estimated the reproductive number. The SI estimates from four studies were: 0.57, 1.42, 1.44 and 1.65 years; the fifth paper presented age-specific estimates ranging from 20 to 30 years (for infants <1 year old) to <5 years (for adults). The reproductive number estimates ranged from 0.24 in the Netherlands (during 1933–2007) to 4.3 in China in 2012. We found a limited number of publications and many high TB burden settings were not represented. Certain features of TB dynamics, such as slow transmission, complicated parameter estimation, require novel methods. Additional efforts to estimate these parameters for TB are needed so that we can monitor and evaluate interventions designed to achieve TB elimination.

scholarly journals The basic reproduction number and prediction of the epidemic size of the novel coronavirus (COVID-19) in Shahroud, Iran

2020 ◽  
Vol 148 ◽  
Author(s):  
A. Khosravi ◽  
R. Chaman ◽  
M. Rohani-Rasaf ◽  
F. Zare ◽  
S. Mehravaran ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Early Stage ◽  
Screening Tests ◽  
The Novel ◽  
Epidemic Size ◽  
Serial Interval ◽  
Novel Coronavirus ◽  
Interval Distribution ◽  
The Basic Reproduction Number

Abstract The aim of this study was to estimate the basic reproduction number (R0) of COVID-19 in the early stage of the epidemic and predict the expected number of new cases in Shahroud in Northeastern Iran. The R0 of COVID-19 was estimated using the serial interval distribution and the number of incidence cases. The 30-day probable incidence and cumulative incidence were predicted using the assumption that daily incidence follows a Poisson distribution determined by daily infectiousness. Data analysis was done using ‘earlyR’ and ‘projections’ packages in R software. The maximum-likelihood value of R0 was 2.7 (95% confidence interval (CI): 2.1−3.4) for the COVID-19 epidemic in the early 14 days and decreased to 1.13 (95% CI 1.03–1.25) by the end of day 42. The expected average number of new cases in Shahroud was 9.0 ± 3.8 cases/day, which means an estimated total of 271 (95% CI: 178–383) new cases for the period between 02 April to 03 May 2020. By day 67 (27 April), the effective reproduction number (Rt), which had a descending trend and was around 1, reduced to 0.70. Based on the Rt for the last 21 days (days 46–67 of the epidemic), the prediction for 27 April to 26 May is a mean daily cases of 2.9 ± 2.0 with 87 (48–136) new cases. In order to maintain R below 1, we strongly recommend enforcing and continuing the current preventive measures, restricting travel and providing screening tests for a larger proportion of the population.

scholarly journals Caveats on COVID-19 herd immunity threshold: the Spain case

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
David García-García ◽  
Enrique Morales ◽  
Eva S. Fonfría ◽  
Isabel Vigo ◽  
Cesar Bordehore
Keyword(s):  
Upper Bound ◽  
Generation Time ◽  
Time Distribution ◽  
Herd Immunity ◽  
Late Summer ◽  
Spanish Population ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Population Estimates ◽  
Parameter Measuring

AbstractAfter a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

scholarly journals On the relationship between serial interval, infectiousness profile and generation time

2021 ◽  
Vol 18 (174) ◽  
pp. 20200756
Author(s):  
Sonja Lehtinen ◽  
Peter Ashcroft ◽  
Sebastian Bonhoeffer
Keyword(s):  
Symptom Onset ◽  
Generation Time ◽  
Time Distribution ◽  
Contact Tracing ◽  
Time Interval ◽  
Single Individual ◽  
Generation Times ◽  
Serial Interval ◽  
The Impact ◽  
The Relationship

The timing of transmission plays a key role in the dynamics and controllability of an epidemic. However, observing generation times—the time interval between the infection of an infector and an infectee in a transmission pair—requires data on infection times, which are generally unknown. The timing of symptom onset is more easily observed; generation times are therefore often estimated based on serial intervals—the time interval between symptom onset of an infector and an infectee. This estimation follows one of two approaches: (i) approximating the generation time distribution by the serial interval distribution or (ii) deriving the generation time distribution from the serial interval and incubation period—the time interval between infection and symptom onset in a single individual—distributions. These two approaches make different—and not always explicitly stated—assumptions about the relationship between infectiousness and symptoms, resulting in different generation time distributions with the same mean but unequal variances. Here, we clarify the assumptions that each approach makes and show that neither set of assumptions is plausible for most pathogens. However, the variances of the generation time distribution derived under each assumption can reasonably be considered as upper (approximation with serial interval) and lower (derivation from serial interval) bounds. Thus, we suggest a pragmatic solution is to use both approaches and treat these as edge cases in downstream analysis. We discuss the impact of the variance of the generation time distribution on the controllability of an epidemic through strategies based on contact tracing, and we show that underestimating this variance is likely to overestimate controllability.

scholarly journals Transmission potential of the novel coronavirus (COVID-19) onboard the Diamond Princess Cruises Ship, 2020

2020 ◽  
Author(s):  
Kenji Mizumoto ◽  
Gerardo Chowell
Keyword(s):  
Mathematical Modeling ◽  
Time Series ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
The Novel ◽  
Epidemic Threshold ◽  
Transmission Potential ◽  
Incidence Data ◽  
The Mean ◽  
Novel Coronavirus

