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Wikipedia / Basic reproduction number

In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate (pronounced R nought or R zero), of an infection is the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition assumes that no other individuals are infected or immunized (naturally or through vaccination). Some definitions, such as that of the Australian Department of Health, add the absence of "any deliberate intervention in disease transmission". The basic reproduction number is not necessarily the same as the effective reproduction number [t), is a dimensionless number (persons infected per person infecting) and not a time rate, which would have units of time−1, or units of time like doubling time.

values are usually estimated from mathematical models, and the estimated values are dependent on the model used and values of other parameters. Thus values given in the literature only make sense in the given context and it is not recommended to compare values based on different models. does not by itself give an estimate of how fast an infection spreads in the population.

are determining if an emerging infectious disease can spread in a population and determining what proportion of the population should be immunized through vaccination to eradicate a disease. In commonly used infection models. This is the so-called herd immunity threshold or herd immunity level. Here, herd immunity means that the disease cannot spread in the population because each infected person, on average, can only transmit the infection to less than one other contact. Conversely, the proportion of the population that remains susceptible to infection in the endemic equilibrium. However, this threshold is based on simple models that assume a fully mixed population with no structured relations may underestimate the herd immunity threshold.

The basic reproduction number is affected by several factors, including the duration of infectivity of affected people, the contagiousness of the microorganism, and the number of susceptible people in the population that the infected people contact.

History

The roots of the basic reproduction concept can be traced through the work of Ronald Ross, Alfred Lotka and others, but its first modern application in epidemiology was by George Macdonald in 1952, who constructed population models of the spread of malaria.

Overview of R0 estimation methods

Compartmental models

Compartmental models are a general modeling technique often applied to the mathematical modeling of infectious diseases.

Epidemic models on networks

Epidemics can be modeled as diseases spreading over networks of contact and disease transmission between people. Nodes in these networks represent individuals and links (edges) between nodes represent the contact or disease transmission between them. If such a network is a locally tree-like network, then the basic reproduction can be written in terms of the average excess degree of the transmission network such that:

is the second moment of the transmission network degree distribution.

Heterogeneous populations

in this case is "the expected number of secondary cases produced, in a completely susceptible population, produced by a typical infected individual".

. Some diseases have multiple possible latency periods, in which case the reproduction number for the disease overall is the sum of the reproduction number for each transition time into the disease.

Effective reproduction number

In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the effective reproduction number is the average number of new infections caused by a single infected individual at time t by the fraction S of the population that is susceptible. When the fraction of the population that is immune increases (i. e. the susceptible population S drops below 1, herd immunity has been achieved and the number of cases occurring in the population will gradually decrease to zero.

Limitations of R0

can be calculated from many different mathematical models, which needs to be interpreted in the context of that model. can still lead to self-perpetuating outbreaks. This is particularly problematic if there are intermediate vectors between hosts (as is the case for zoonoses), such as malaria. of well-known contagious diseases" table should be conducted with caution.

cannot be modified through vaccination or other changes in population susceptibility, it can vary based on a number of biological, sociobehavioral, and environmental factors. It can also be modified by physical distancing and other public policy or social interventions, although some historical definitions exclude any deliberate intervention in reducing disease transmission, including nonpharmacological interventions. often depends on the paper, disease, and what if any intervention is being studied. is not a constant; whereas most mathematical parameters with "nought" subscripts are constants.

, but which are more straightforward to estimate, such as doubling time or half-life).

include the survival function, rearranging the largest eigenvalue of the Jacobian matrix, the next-generation method, calculations from the intrinsic growth rate, existence of the endemic equilibrium, the number of susceptibles at the endemic equilibrium, the average age of infection and the final size equation. Few of these methods agree with one another, even when starting with the same system of differential equations. is rarely observed in the field and is usually calculated via a mathematical model, this severely limits its usefulness.

Sample values for various contagious diseases

mentioned in the previous section, estimates have been made for a number of genera, and are shown in this table. Each genus may be composed of many species, strains, or variants for species, strains, and variants are typically less accurate than for genera, and so are provided in separate tables below for diseases of particular interest (influenza and COVID-19).Estimates for strains of influenza.Estimates for variants of SARS-CoV-2.

In popular culture

In the 2011 film Contagion.