scholarly journals Inferring R 0 in emerging epidemics—the effect of common population structure is small

2016 ◽  
Vol 13 (121) ◽  
pp. 20160288 ◽  
Author(s):  
Pieter Trapman ◽  
Frank Ball ◽  
Jean-Stéphane Dhersin ◽  
Viet Chi Tran ◽  
Jacco Wallinga ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Population Structure ◽  
Robust Control ◽  
Reproduction Number ◽  
Contact Structures ◽  
Emerging Infections ◽  
Control Effort ◽  
Large Outbreak ◽  
Epidemiological Parameters ◽  
The Basic Reproduction Number

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R 0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R 0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort.

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.

The basic reproduction number

2012 ◽  
Author(s):  
Odo Diekmann ◽  
Hans Heesterbeek ◽  
Tom Britton
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infected Individual ◽  
Vital Role ◽  
Point Of View ◽  
Epidemiological Models ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
The Basic Reproduction Number

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.

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

2009 ◽  
Vol 6 (40) ◽  
pp. 979-987 ◽  
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.

scholarly journals Evaluating strategies for spatial allocation of vaccines based on risk and centrality

2021 ◽  
Author(s):  
Benjamin J Singer ◽  
Robin N Thompson ◽  
Michael B Bonsall
Keyword(s):  
Infectious Disease ◽  
Random Walk ◽  
Reproduction Number ◽  
Large Population ◽  
Relative Effectiveness ◽  
Spatial Allocation ◽  
Location Methods ◽  
Vaccine Availability ◽  
Targeting Strategy ◽  
The Basic Reproduction Number

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritise some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritisation include strategies which target those regions most at risk of importing the pathogen, and strategies which target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network, and vaccine availability. We conclude that, when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

scholarly journals The pluses and minuses of 0

2007 ◽  
Vol 4 (16) ◽  
pp. 949-961 ◽  
Author(s):  
M.G Roberts
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Central Place ◽  
Sir Model ◽  
Direct Measure ◽  
Control Effort ◽  
Epidemic Theory ◽  
The Basic Reproduction Number

The concept of the basic reproduction number ( 0 ) occupies a central place in epidemic theory. The value of 0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if 0 >1, (ii) the value of 0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of 0 . These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.

scholarly journals Modeling and Analyzing the Propagation of COVID-19 in Wuhan Based On Game Theory: Quarantine or Not?

2020 ◽  
Author(s):  
Maoxing Liu ◽  
Rongping Zhang ◽  
Boli Xie
Keyword(s):  
Infectious Disease ◽  
Game Theory ◽  
Reproduction Number ◽  
Virus Disease ◽  
National Strategy ◽  
Working At Home ◽  
Simulation Process ◽  
Existence And Stability ◽  
Simulation Results ◽  
The Basic Reproduction Number

Abstract The isolation strategy and quarantine strategy played a crucial role in the prevention of the Corona Virus Disease 2019 in China.This paper establishes a two-layer network model that couples epidemics and the behavior of individuals based on game theory.We calculated the basic reproduction number of the infectious disease, and analyzed the existence and stability of the positiveequilibrium point in the behavioral dynamic model. Through simulation, we adjusted the behavior parameters to fit the actualdata, and then analyzed the sensitivity of each parameter to the system. The contradiction between national strategy andindividual behavior was found in the simulation process. The simulation results show that increasing the awareness of peoplecan accelerate changes in behavior, and improving the efficiency of working at home can reduce the relative loss of isolation,all of which can reduce the severity of the infectious disease.

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

2007 ◽  
Vol 39 (04) ◽  
pp. 922-948 ◽  
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.

scholarly journals Estimation of Hospital Potential Capacity and Basic Reproduction Number

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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