On realized serial and generation intervals given control measures: The COVID-19 pandemic case

The SARS-CoV-2 pathogen is currently spreading worldwide and its propensity for presymptomatic and asymptomatic transmission makes it difficult to control. The control measures adopted in several countries aim at isolating individuals once diagnosed, limiting their social interactions and consequently their transmission probability. These interventions, which have a strong impact on the disease dynamics, can affect the inference of the epidemiological quantities. We first present a theoretical explanation of the effect caused by non-pharmaceutical intervention measures on the mean serial and generation intervals. Then, in a simulation study, we vary the assumed efficacy of control measures and quantify the effect on the mean and variance of realized generation and serial intervals. The simulation results show that the realized serial and generation intervals both depend on control measures and their values contract according to the efficacy of the intervention strategies. Interestingly, the mean serial interval differs from the mean generation interval. The deviation between these two values depends on two factors. First, the number of undiagnosed infectious individuals. Second, the relationship between infectiousness, symptom onset and timing of isolation. Similarly, the standard deviations of realized serial and generation intervals do not coincide, with the former shorter than the latter on average. The findings of this study are directly relevant to estimates performed for the current COVID-19 pandemic. In particular, the effective reproduction number is often inferred using both daily incidence data and the generation interval. Failing to account for either contraction or mis-specification by using the serial interval could lead to biased estimates of the effective reproduction number. Consequently, this might affect the choices made by decision makers when deciding which control measures to apply based on the value of the quantity thereof.

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Epidemiology of a bubonic plague outbreak in Glasgow, Scotland in 1900

Royal Society Open Science ◽

10.1098/rsos.181695 ◽

2019 ◽

Vol 6 (1) ◽

pp. 181695 ◽

Cited By ~ 8

Author(s):

Katharine R. Dean ◽

Fabienne Krauer ◽

Boris V. Schmid

Keyword(s):

Yersinia Pestis ◽

Reproduction Number ◽

Control Measures ◽

High Rate ◽

Bubonic Plague ◽

The Third ◽

Serial Interval ◽

The Mean ◽

First Time ◽

Epidemiological Parameters

On 3 August 1900, bubonic plague ( Yersinia pestis ) broke out in Glasgow for the first time during the Third Pandemic. The local sanitary authorities rigorously tracked the spread of the disease and they found that nearly all of the 35 cases could be linked by contact with a previous case. Despite trapping hundreds of rats in the area, there was no evidence of a rat epizootic and the investigators speculated that the outbreak could be due to human-to-human transmission of bubonic plague. Here we use a likelihood-based method to reconstruct transmission trees for the outbreak. From the description of the outbreak and the reconstructed trees, we infer several epidemiological parameters. We found that the estimated mean serial interval was 7.4–9.2 days and the mean effective reproduction number dropped below 1 after implementation of control measures. We also found a high rate of secondary transmissions within households and observations of transmissions from individuals who were not terminally septicaemic. Our results provide important insights into the epidemiology of a bubonic plague outbreak during the Third Pandemic in Europe.

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Early reports of epidemiological parameters of the COVID-19 pandemic

Western Pacific Surveillance and Response ◽

10.5365/wpsar.2020.11.4.001 ◽

2021 ◽

Vol 12 (2) ◽

pp. 65-81

Author(s):

Keeley Allen ◽

Ame Elizabeth Parry ◽

Kathryn Glass

Keyword(s):

