Joint estimation of the basic reproduction number and generation time parameters for infectious disease outbreaks

The basic reproduction number (or ratio) R₀ is arguably the most important quantity in infectious disease epidemiology. It is among the quantities most urgently estimated for infectious diseases in outbreak situations, and its value provides insight when designing control interventions for established infections. From a theoretical point of view R₀ plays a vital role in the analysis of, and consequent insight from, infectious disease models. There is hardly a paper on dynamic epidemiological models in the literature where R₀ does not play a role. R₀ is defined as the average number of new cases of an infection caused by one typical infected individual, in a population consisting of susceptibles only. This chapter shows how R₀ can be characterized mathematically and provides detailed examples of its calculation in terms of parameters of epidemiological models, culminating in a set of algorithms (or “recipes”) for the calculation for compartmental epidemic systems.

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Threshold parameters for a model of epidemic spread among households and workplaces

Journal of The Royal Society Interface ◽

10.1098/rsif.2008.0493 ◽

2009 ◽

Vol 6 (40) ◽

pp. 979-987 ◽

Cited By ~ 36

Author(s):

L. Pellis ◽

N. M. Ferguson ◽

C. Fraser

Keyword(s):

Infectious Disease ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Model Parameters ◽

Epidemic Spread ◽

Threshold Parameter ◽

Disease Epidemiology ◽

Infectious Disease Epidemiology ◽

Complex Models ◽

The Basic Reproduction Number

The basic reproduction number R 0 is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number R H for it. We show how R H overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.

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

Epidemiology and Infection ◽

10.1017/s0950268898001113 ◽

1998 ◽

Vol 121 (2) ◽

pp. 309-324 ◽

Cited By ~ 36

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.

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Graphs with specified degree distributions, simple epidemics, and local vaccination strategies

Advances in Applied Probability ◽

10.1017/s0001867800002172 ◽

2007 ◽

Vol 39 (04) ◽

pp. 922-948 ◽

Cited By ~ 13

Author(s):

Tom Britton ◽

Svante Janson ◽

Anders Martin-Löf

Keyword(s):

Infectious Disease ◽

Social Structure ◽

Basic Reproduction Number ◽

Degree Distribution ◽

Reproduction Number ◽

Final Size ◽

Vaccination Strategies ◽

The Social ◽

Major Outbreak ◽

The Basic Reproduction Number

Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R 0, the basic reproduction number, and τ0, the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine R v , the reproduction number, and τ v , the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.

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Estimation of Hospital Potential Capacity and Basic Reproduction Number

Abstract and Applied Analysis ◽

10.1155/2014/875474 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5

Author(s):

Fei Wang ◽

Linhua Wang ◽

Peng Wang

Keyword(s):

Infectious Disease ◽

Decision Making ◽

Resource Allocation ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Medical Resource ◽

Population Dynamic Model ◽

Potential Capacity ◽

And Control ◽

The Basic Reproduction Number

In order to reflect the population covered by institutional medical services, the concept of hospital potential capacity is proposed and a formula for its estimation is developed based on a population dynamic model. Using the collected data on hospital outpatient and inpatient services and the demographical information on Chongqing as an example, the demand for medical resource allocation in Chongqing is dynamically estimated. Moreover, the proposed formula is also useful in the estimation of the basic reproduction number in epidemiology. The results can be contributed to the improvement of decision-making in the allocation of medical resources and the evaluation of the interventions and control efforts of the infectious disease.

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Estimation of the Basic Reproduction Numbers of the Subtypes H5N1, H5N8, and H5N6 During the Highly Pathogenic Avian Influenza Epidemic Spread Between Farms

Frontiers in Veterinary Science ◽

10.3389/fvets.2021.597630 ◽

2021 ◽

Vol 8 ◽

Author(s):

Woo-Hyun Kim ◽

Seongbeom Cho

Keyword(s):

