scholarly journals Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China

2020 ◽  
Vol 5 ◽  
pp. 67 ◽  
Author(s):  
Akira Endo ◽  
Sam Abbott ◽  
Adam J. Kucharski ◽  
Sebastian Funk ◽  
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Process Model ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Joint Estimation ◽  
World Health ◽  
Level Variation ◽  
Individual Level ◽  
Novel Coronavirus

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R0 and k (95% CrIs: R0 1.4-12; k 0.04-0.2); however, the upper bound of R0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

scholarly journals Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China

2020 ◽  
Vol 5 ◽  
pp. 67 ◽  
Author(s):  
Akira Endo ◽  
Sam Abbott ◽  
Adam J. Kucharski ◽  
Sebastian Funk ◽  
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Process Model ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Joint Estimation ◽  
World Health ◽  
Level Variation ◽  
Individual Level ◽  
Novel Coronavirus

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R0 and k (95% CrIs: R0 1.4-12; k 0.04-0.2); however, the upper bound of R0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

scholarly journals Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China

2020 ◽  
Vol 5 ◽  
pp. 67 ◽  
Author(s):  
Akira Endo ◽  
Sam Abbott ◽  
Adam J. Kucharski ◽  
Sebastian Funk ◽  
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Process Model ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Joint Estimation ◽  
World Health ◽  
Level Variation ◽  
Individual Level ◽  
Novel Coronavirus

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R0 and k (95% CrIs: R0 1.4-12; k 0.04-0.2); however, the upper bound of R0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

scholarly journals Superspreading in Early Transmissions of COVID-19 in Indonesia

2020 ◽  
Author(s):  
A. Hasan ◽  
H. Susanto ◽  
M.F. Kasim ◽  
N. Nuraini ◽  
D. Triany ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Negative Binomial Distribution ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Early Stage ◽  
Level Variation ◽  
Individual Level ◽  
High Degree ◽  
Overdispersion Parameter ◽  
The Basic Reproduction Number

AbstractWe estimate the basic reproduction number ℛ0 and the overdispersion parameter K at two COVID-19 clusters in Indonesia: Jakarta-Depok and Batam. Based on the first 397 confirmed cases in both clusters, we find a high degree of individual-level variation in the transmission. The basic reproduction number ℛ0 is estimated at 6.79 and 2.47, while the overdispersion parameter K of a negative-binomial distribution is estimated at 0.08 and 0.2 for Jakarta-Depok and Batam, respectively. This suggests that superspreading events played a key role in the early stage of the outbreak, i.e., a small number of infected individuals are responsible for large amounts of COVID-19 transmission.

scholarly journals Superspreading in early transmissions of COVID-19 in Indonesia

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Agus Hasan ◽  
Hadi Susanto ◽  
Muhammad Firmansyah Kasim ◽  
Nuning Nuraini ◽  
Bony Lestari ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Early Stage ◽  
Secondary Case ◽  
Isolation And Identification ◽  
Overdispersion Parameter ◽  
The Basic Reproduction Number

AbstractThis paper presents a study of early epidemiological assessment of COVID-19 transmission dynamics in Indonesia. The aim is to quantify heterogeneity in the numbers of secondary infections. To this end, we estimate the basic reproduction number $$\mathscr {R}_0$$ R 0 and the overdispersion parameter $$\mathscr {K}$$ K at two regions in Indonesia: Jakarta–Depok and Batam. The method to estimate $$\mathscr {R}_0$$ R 0 is based on a sequential Bayesian method, while the parameter $$\mathscr {K}$$ K is estimated by fitting the secondary case data with a negative binomial distribution. Based on the first 1288 confirmed cases collected from both regions, we find a high degree of individual-level variation in the transmission. The basic reproduction number $$\mathscr {R}_0$$ R 0 is estimated at 6.79 and 2.47, while the overdispersion parameter $$\mathscr {K}$$ K of a negative-binomial distribution is estimated at 0.06 and 0.2 for Jakarta–Depok and Batam, respectively. This suggests that superspreading events played a key role in the early stage of the outbreak, i.e., a small number of infected individuals are responsible for large numbers of COVID-19 transmission. This finding can be used to determine effective public measures, such as rapid isolation and identification, which are critical since delay of diagnosis is the most common cause of superspreading events.

Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

2019 ◽  
Vol 53 (5) ◽  
pp. 417-422
Author(s):  
P. De los Ríos ◽  
E. Ibáñez Arancibia
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Rocky Shore ◽  
Negative Binomial ◽  
Null Model ◽  
Easter Island ◽  
Published Data ◽  
Distribution Analysis ◽  
Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

2011 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Y. ARBI ◽  
R. BUDIARTI ◽  
I G. P. PURNABA
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Financial Institution ◽  
Expected Value ◽  
Insurance Companies ◽  
Limited Data ◽  
Loss Distribution Approach ◽  
Potential Loss ◽  
The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

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