scholarly journals A stochastic epidemiological model to estimate the size of an outbreak at the first case identification

2020 ◽  
Author(s):  
Peter Czuppon ◽  
François Blanquart ◽  
Florence Débarre
Keyword(s):  
Branching Processes ◽  
Single Point ◽  
Basic Reproductive Number ◽  
Contact Tracing ◽  
Upper And Lower Bounds ◽  
Reproductive Number ◽  
Related Case ◽  
Epidemic Size ◽  
First Case ◽  
Over Time

AbstractThe identification of a first case (e.g. by a disease-related death or hospitalization event) raises the question of the actual size of a local outbreak. Quick estimates of the outbreak size are required to assess the necessary testing, contact tracing and potential containment effort. Using general branching processes and assuming that epidemic parameters (including the basic reproductive number) are constant over time, we characterize the distribution of the first hospitalization time and of the epidemic size at this random time. We find that previous estimates either overestimate or largely underestimate the actual epidemic size. In addition, we provide upper and lower bounds for the number of infectious individuals of the local outbreak over time. The upper bound is the cumulative epidemic size, and the lower bound is a constant fraction of it. Lastly, we compute the number of detectable cases if one were to test the whole local outbreak at a single point in time. In a growing epidemic, most individuals have been infected recently, which can strongly limit the detection of infected individuals when there is a delay between an infection and its potential detection. Overall, our analysis provides new analytical estimates about the epidemic size at identification of a first disease-related case. This piece of information is important to inform policy makers during the early stages of an epidemic outbreak.

scholarly journals Beyond R 0 : heterogeneity in secondary infections and probabilistic epidemic forecasting

2020 ◽  
Vol 17 (172) ◽  
pp. 20200393 ◽  
Author(s):  
Laurent Hébert-Dufresne ◽  
Benjamin M. Althouse ◽  
Samuel V. Scarpino ◽  
Antoine Allard
Keyword(s):  
Random Network ◽  
Emerging Infectious Diseases ◽  
Disease Outbreaks ◽  
Basic Reproductive Number ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Emerging Pathogens ◽  
Epidemic Size ◽  
Classic Result ◽  
Secondary Infections

The basic reproductive number, R 0 , is one of the most common and most commonly misapplied numbers in public health. Often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that different epidemics can exhibit, even when they have the same R 0 . Here, we reformulate and extend a classic result from random network theory to forecast the size of an epidemic using estimates of the distribution of secondary infections, leveraging both its average R 0 and the underlying heterogeneity. Importantly, epidemics with lower R 0 can be larger if they spread more homogeneously (and are therefore more robust to stochastic fluctuations). We illustrate the potential of this approach using different real epidemics with known estimates for R 0 , heterogeneity and epidemic size in the absence of significant intervention. Further, we discuss the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19 the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond R 0 .

scholarly journals Beyond R0: Heterogeneity in secondary infections and probabilistic epidemic forecasting

2020 ◽  
Author(s):  
Laurent Hébert-Dufresne ◽  
Benjamin M. Althouse ◽  
Samuel V. Scarpino ◽  
Antoine Allard
Keyword(s):  
Random Network ◽  
Emerging Infectious Diseases ◽  
Disease Outbreaks ◽  
Basic Reproductive Number ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Emerging Pathogens ◽  
Epidemic Size ◽  
Secondary Infections ◽  
Outbreak Size

The basic reproductive number — R0 — is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same R0 [1–3]. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average R0 and the underlying heterogeneity. To do so, we reformulate and extend a classic result from random network theory [4] that relies on contact tracing data to simultaneously determine the first moment (R0) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19, the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond R0 when predicting epidemic size.

scholarly journals Antiviral treatment for the control of pandemic influenza: some logistical constraints

2007 ◽  
Vol 5 (22) ◽  
pp. 545-553 ◽  
Author(s):  
N Arinaminpathy ◽  
A.R McLean
Keyword(s):  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Size ◽  
Conservative Policy ◽  
Control Programmes ◽  
Final Epidemic Size ◽  
Number Of Treatment ◽  
Modelling Approach

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach. We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R 0 is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed. Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.

scholarly journals The Novel Coronavirus, 2019-nCoV, is Highly Contagious and More Infectious Than Initially Estimated