Avian Influenza ◽

Basic Reproduction Number ◽

Generation Time ◽

Reproduction Number ◽

Highly Pathogenic Avian Influenza ◽

Pairwise Comparison ◽

Prevention Policy ◽

Highly Pathogenic ◽

Pathogenic Avian Influenza ◽

The Basic Reproduction Number

It is important to understand pathogen transmissibility in a population to establish an effective disease prevention policy. The basic reproduction number (R0) is an epidemiologic parameter for understanding the characterization of disease and its dynamics in a population. We aimed to estimate the R0 of the highly pathogenic avian influenza (HPAI) subtypes H5N1, H5N8, and H5N6, which were associated with nine outbreaks in Korea between 2003 and 2018, to understand the epidemic transmission of each subtype. According to HPAI outbreak reports of the Animal and Plant Quarantine Agency, we estimated the generation time by calculating the time of infection between confirmed HPAI-positive farms. We constructed exponential growth and maximum likelihood (ML) models to estimate the basic reproduction number, which assumes the number of secondary cases infected by the index case. The Kruskal-Wallis test was used to analyze the epidemic statistics between subtypes. The estimated generation time of H5N1, H5N8, and H5N6 were 4.80 days [95% confidence interval (CI) 4.23–5.38] days, 7.58 (95% CI 6.63–8.46), and 5.09 days (95% CI 4.44–5.74), respectively. A pairwise comparison showed that the generation time of H5N8 was significantly longer than that of the subtype H5N1 (P = 0.04). Based on the ML model, R0 was estimated as 1.69 (95% CI 1.48–2.39) for subtype H5N1, 1.60 (95%CI 0.97–2.23) for subtype H5N8, and 1.49 (95%CI 0.94–2.04) for subtype H5N6. We concluded that R0 estimates may be associated with the poultry product system, climate, species specificity based on the HPAI virus subtype, and prevention policy. This study provides an insight on the transmission and dynamics patterns of various subtypes of HPAI occurring worldwide. Furthermore, the results are useful as scientific evidence for establishing a disease control policy.

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Estimation of the Basic Reproduction Number of SARS-CoV-2 in Bangladesh Using Exponential Growth Method

10.1101/2020.09.29.20203885 ◽

2020 ◽

Author(s):

Riaz Mahmud ◽

H. M. Abrar Fahim Patwari

Keyword(s):

Standard Deviation ◽

Basic Reproduction Number ◽

Exponential Growth ◽

Generation Time ◽

Reproduction Number ◽

First Case ◽

The World ◽

Growth Method ◽

Novel Coronavirus ◽

The Basic Reproduction Number

Objectives: In December 2019, a novel coronavirus (SARS-CoV-2) outbreak emerged in Wuhan, Hubei Province, China. Soon, it has spread out across the world and become an ongoing pandemic. In Bangladesh, the first case of novel coronavirus (SARS-CoV-2) was detected on March 8, 2020. Since then, not many significant studies have been conducted to understand the transmission dynamics of novel coronavirus (SARS-CoV-2) in Bangladesh. In this study, we estimated the basic reproduction number R0 of novel coronavirus (SARS-CoV-2) in Bangladesh. Methods: The data of daily confirmed cases of novel coronavirus (SARS-CoV-2) in Bangladesh and the reported values of generation time of novel coronavirus (SARS-CoV-2) for Singapore and Tianjin, China, were collected. We calculated the basic reproduction number R0 by applying the exponential growth (EG) method. Epidemic data of the first 76 days and different values of generation time were used for the calculation. Results: The basic reproduction number R0 of novel coronavirus (SARS-CoV-2) in Bangladesh is estimated to be 2.66 [95% CI: 2.58-2.75], optimized R0 is 2.78 [95% CI: 2.69-2.88] using generation time 5.20 with a standard deviation of 1.72 for Singapore. Using generation time 3.95 with a standard deviation of 1.51 for Tianjin, China, R0 is estimated to be 2.15 [95% CI: 2.09-2.20], optimized R0 is 2.22 [95% CI: 2.16-2.29]. Conclusions: The calculated basic reproduction number R0 of novel coronavirus (SARS-CoV-2) in Bangladesh is significantly higher than 1, which indicates its high transmissibility and contagiousness.

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