Incubation Period ◽

Reproduction Number ◽

Rapid Assessment ◽

Control Measures ◽

Inclusion Criteria ◽

Early Analysis ◽

Outbreak Response ◽

Median Length ◽

Serial Interval ◽

The Mean

Background: The emergence of a new pathogen requires a rapid assessment of its transmissibility, to inform appropriate public health interventions. Methods: The peer-reviewed literature published between 1 January and 30 April 2020 on COVID-19 in PubMed was searched. Estimates of the incubation period, serial interval and reproduction number for COVID-19 were obtained and compared. Results: A total of 86 studies met the inclusion criteria. Of these, 33 estimated the mean incubation period (4–7 days) and 15 included estimates of the serial interval (mean 4–8 days; median length 4–5 days). Fifty-two studies estimated the reproduction number. Although reproduction number estimates ranged from 0.3 to 14.8, in 33 studies (63%), they fell between 2 and 3. Discussion: Studies calculating the incubation period and effective reproduction number were published from the beginning of the pandemic until the end of the study period (30 April 2020); however, most of the studies calculating the serial interval were published in April 2020. The calculated incubation period was similar over the study period and in different settings, whereas estimates of the serial interval and effective reproduction number were setting-specific. Estimates of the serial interval were shorter at the end of the study period as increasing evidence of pre-symptomatic transmission was documented and as jurisdictions enacted outbreak control measures. Estimates of the effective reproduction number varied with the setting and the underlying model assumptions. Early analysis of epidemic parameters provides vital information to inform the outbreak response.

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Epidemiology of a bubonic plague outbreak in Glasgow, Scotland in 1900

10.1101/340547 ◽

2018 ◽

Cited By ~ 1

Author(s):

Katharine R. Dean ◽

Fabienne Krauer ◽

Boris V. Schmid

Keyword(s):

Yersinia Pestis ◽

Reproduction Number ◽

Control Measures ◽

High Rate ◽

Bubonic Plague ◽

The Third ◽

Serial Interval ◽

The Mean ◽

First Time ◽

Epidemiological Parameters

AbstractOn August 3, 1900, bubonic plague (Yersinia pestis) broke out in Glasgow for the first time during the Third Pandemic. The local sanitary authorities rigorously tracked the spread of the disease and they found that nearly all of the 35 cases could be linked by contact with a previous case. Despite trapping hundreds of rats in the area, there was no evidence of a rat epizootic and the investigators speculated that the outbreak could be due to human-to-human transmission of bubonic plague. Here we use a likelihood-based method to reconstruct transmission trees for the outbreak. From the description of the outbreak and the reconstructed trees, we infer several epidemiological parameters. We found that the estimated mean serial interval was 7.4 days and the mean effective reproduction number dropped below 1 after implementation of control measures. We also found that there was a high rate of secondary transmissions within households and observations of transmissions from individuals who were not terminally septicemic. Our results provide important insights into the epidemiology of plague that are useful for modeling current and historic plague epidemics.

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Modelling the Evolution of COVID-19 in High-Incidence European Countries and Regions: Estimated Number of Infections and Impact of Past and Future Intervention Measures

Journal of Clinical Medicine ◽

10.3390/jcm9061825 ◽

2020 ◽

Vol 9 (6) ◽

pp. 1825 ◽

Cited By ~ 3

Author(s):

Juan Fernández-Recio

Keyword(s):

Reproduction Number ◽

Mechanistic Model ◽

Control Measures ◽

European Countries ◽

Intervention Measures ◽

High Incidence ◽

Future Outcomes ◽

Long Term Impact ◽

The Impact

A previously developed mechanistic model of COVID-19 transmission has been adapted and applied here to study the evolution of the disease and the effect of intervention measures in some European countries and territories where the disease has had a major impact. A clear impact of the major intervention measures on the reproduction number (Rt) has been found in all studied countries and territories, as already suggested by the drop in the number of deaths over time. Interestingly, the impact of such major intervention measures seems to be the same in most of these countries. The model has also provided realistic estimates of the total number of infections, active cases and future outcomes. While the predictive capabilities of the model are much more uncertain before the peak of the outbreak, we could still reliably predict the evolution of the disease after a major intervention by assuming the subsequent reproduction number from the current study. A greater challenge is to foresee the long-term impact of softer intervention measures, but this model can estimate the outcome of different scenarios and help to plan changes for the implementation of control measures in a given country or region.