2020 ◽  
Author(s):  
Steven Sanche ◽  
Yen Ting Lin ◽  
Chonggang Xu ◽  
Ethan Romero-Severson ◽  
Nick Hengartner ◽  
...  
Keyword(s):  
Case Reports ◽  
Individual Case ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Contact Tracing ◽  
Reproductive Number ◽  
The Novel ◽  
Transmission Potential ◽  
Novel Coronavirus ◽  
Strong Control

AbstractThe novel coronavirus (2019-nCoV) is a recently emerged human pathogen that has spread widely since January 2020. Initially, the basic reproductive number, R0, was estimated to be 2.2 to 2.7. Here we provide a new estimate of this quantity. We collected extensive individual case reports and estimated key epidemiology parameters, including the incubation period. Integrating these estimates and high-resolution real-time human travel and infection data with mathematical models, we estimated that the number of infected individuals during early epidemic double every 2.4 days, and the R0 value is likely to be between 4.7 and 6.6. We further show that quarantine and contact tracing of symptomatic individuals alone may not be effective and early, strong control measures are needed to stop transmission of the virus.One-sentence summaryBy collecting and analyzing spatiotemporal data, we estimated the transmission potential for 2019-nCoV.

scholarly journals Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Felix Okoe Mettle ◽  
Prince Osei Affi ◽  
Clement Twumasi
Keyword(s):  
Deterministic Model ◽  
Equilibrium Points ◽  
Herd Immunity ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Seir Model ◽  
High Burden ◽  
Ashanti Region ◽  
Over Time

Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. The deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. The effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.

scholarly journals Contact tracing evaluation for COVID-19 transmission in the different movement levels of a rural college town in the USA

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sifat A. Moon ◽  
Caterina M. Scoglio
Keyword(s):  
Basic Reproductive Number ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Contact Network ◽  
Model Parameters ◽  
Maximum Point ◽  
College Town ◽  
Interesting Phenomenon ◽  
The Usa ◽  
Rural College

AbstractContact tracing can play a key role in controlling human-to-human transmission of a highly contagious disease such as COVID-19. We investigate the benefits and costs of contact tracing in the COVID-19 transmission. We estimate two unknown epidemic model parameters (basic reproductive number $$R_0$$ R 0 and confirmed rate $$\delta _2$$ δ 2 ) by using confirmed case data. We model contact tracing in a two-layer network model. The two-layer network is composed by the contact network in the first layer and the tracing network in the second layer. In terms of benefits, simulation results show that increasing the fraction of traced contacts decreases the size of the epidemic. For example, tracing $$25\%$$ 25 % of the contacts is enough for any reopening scenario to reduce the number of confirmed cases by half. Considering the act of quarantining susceptible households as the contact tracing cost, we have observed an interesting phenomenon. The number of quarantined susceptible people increases with the increase of tracing because each individual confirmed case is mentioning more contacts. However, after reaching a maximum point, the number of quarantined susceptible people starts to decrease with the increase of tracing because the increment of the mentioned contacts is balanced by a reduced number of confirmed cases. The goal of this research is to assess the effectiveness of contact tracing for the containment of COVID-19 spreading in the different movement levels of a rural college town in the USA. Our research model is designed to be flexible and therefore, can be used to other geographic locations.

scholarly journals Epidemic size, trend and spatiotemporal mapping of SARS-CoV-2 using geographical information system in Alborz Province, Iran

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Kourosh Kabir ◽  
Ali Taherinia ◽  
Davoud Ashourloo ◽  
Ahmad Khosravi ◽  
Hossien Karim ◽  
...  
Keyword(s):  
Preventive Measures ◽  
Hot Spot ◽  
Geographical Area ◽  
Geographical Information ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Spatiotemporal Mapping ◽  
Spot Area ◽  
Epidemic Size ◽  
Arc Gis

