3. Primary reproductive number: R None (2023)

R has no epidemiological concept (R₀) has been in the news recently. This number, the basic reproduction number, is used to calculate the spread of COVID-19 and is a key part of the debate about when to start allowing cities and states to reopen.

Co R Brak (R₀) method

R Brak (R₀), Tenbasic reproductive number, is one of the most basic and most commonly used indicators for studying disease transmission. symbolNormalrepresents the true rate of disease transmission, representing reproduction. None or zero for generation zero (patient zero). This is the first documented case of a patient contracting a disease during the epidemic.

Normal₀it is an indicator of contagiousness or transmissibility of infectious and parasitic agents and is an estimate of the number of new infections caused by one case in a population that has never suffered from that disease. if R₀2, one person is expected to infect two new people on average (Anastassopoulou et al., 2020).

To provide some perspective, seasonal influenza viruses have R₀Between 0.9 and 2.1. R₀The R value for the 1918 influenza pandemic was estimated to be between 1.4 and 2.8, and for a highly contagious disease such as measles, the R value₀He is believed to be between 12 and 18 years old (Healthline, 2020).

Normal₀This is one of the key values ​​that predict whether an infectious disease will spread or disappear in a population. It is used to assess the severity of an outbreak and the strength of medical and/or behavioral interventions needed to control it (Breban et al., 2007).

Covid-19 br

R₀The R-value for Covid-19 was originally estimated at 2.2-2.7, but data collected from case reports across China shows a much higher R-value.₀. The results showed that the doubling time in the early stages of the Wuhan outbreak was between 2.3 and 3.3 days. Based on this data, the researchers calculated the median R₀The value is 5.7. This means that each person who becomes infected with the virus can transmit it to 5-6 people instead of only 2-3 as previously thought (Sanche et al., 2020).

History of R₀

The mathematical demographer Alfred Lotka elaboratedtheory of stable populationResearch the changes and growth rates of some populations in the early 20th century. In the 1920s, he proposed the reproduction number as a measure of the reproduction rate of a certain population and used it to count offspring.

In the 1950s, epidemiologist George MacDonald proposed the use of R₀Describe the transmission of malaria. He suggested that if R₀Less than 1, the disease will disappear from the population because the average infected person spreads to less than 1 other susceptible person. On the other hand, if R₀A value greater than 1 indicates the spread of the disease (Eisenberg, 2020). Since then, the reproduction number has been widely used in epidemiology.

How are you₀used to

Normal₀The values ​​indicate whether the disease will spread or decrease within the community, to what extent and how quickly. It can also inform public health policy decisions to reduce transmission.

The higher the R₀, the disease is more likely to become an epidemic. R can communicate three different possibilities₀(Healthline, 2020):

1. I am R₀Less than 1, the disease will not spread and will eventually disappear.
2. I am R₀When it is 1, the disease remains stable in the community but does not cause epidemics.
3. I am R₀If it is greater than 1, the disease will spread and may cause an epidemic.

How are you₀Calculated

Normal₀It is determined by complex mathematical equations that take into account data on the characteristics and transmissibility of the disease, human behavior, how often sick and susceptible people are expected to come into contact with each other, and the locations of affected communities. Scientists can also add fictional guesses.

One-sided epidemiologists calculate R₀It uses contact tracing data obtained during the outbreak. Once a person is diagnosed, their contacts are followed and tested. Normal₀It is then calculated by averaging the number of secondary cases from those diagnosed (Breban et al., 2007).

However, counting the number of infections during an outbreak can be extremely difficult, even if public health officials use active surveillance and contact tracing to find all infected people. When measuring the actual R₀Value is possible in emerging disease outbreaks, but few data collection systems exist to capture the early stages of an outbreak of R.₀Probably the most accurate measurement (EID, 2019).

result,₀It is almost always assessed retrospectively, based on seroepidemiological data (looking for the presence of antibodies in the blood) or using theoretical mathematical models. Estimated R value₀The results generated by a mathematical model depend on many decisions made by the modeler (EID, 2019).