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Is Nigeria really on top of COVID-19? Message from effective reproduction number

10.1101/2020.05.16.20104471 ◽

2020 ◽

Author(s):

Adeshina Israel Adekunle ◽

Oyelola Adegboye ◽

Ezra Gayawan ◽

Emma McBryde

Keyword(s):

Public Health ◽

Compartmental Model ◽

Reproduction Number ◽

Transmission Rate ◽

Credible Interval ◽

Control Measures ◽

Maximum Value ◽

Intervention Measures ◽

Death Cases ◽

Epidemiological Parameters

Following the importation of Covid-19 into Nigeria on the 27 February 2020 and then the outbreak, the question is: how do we anticipate the progression of the ongoing epidemics following all the intervention measures put in place? This kind of question is appropriate for public health responses and it will depend on the early estimates of the key epidemiological parameters of the virus in a defined population. In this study, we combined a likelihood-based method using a Bayesian framework and compartmental model of the epidemic of Covid-19 in Nigeria to estimate the effective reproduction number (R(t)) and basic reproduction number (R_0). This also enables us to estimate the daily transmission rate (β) that determines the effect of social distancing. We further estimate the reported fraction of symptomatic cases. The models are applied to the NCDC data on Covid-19 symptomatic and death cases from 27 February 2020 and 7 May 2020. In this period, the effective reproduction number is estimated with a minimum value of 0.18 and a maximum value of 1.78. Most importantly, the R(t) is strictly greater than one from April 13 till 7 May 2020. The R_0 is estimated to be 2.42 with credible interval: (2.37, 2.47). Comparing this with the R(t) shows that control measures are working but not effective enough to keep R(t) below one. Also, the estimated fractional reported symptomatic cases are between 10 to 50%. Our analysis has shown evidence that the existing control measures are not enough to end the epidemic and more stringent measures are needed.

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Investigating the impact of vaccination and non-pharmaceutical measures in curbing COVID-19 spread: A South Africa perspective

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022049 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1058-1077

Author(s):

Shina D. Oloniiju ◽

◽

Olumuyiwa Otegbeye ◽

Absalom E. Ezugwu ◽

◽

...

Keyword(s):

Reproduction Number ◽

Transmission Probability ◽

Control Measures ◽

World Population ◽

Reproduction Rate ◽

Secondary Infections ◽

Perform Sensitivity Analysis ◽

African Context ◽

The Impact ◽

Effective Reaction

<abstract><p>The year 2020 brought about a pandemic that caught most of the world population by surprise and wreaked unimaginable havoc before any form of effective reaction could be put in place. COVID-19 is proving to be an epidemic that keeps on having an upsurge whenever it looks like it is being curbed. This pandemic has led to continuous strategizing on approaches to quelling the surge. The recent and welcome introduction of vaccines has led to renewed optimism for the population at large. The introduction of vaccines has led to the need to investigate the effect of vaccination among other control measures in the fight against COVID-19. In this study, we develop a mathematical model that captures the dynamics of the disease taking into consideration some measures that are easier to implement majorly within the African context. We consider quarantine and vaccination as control measures and investigate the efficacy of these measures in curbing the reproduction rate of the disease. We analyze the local stability of the disease-free equilibrium point. We also perform sensitivity analysis of the effective reproduction number to determine which parameters significantly lowers the effective reproduction number. The results obtained suggest that quarantine and a vaccine with at least $ 75\% $ efficacy and reducing transmission probability through sanitation and wearing of protective gears can significantly reduce the number of secondary infections.</p></abstract>

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Estimating transmission dynamics and serial interval of the first wave of COVID-19 infections under different control measures: A statistical analysis in Tunisia from February 29 to May 5, 2020

10.21203/rs.3.rs-31349/v1 ◽

2020 ◽

Author(s):

Khouloud Talmoudi ◽

Mouna Safer ◽

Hejer Letaief ◽

Aicha Hchaichi ◽

Chahida Harizi ◽

...