AbstractAn outbreak of COVID-19 developed aboard the Princess Cruises Ship during January-February 2020. Using mathematical modeling and time-series incidence data describing the trajectory of the outbreak among passengers and crew members, we characterize how the transmission potential varied over the course of the outbreak. Our estimate of the mean reproduction number in the confined setting reached values as high as ∼11, which is higher than mean estimates reported from community-level transmission dynamics in China and Singapore (approximate range: 1.1-7). Our findings suggest that Rt decreased substantially compared to values during the early phase after the Japanese government implemented an enhanced quarantine control. Most recent estimates of Rt reached values largely below the epidemic threshold, indicating that a secondary outbreak of the novel coronavirus was unlikely to occur aboard the Diamond Princess Ship.

The discrete-time Kermack–McKendrick model: A versatile and computationally attractive framework for modeling epidemics

2021 ◽  
Vol 118 (39) ◽  
pp. e2106332118
Author(s):  
Odo Diekmann ◽  
Hans G. Othmer ◽  
Robert Planqué ◽  
Martin C. J. Bootsma
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Generation Time ◽  
Time Distribution ◽  
Reproduction Number ◽  
Compartmental Models ◽  
Infectious Period ◽  
Initial Growth ◽  
Fixed Duration ◽  
Spread Of Infection

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuous-time Kermack–McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

scholarly journals The long-term dynamics of tuberculosis and other diseases with long serial intervals: implications of and for changing reproduction numbers

1998 ◽  
Vol 121 (2) ◽  
pp. 309-324 ◽  
Author(s):  
E. VYNNYCKY ◽  
P. E. M. FINE
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
England And Wales ◽  
Transmission Potential ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Net Reproduction ◽  
Epidemiological Parameters ◽  
The Basic Reproduction Number

The net and basic reproduction numbers are among the most widely-applied concepts in infectious disease epidemiology. A net reproduction number (the average number of secondary infectious cases resulting from each case in a given population) of above 1 is conventionally associated with an increase in incidence; the basic reproduction number (defined analogously for a ‘totally susceptible’ population) provides a standard measure of the ‘transmission potential’ of an infection. Using a model of the epidemiology of tuberculosis in England and Wales since 1900, we demonstrate that these measures are difficult to apply if disease can follow reinfection, and that they lose their conventional interpretations if important epidemiological parameters, such as the rate of contact between individuals, change over the time interval between successive cases in a chain of transmission (the serial interval).The net reproduction number for tuberculosis in England and Wales appears to have been approximately 1 from 1900 until 1950, despite concurrent declines in morbidity and mortality rates, and it declined rapidly in the second half of this century. The basic reproduction number declined from about 3 in 1900, reached 2 by 1950, and first fell below 1 in about 1960. Reductions in effective contact between individuals over this period, measured in terms of the average number of individuals to whom each case could transmit the infection, meant that the conventional basic reproduction number measure (which does not consider subsequent changes in epidemiological parameters) for a given year failed to reflect the ‘actual transmission potential’ of the infection. This latter property is better described by a variant of the conventional measure which takes secular trends in contact into account. These results are relevant for the interpretation of trends in any infectious disease for which epidemiological parameters change over time periods comparable to the infectious period, incubation period or serial interval.

scholarly journals China’s effective control and other countries’ uncharted challenge against COVID-19: an epidemiological and modelling study

2020 ◽  
Author(s):  
Lingling Zheng ◽  
Qin Kang ◽  
Xiujuan Chen ◽  
Shuai Huang ◽  
Dong Liu ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Case Reports ◽  
Effective Control ◽  
Second Step ◽  
Incidence Data ◽  
Step Procedure ◽  
Serial Interval ◽  
More Care ◽  
Interval Distribution ◽  
Over Time

Abstract Objective: In this study, we use the time-dependent reproduction number (Rt) to comprise the COVID transmissibility across different countries.Methods: We used data from Jan 20, 2019, to Feb 29, 2020, on the number of newly confirmed cases, obtained from the reports published by the CDC, to infer the incidence of infectious over time. A two-step procedure was used to estimate the Rt. The first step used data on known index-secondary cases pairs, from publicly available case reports, to estimate the serial interval distribution. The second step estimated the Rt jointly from the incidence data and the information data in the first step. Rt was then used to simulate the epidemics across all major cities in China and typical countries worldwide. Results: Based on a total of 126 index-secondary cases pairs from 4 international regions, we estimated that the serial interval for SARS-2-CoV was 4.18 (IQR 1.92 – 6.65) days. Domestically, Rt of China, Hubei province, Wuhan had fallen below 1.0 on 9 Feb, 10 Feb and 13 Feb (Rt were 0.99±0.02, 0.99±0.02 and 0.96±0.02), respectively. Internationally, as of 26 Feb, statistically significant periods of COVID spread (Rt >1) were identified for most regions, except for Singapore (Rt was 0.92±0.17).Conclusions: The epidemic in China has been well controlled, but the worldwide pandemic has not been well controlled. Worldwide preparedness and vulnerability against COVID-19 should be regarded with more care.

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