Basic reproduction number

In epidemiology, the basic reproduction number (sometimes called basic reproductive rate) of an infection is the mean number of secondary cases a typical single infected case will cause in a population with no immunity to the disease in the absence of interventions to control the infection. It is often denoted R₀. This metric is useful because it helps determine whether or not an infectious disease will spread through a population. It was originally used by George MacDonald in 1952, who constructed population models of the spread of malaria.

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When

R₀ < 1

the infection will die out in the long run (provided infection rates are constant). But if

R₀ > 1

the infection will be able to spread in a population. Large values of R₀ may indicate the possibility of a major epidemic.

Generally, the larger the value of R₀, the harder it is to control the epidemic. In particular, the proportion of the population that needs to be vaccinated to provide herd immunity and prevent sustained spread of the infection is given by 1-1/R₀. The basic reproductive rate 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.

Other uses

R₀ is also used as a measure of individual reproductive success in population ecology^[5], evolutionary invasion analysis and life history theory.

References