## The Basic Reproductive Number

The basic reproductive number, R0 (also known as the basic reproductive ratio or, again incorrectly, rate), is the measure used to characterize the potential for an infectious organism to spread through a population in which there is no prior immunity and thus gives a measure of the maximum potential rate of spread in a given population (though differing social, economic, demographic and health characteristics of populations may provide widely differing opportunities for an infectious organism to disseminate) (Anderson and May, 1991). Clearly when everyone in a population is susceptible to infection R and R0 will have the same value, but assuming some degree of immunity is produced, however short term, R will decrease as the infection spreads whereas R0 by definition remains constant.

When an infection is at equilibrium, R = 1.0, as noted above. If R0 is greater than R (R0 > R), a proportion of the potential transmission events implied by R0 will fail because a proportion of potential contacts are already immune to infection in these circumstances, and only effective contacts with susceptible individuals will result in transmission. The symbol X is often used to represent the number of susceptible individuals in a population of N individuals, and x (= X/N) to represent the proportion of susceptible individuals in the population. In a theoretically uniformly homogeneous population, if x* represents the proportion of susceptible individuals when the infection is at equilibrium, x* can be used to estimate R0 as R0x* = R = 1.0. Anderson and May (1991) quote from their earlier work a range of values for R0 for different infections and different epidemiological settings; that for measles, for example, varying from 5 to 6 in post-World War I Kansas, USA to 16 to 18 in post-World War II England and Wales. Although in theory when R0 = 1 an infection has the capacity to spread in a wholly susceptible population, in practice it needs to exceed this value by a sufficient amount to ensure that the chain of infection is not terminated purely through chance events.

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