Abstract Background The first confirmed cases of COVID-19 in Iran were reported in Qom city. Subsequently, the neighboring provinces and gradually all 31 provinces of Iran were involved. This study aimed to investigate the case fatility rate, basic reproductive number in different period of epidemic, projection of daily and cumulative incidence cases and also spatiotemporal mapping of SARS-CoV-2 in Alborz province, Iran. Methods A confirmed case of COVID-19 infection was defined as a case with a positive result of viral nucleic acid testing in respiratory specimens. Serial interval (SI) was fitted by gamma distribution and considered the likelihood-based R0 using a branching process with Poisson likelihood. Seven days average of cases, deaths, doubling times and CFRs used to draw smooth charts. kernel density tool in Arc GIS (Esri) software has been employed to compute hot spot area of the study site. Results The maximum-likelihood value of R0 was 2.88 (95%, CI: 2.57–3.23) in the early 14 days of epidemic. The case fatility rate for Alborz province (Iran) on March 10, was 8.33% (95%, CI:6.3–11), and by April 20, it had an increasing trend and reached 12.9% (95%,CI:11.5–14.4). The doubling time has been increasing from about two days and then reached about 97 days on April 20, 2020, which shows the slowdown in the spread rate of the disease. Also, from March 26 to April 2, 2020 the whole Geographical area of Karj city was almost affected by SARS-CoV-2. Conclusions The R0 of COVID-19 in Alborz province was substantially high at the beginning of the epidemic, but with preventive measures and public education and GIS based monitoring of the cases,it has been reduced to 1.19 within two months. This reduction highpoints the attainment of preventive measures in place, however we must be ready for any second epidemic waves during the next months.

scholarly journals Modelling the effect of vertical transmission in the dynamics of HIV/AIDS in an age-structured population

2003 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Vertical Transmission ◽  
Equilibrium Points ◽  
Age Groups ◽  
Endemic Equilibrium ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
First Case ◽  
Age Structured ◽  
Hiv Aids

We use a continuous age-structured model of McKendrick-von-Foerster type to derive a two-age groups HIV/AIDS epidemic model. In the analysis of the model, keen interest is put on the role of vertical transmission in the dynamics of the spread of the epidemic. The model is analysed in two scenarios: the case when the force of infection is a constant and the case when we have it as a mass action. In the first case, the only possible equilibrium is the endemic equilibrium. In this situation, we show that if all babies born to infected mothers are HIV-free we have the basic reproductive number R0 = 0 and as such the epidemic will die out. In the second case, we show that both the disease-free and endemic equilibrium points exist. We also derive conditions for their stability.

scholarly journals Infectious disease phylodynamics with occurrence data

2019 ◽  
Author(s):  
Leo A. Featherstone ◽  
Francesca Di Giallonardo ◽  
Edward C. Holmes ◽  
Timothy G. Vaughan ◽  
Sebastián Duchêne
Keyword(s):  
Sequence Data ◽  
Exponential Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sampling Process ◽  
Occurrence Data ◽  
Source Of Information ◽  
Pathogen Genome ◽  
Over Time ◽  
Birth Death

AbstractPoint 1Phylodynamic models use pathogen genome sequence data to infer epidemiological dynamics. With the increasing genomic surveillance of pathogens, especially amid the SARS-CoV-2 outbreak, new practical questions about their use are emerging.Point 2One such question focuses on the inclusion of un-sequenced case occurrence data alongside sequenced data to improve phylodynamic analyses. This approach can be particularly valuable if sequencing efforts vary over time.Point 3Using simulations, we demonstrate that birth-death phylodynamic models can employ occurrence data to eliminate bias in estimates of the basic reproductive number due to misspecification of the sampling process. In contrast, the coalescent exponential model is robust to such sampling biases, but in the absence of a sampling model it cannot exploit occurrence data. Subsequent analysis of the SARS-CoV-2 epidemic in the northwest USA supports these results.Point 4We conclude that occurrence data are a valuable source of information in combination with birth-death models. These data should be used to bolster phylodynamic analyses of infectious diseases and other rapidly spreading species in the future.

scholarly journals Novel coronavirus 2019-nCoV (COVID-19): early estimation of epidemiological parameters and epidemic size estimates

2021 ◽  
Vol 376 (1829) ◽  
pp. 20200265
Author(s):  
Jonathan M. Read ◽  
Jessica R. E. Bridgen ◽  
Derek A. T. Cummings ◽  
Antonia Ho ◽  
Chris P. Jewell
Keyword(s):  
Prediction Interval ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
Theme Issue ◽  
Epidemic Size ◽  
Pandemic Response ◽  
Novel Coronavirus ◽  
The Uk ◽  
Size Estimates

Since it was first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. Using a transmission model, we estimate a basic reproductive number of 3.11 (95% CI, 2.39–4.13), indicating that 58–76% of transmissions must be prevented to stop increasing. We also estimate a case ascertainment rate in Wuhan of 5.0% (95% CI, 3.6–7.4). The true size of the epidemic may be significantly greater than the published case counts suggest, with our model estimating 21 022 (prediction interval, 11 090–33 490) total infections in Wuhan between 1 and 22 January. We discuss our findings in the light of more recent information. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

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