Basic reproduction number

In epidemiology, the basic reproduction number (sometimes called basic reproductive ratio, or incorrectly basic reproductive rate, and denoted R₀, r nought) of an infection can be thought of as the number of cases one case generates on average over the course of its infectious period, in an otherwise uninfected population.

This metric is useful because it helps determine whether or not an infectious disease can spread through a population. The roots of the basic reproduction concept can be traced through the work of Alfred Lotka, Ronald Ross, and others, but its first modern application in epidemiology was by George MacDonald in 1952, who constructed population models of the spread of malaria.

When

the infection will die out in the long run. But if

the infection will be able to spread in a population.

Generally, the larger the value of R₀, the harder it is to control the epidemic. For simple models and a 100%-effective vaccine, the proportion of the population that needs to be vaccinated to prevent sustained spread of the infection is given by 1 − 1/R₀. The basic reproduction number is affected by several factors including the duration of infectivity of affected patients, the infectiousness of the organism, and the number of susceptible people in the population that the affected patients are in contact with.

In populations that are not homogeneous, the definition of R₀ is more subtle. The definition must account for the fact that a typical infected individual may not be an average individual. As an extreme example, consider a population in which a small portion of the individuals mix fully with one another while the remaining individuals are all isolated. A disease may be able to spread in the fully mixed portion even though a randomly selected individual would lead to fewer than one secondary case. This is because the typical infected individual is in the fully mixed portion and thus is able to successfully cause infections. In general, if the individuals who become infected early in an epidemic may be more (or less) likely to transmit than a randomly chosen individual late in the epidemic, then our computation of R₀ must account for this tendency. An appropriate definition for R₀ in this case is "the expected number of secondary cases produced by a typical infected individual early in an epidemic".

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