Using mathematical models, R₀Values ​​are often estimated using ordinary differential equations, but high-quality data for all model elements are rarely available. The population structure of the model includes those who have been exposed but not yet infected, as well as assumptions about demographic data such as births, deaths and migration over time (EID, 2019).

The effect of vaccination

When studying the effects of vaccination, the term is more appropriateEffective reproduction number (R),Similar to R₀However, it is not assumed that the population is completely susceptible, so it can be estimated from the population with resistant members (EID, 2019).

Efforts to reduce the number of susceptible individuals in the population by vaccination will result in a decrease in the R-value, not a decrease in the R-value₀value. In this case, if R can be reduced to <1, vaccination has the potential to end the epidemic. You can also specify the number of effective plays within a certain time periodT, expressed as R(t) orkeep time, which can be used to track changes in R as the number of susceptible members of the population decreases. When the goal is to measure the effectiveness of vaccination campaigns or other public health interventions, R₀Not necessarily the best indicator (EID, 2019).

The potential size of an outbreak or epidemic usually depends on the size of R₀value and R₀It can be used to estimate the proportion of a population that needs to be vaccinated to eradicate an infection in that population - the higher the R₀the more people need to be vaccinated (EID, 2019).

Vaccination campaigns reduce the proportion of the population at risk of infection and are very effective in mitigating future outbreaks. This conclusion is sometimes used to suggest that the goal of a vaccination campaign is eliminationeasily influencedMembers of the R reduction population₀Generate events less than 1. Although removing susceptible members of the population affects the spread of infection by reducing the number of contacts between infected and susceptible people, it does not technically reduce R₀value becauseR definition₀Assume that there is a fully susceptible population(Id al-Fitr, 2019).

cumulative incidence model

Another common way is to get R₀zCumulative frequency dataIt is "the probability of developing a disease in a certain period of time". Theorists build models based on ordinary differential equations (ODEs), which describe the dynamics of the expected population size at different stages of the disease, without tracking individual individuals. Such modeling assumptions are hypothetical and cannot be tested using population-level data (Breban et al., 2007).

The ODE model is formulated based on the rate of transmission and progression of the disease in the population, which results in the threshold parameters of the epidemic. This oneThe threshold of morbidity is the limit at which the balance of the disease becomes unstable (R₀Greater than 1) and may become popular (Breban et al., 2007).

R calculation₀Data using cumulative prevalence data typically use three main parameters:

1. Duration of infectivity (how long an infected person can carry the virus) after the person is infected. The longer someone infects, the higher the R₀So.
2. Probability of infection due to contact between a susceptible person and an infected person or vector.
3. Contact rate (frequency of encounters between an infected person and a susceptible person).

Other parameters are sometimes added, such as the availability of public health resources, the political environment, aspects of the built environment, and other factors that may influence transmission.

Normal₀It also depends on the characteristics of the virus, how it spreads and how long it survives in the air and on objects. It also depends on where in the world the virus is located. "There are many social, cultural and demographic characteristics that can cause R-values ​​to vary from place to place," says Paul Delamater of the University of North Carolina at Chapel Hill. The scientific literature may suggest that for any source of infection, many R₀value (EID, 2019).

Difficulty in counting R₀

Although R concepts are at the forefront of mathematical epidemiology,₀There are so many disadvantages that it is difficult to define them. Several outbreaks have been observed when an infected person enters a susceptible population, allowing the R-value to be calculated₀Rely on supportive methods for specific diseases (Li et al., 2016).

In the hands of expert R₀This can be a valuable concept. However, the process of defining, calculating, interpreting and applying R₀It's not simple. R simplicity₀Value defies metric complexity. Although R₀is a biological reality, interpreted by R₀Estimates derived from different models require knowledge of model structure, inputs, and interactions. "Since many researchers use R₀No training in complex mathematical techniques, R₀they are vulnerable to misrepresentation, misunderstanding and abuse" (EID, 2019).