Keyword(s):

Emerging Diseases ◽

Control Measures ◽

Transmission Dynamics ◽

Contact Tracing ◽

Epidemic Threshold ◽

Illness Onset ◽

Intervention Measures ◽

Temporal Reproduction ◽

Prevention Measure ◽

Serial Interval

Abstract Background Describing transmission dynamics of the outbreak and impact of intervention measures are critical to planning responses to future outbreaks and providing timely information to guide policy makers decision. We estimate serial interval (SI) and temporal reproduction number (Rt) of SARS-CoV-2 in Tunisia. Methods We collected data of investigations and contact tracing between March 1, 2020 and May 5, 2020 as well as illness onset data during the period February 29-May 5, 2020 from National Observatory of New and Emerging Diseases of Tunisia. Maximum likelihood (ML) approach is used to estimate dynamics of Rt. Results 491 of infector-infectee pairs were involved, with 14.46% reported pre-symptomatic transmission. SI follows Gamma distribution with mean 5.30 days [95% CI 4.66–5.95] and standard deviation 0.26 [95% CI 0.23–0.30]. Also, we estimated large changes in Rt in response to the combined lockdown interventions. The Rt moves from 3.18 [95% CI 2.73–3.69] to 1.77 [95% CI 1.49–2.08] with curfew prevention measure, and under the epidemic threshold (0.89 [95% CI 0.84–0.94]) by national lockdown measure. Conclusions Overall, our findings highlight contribution of interventions to interrupt transmission of SARS-CoV-2 in Tunisia.

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Modelling the evolution of COVID-19 in high-incidence European countries and regions: estimated number of infections and impact of past and future intervention measures

10.1101/2020.05.09.20096735 ◽

2020 ◽

Author(s):

Juan Fernandez-Recio

Keyword(s):

Reproduction Number ◽

Mechanistic Model ◽

Control Measures ◽

European Countries ◽

Intervention Measures ◽

High Incidence ◽

Long Term Impact ◽

The Impact ◽

Over Time

A previously developed mechanistic model of COVID-19 transmission has been adapted and applied here to study the evolution of the disease and the effect of intervention measures in some European countries and territories where the disease had major impact. A clear impact of the major intervention measures on the reproduction number (Rt) has been found in all studied countries and territories, as already suggested by the drop in the number of deaths over time. Interestingly, the impact of such major intervention measures seems to be the same in most of these countries. The model has also provided realistic estimates of the total number of infections, active cases and future outcome. While the predictive capabilities of the model are much more uncertain before the peak of the outbreak, we could still reliably predict the evolution of the disease after a major intervention by assuming the afterwards reproduction number from current study. More challenging is to foresee the long-term impact of softer intervention measures, but this model can estimate the outcome of different scenarios and help planning changes in the implementation of control measures in a given country or region.

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

10.1101/2020.02.24.20027649 ◽

2020 ◽

Cited By ~ 8

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.

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

10.1101/2020.04.28.20083899 ◽

2020 ◽

Author(s):

Lingling Zheng ◽

Qin Kang ◽

Weiyao Liao ◽

Xiujuan Chen ◽

Shuai Huang ◽

...

Keyword(s):

Disease Transmission ◽

Reproduction Number ◽

Case Reports ◽

Epidemiological Data ◽

Control Measures ◽

Time Dependent ◽

Effective Control ◽

List Type ◽

Global Epidemic ◽

Serial Interval

AbstractBackgroundOn the present trajectory, COVID is inevitably becoming a global epidemic, leading to concerns regarding the pandemic potential in China and other countries.ObjectiveIn this study, we use the time-dependent reproduction number (Rt) to comprise the COVID transmissibility across different countries.MethodsWe 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.ResultsBased 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).ConclusionsThe 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.What is already known on this subject?The basic reproduction number (R0) and the-time-dependent reproduction number (Rt) are two important indicators of infectious disease transmission. In addition, Rt as a derivative of R0 could be used to assess the epidemiological development of the disease and effectiveness of control measures. Most current researches used data from earlier periods in Wuhan and refer to the epidemiological features of SARS, which are possibly biased. Meanwhile, there are fewer studies discussed the Rt of COVID-19. Current clinical and epidemiological data are insufficient to help us understand the full view of the potential transmission of this disease.What this study adds?We use up-to-data observation of the serial interval and cases arising from local transmission to calculate the Rt in different outbreak level area and every province in China as well as five-top sever outbreak countries and other overseas. By comparing the Rt, we discussed the situation of outbreak around the world.

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