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.

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 Sustainable social distancing through facemask use and testing during the Covid-19 pandemic

2020 ◽  
Author(s):  
Diego Chowell ◽  
Kimberlyn Roosa ◽  
Ranu Dhillon ◽  
Gerardo Chowell ◽  
Devabhaktuni Srikrishna
Keyword(s):  
Basic Reproduction Number ◽  
Symptom Onset ◽  
Social Protection ◽  
Reproduction Number ◽  
Type Model ◽  
Protective Behaviors ◽  
Social Distancing ◽  
And Control ◽  
Different Levels ◽  
The Basic Reproduction Number

We investigate how individual protective behaviors, different levels of testing, and isolation influence the transmission and control of the COVID-19 pandemic. Based on an SEIR-type model incorporating asymptomatic but infectious individuals (40%), we show that the pandemic may be readily controllable through a combination of testing, treatment if necessary, and self-isolation after testing positive (TTI) of symptomatic individuals together with social protection (e.g., facemask use, handwashing). When the basic reproduction number, R0, is 2.4, 65% effective social protection alone (35% of the unprotected transmission) brings the R below 1. Alternatively, 20% effective social protection brings the reproduction number below 1.0 so long as 75% of the symptomatic population is covered by TTI within 12 hours of symptom onset. Even with 20% effective social protection, TTI of 1 in 4 symptomatic individuals can substantially 'flatten the curve' cutting the peak daily incidence in half.

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.

scholarly journals Rich Dynamics of an Epidemic Model with Saturation Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Medical Resource ◽  
Sir Epidemic Model ◽  
The Impact ◽  
The Basic Reproduction Number

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

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 On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Antiviral Treatment ◽  
Stability Properties ◽  
Local Asymptotic Stability ◽  
Proposed Model ◽  
And Control ◽  
The Basic Reproduction Number

AbstractIn this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

scholarly journals The effect of control measures on COVID-19 transmission in Italy: Comparison with Guangdong province in China

2020 ◽  
Author(s):  
Peiyu Liu ◽  
Sha He ◽  
Libin Rong ◽  
Sanyi Tang
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Control Measures ◽  
Seir Model ◽  
Diagnosis Rate ◽  
And Control ◽  
Parameter Values ◽  
Test Result ◽  
The Basic Reproduction Number

Abstract Background COVID-19 is spreading in many countries around the world. Italy is the hardest hit in Europe and its number of new infections is still increasing. This study aims to evaluate the reason for the rapidly growing epidemic in Italy.Methods We compared Italy’s data of outbreak and control measures with the province of Guangdong in China. Then, a modified SEIR model was applied to estimate the basic reproduction number. Finally, we utilized a time-dependent dynamic model to study the future disease dynamics in Italy.Results The comparison of specific measures implemented in the two places and the time when the measures were initiated shows that the prevention and control actions in Italy were not sufficiently timely and effective. Using a modified SEIR model, we estimated parameter values based on available cumulative data and calculate the basic reproduction number to be 4.32 before the national lockdown in Italy. Numerical simulations revealed that under a scenario in which very strict interventions are taken when the minimum contact rate is 1 with the exponential decreasing rate is 0.5 and the fast diagnosis rate is 0.5 with the exponential increasing rate is 0.5 (i.e. the test result will be available in two days). In this scenario, Italy will reach the peak (i.e. 23900) after 43 days.Conclusion This study suggests that Italy is currently in a very serious epidemic status since control measures such as blockade of schools, isolation, medical supports and media coverage are not sufficiently timely and effective.

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