Even with constant infectivity and infectious time of the pathogen, R₀This value will change if the pace at which people interact with each other or with the medium changes. Everything that affects exposure rates—including population density, social organization, and seasonality—ultimately affects R₀(Eid of Ramadan, 2019). Because pandemics occur in different populations, geographic areas, and climates, R₀There can be great differences between countries and even within the same country.

because₀is a function of the contact speed, the value of R₀it is a function of human behavior and social organization and the innate biology of pathogens. Over 20 different Rs₀Values ​​for measles have been reported in different study areas and periods, and a 2017 review identified the actual possibility of R for measles₀Values ​​range from 3.7 to 203.3. This wide range highlights the potential volatility of R values₀Infectious diseases depending on local social behavior and environmental situation (EID, 2019).

There are many diseases that can overcome R₀<1, while R₀>1 may disappear, reducing the utility of the concept as an epidemic threshold. For example, a disease may exist in an already existing population, but it is not severe enough to invade. Moreover, the commonly calculated threshold is rarely the average number of secondary infections, which further weakens the utility of this concept (Li et al., 2011).

Many parameters included in the model are used to estimate R₀Just a guess; the true value is often unknown or difficult or impossible to measure directly. This limitation becomes more complex as the model becomes more complex. So while there is only one true R₀There is a value of an infectious disease event at a particular place and time, and models with small differences in structure and assumptions can produce different estimates of that value, even using the same epidemiological data (EID, 2019).

Public health measures to reduce R₀

when R₀Emerging diseases indicate the possibility of an epidemic, so it is important to understand the processes that can limit the spread (R) of a disease in a fully susceptible population in order to prevent (or limit) an outbreak. Once a country becomes aware of a new virus, steps must be taken to break the chain of infection until a treatment and vaccine is developed.

Measures successfully used in previous outbreaks have been shown to reduce the risk of infection by R₀The disease is characterized by:

• blankets
• social isolation
• Monitor exposed persons and their contacts
• Hand washing
• camouflage
• compare
• Appropriate protective equipment for healthcare workers
• Vaccine

super widespread event

Although we still know a lot about the epidemiology of the coronavirus disease, many cases of superspreading have been reported. During the recent large outbreaks of SARS, Middle East respiratory syndrome (MERS), and Ebola disease, superspreading events were associated with a spike early in the outbreak and sustained transmission later in the outbreak (Frieden and Lee, June 2020).

The Superspreading event highlights the main limitations of the R language concept₀. Basic R reproduction number₀Expressed as mean or median, it does not reflect the heterogeneity of transmission among infected individuals; two pathogens with the same R₀Assessments can have significantly different modes of transmission. The goal of the public health response is to reduce the number of infections to <1, which in some cases may not be possible without better prevention, identification and response to high-spread events. The meta-analysis estimated the baseline median R₀The infection rate for COVID-19 is 2.79 (meaning that 1 infected person infects 2.79 others on average), although current estimates may vary due to insufficient data (Frieden and Lee, June 2020).

Countermeasures can significantly reduce litter numbers; on a Diamond Princess cruise, initial estimates of R₀14.8 (about 4 times more than R)₀After the implementation of isolation and quarantine measures on the ship, the estimated effective reproductive number decreased to 1.78 (Frieden and Lee, June 2020).

Non-drug community-based interventions have been actively implemented in Wuhan, includingsanitary cordon*city; suspension of public transport, schools and most workplaces; canceling all public events reduced the number of plays from 3.86 to 0.32 in 5 weeks. However, these interventions may not be sustainable (Frieden and Lee, June 2020).

*Lina sanitary: An isolated geographic area that is monitored to prevent movement in and out of this area.

Although superspreading events appear to be difficult to predict and therefore prevent, understanding the pathogen, host, environmental, and behavioral factors of superspreading events can aid in prevention and control strategies. This includes:

• pathogen-specific factors
  • binding site
  • environmental sustainability
  • Virulence
  • infectious dose
• host factor
  • Duration of infection (long-term transmission)
  • Site and severity of infection (e.g. laryngeal or oral tuberculosis)
  • symptomatology
• ecological factor
  • Population density
  • Availability and application of infection prevention and control measures in healthcare institutions
• behavioral factors
  • cough hygiene
  • social customs
  • looking for healthy behavior
  • follow public health guidelines
• response factor
  • Timely and effective implementation of prevention and control measures in the community and health institutions
  • Rapid identification and isolation of cases
  • Effective case isolation and contact tracing (Frieden & Lee, June 2020)