scholarly journals Elementi metodologici per una riflessione sui dati dell’epidemia di sars-cov-2

2020 ◽  
Vol 32 (1) ◽  
pp. 127-130
Author(s):  
Anteo Di Napoli ◽  
Francesco Franco ◽  
Giuseppe Quintaliani
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Critical Threshold ◽  
Primary Case ◽  
Containment Measures ◽  
Over Time

Findings of the seroprevalence survey conducted by Istat between May 25 and July 15 2020, on a sample of 64,660 people, show that only 2.5% of Italian people developed antibodies to SARS-CoV-2, a prevalence very far from the hypothesis of achieving herd immunity. Starting from the comment on these results, we summarized some of the main indicators used to evaluate the epidemic curves (R, R0, Rt) and the concept of herd immunity. R0, basic reproduction number, represents the average number of secondary cases we expect to observe from a single primary case in a population with no immunity to the disease before prevention and containment measures have been planned. Rt, effective reproduction number, is calculated over time and considers how the outbreak progresses, as a result of the containment measures and of people who might have gained immunity, because they survived from infection or were vaccinated. We presented the issue of herd immunity, or community immunity, a state of protection in a population obtained because the number of people in the population who are immune to infectious disease is above a critical threshold, resulting in a protection even for those who are not immune.

scholarly journals What Is the Estimated COVID-19 Reproduction Number and the Proportion of the Population That Needs to Be Immunized to Achieve Herd Immunity in Malaysia? A Mathematical Epidemiology Synthesis

COVID ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 13-19
Author(s):  
Kurubaran Ganasegeran ◽  
Alan Swee Hock Ch’ng ◽  
Irene Looi
Keyword(s):  
Reproduction Number ◽  
Herd Immunity ◽  
Control Measures ◽  
Threshold Estimate ◽  
Mathematical Epidemiology ◽  
Incidence Data ◽  
Malaysian Population ◽  
Containment Measures ◽  
Efficacious Vaccine ◽  
Over Time

We aimed to determine Malaysia’s COVID-19 reproduction number and herd immunity threshold through a mathematical epidemiology synthesis. Using time-series incidence data, the time-dependent reproduction number (Rt) was yielded over time during the COVID-19 containment measures in Malaysia. The value of Rt at the beginning of the epidemic and prior to any interventions in place was used to determine the proportion of the population that needs to be immunized to achieve herd immunity. Rt was strongly influenced by interventions being put in place. We established that at least 74% of the Malaysian population needs to be vaccinated to achieve herd immunity against COVID-19. This threshold estimate is somewhat influenced by the availability of an efficacious vaccine. A vaccine with 95% efficacy would approximately synthesize a herd immunity threshold of 78%. We conclude that Rt is a valid estimator to determine the effectiveness of control measures and a parameter of use to synthesize herd immunity thresholds in the current COVID-19 pandemic.

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 Covid 19: Need of vaccine induced herd immunity in India

2020 ◽  
Vol 2 (4) ◽  
pp. 82-84
Author(s):  
D. Pragathi ◽  
Dinesh Kumar Kukunuri ◽  
Venkatesh Paturu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Traditional Concept ◽  
Contagious Diseases ◽  
Research Article ◽  
Past Data ◽  
The Mean ◽  
Novel Coronavirus ◽  
Indirect Protection

Introduction: Herd immunity is a traditional concept nothing but a form of indirect protection from contagious diseases. In a mass community, there is no need to be everyone immune. If a high proportion of members in the community are immune, spreading of the disease is reduced even to non-immunized patients. This study offers an overview of vaccine-induced herd immunity importance in this pandemic and how it will be achieved. Methodology: The data of basic reproduction number Ro values for COVID 19 of 10 weeks in India which were estimated by Ro package in R software are extracted from a research article (reference no.4) and taken the mean Ro value due to fluctuations as well as to avoid great errors by using MS Excel. Herd immunity is calculated by using a standard equation stated as R=(1-Pc )(1-P1)Ro   Results:  The mean basic reproduction number Ro for COVID 19 in India was calculated as 1.671 by using MS excel and the herd 3 determines that only 40.16% proportion of individuals need to immunized through a vaccine to achieve herd immunity towards COVID 19 in India. Conclusion: This study estimates mean base reproduction Ro as 1.671 and Herd Immunity Threshold (HIT) as 40.16% by using past data. This study concludes that vaccine-induced herd immunity helps us by playing a key role to eliminate novel coronavirus.

scholarly journals Herd Immunity in India: A Review

2021 ◽  
Vol 3 (1) ◽  
pp. 18-21
Author(s):  
Sheema Fatima Khan
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Natural Infection ◽  
Herd Immunity ◽  
Herd Effect ◽  
Susceptible Population ◽  
Herd Protection ◽  
Cdc Guidelines ◽  
And Control

Herd Immunity is a brilliant solution to tackle and control global pandemics, if taken proper route for immunization such as through vaccination. It is defined as the number of immune individuals against a transmissible virus in a completely susceptible population. The term herd protection or herd effect is the protection to the whole population due to herd immunity. Herd immunity threshold is the minimum proportion of immune population required for herd effect or herd protection. To calculate the threshold, we use basic reproduction number (R0) to measure the rate of transmission of pathogen, in this case SARS-CoV-2. However, a better measure is effective reproduction number (Re). India is major example of herd immunity. Despite strict lockdown and other Covid measure, due to already crowded area the virus could spread fast and to vast majority of people if one of them were to catch it. This explains the steady decline in the number of coronavirus cases in India. At the end, until an approved effective vaccination available, public will still need to follow all the CDC guidelines in order to avoid the large deaths along with natural infection.

scholarly journals SEIHCRD Model for COVID-19 spread scenarios, disease predictions and estimates the basic reproduction number, case fatality rate, hospital, and ICU beds requirement

2020 ◽  
Author(s):  
Avaneesh Singh ◽  
Manish Kumar Bajpai
Keyword(s):  
Basic Reproduction Number ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Case Fatality ◽  
The United States ◽  
Fatality Rate ◽  
Hospital Beds ◽  
The Impact ◽  
Over Time ◽  
The Basic Reproduction Number

We have proposed a new mathematical method, SEIHCRD-Model that is an extension of the SEIR-Model adding hospitalized and critical twocompartments. SEIHCRD model has seven compartments: susceptible (S), exposed (E), infected (I), hospitalized (H), critical (C), recovered (R), and deceased or death (D), collectively termed SEIHCRD. We have studied COVID- 19 cases of six countries, where the impact of this disease in the highest are Brazil, India, Italy, Spain, the United Kingdom, and the United States. SEIHCRD model is estimating COVID-19 spread and forecasting under uncertainties, constrained by various observed data in the present manuscript. We have first collected the data for a specific period, then fit the model for death cases, got the values of some parameters from it, and then estimate the basic reproduction number over time, which is nearly equal to real data, infection rate, and recovery rate of COVID-19. We also compute the case fatality rate over time of COVID-19 most affected countries. SEIHCRD model computes two types of Case fatality rate one is CFR daily and the second one is total CFR. We analyze the spread and endpoint of COVID-19 based on these estimates. SEIHCRD model is time-dependent hence we estimate the date and magnitude of peaks of corresponding to the number of exposed cases, infected cases, hospitalized cases, critical cases, and the number of deceased cases of COVID-19 over time. SEIHCRD model has incorporated the social distancing parameter, different age groups analysis, number of ICU beds, number of hospital beds, and estimation of how much hospital beds and ICU beds are required in near future.

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.

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