1.3 The effective reproduction number R_E

Since most populations will have some level of immunity to an infectious disease, the rate of spread will be less than indicated by the R₀ value. The measure of how a disease spreads in real situations is given by another dimensionless variable R_E – the effective reproduction number (Figure 3), which is often just called the R-value.

Figure 3 Diagrammatic representation of the effective reproduction number RE . (a) A single infected person (the purple dot) is introduced into a population where half are susceptible (yellow dots) and half are resistant (green dots). For this infection R0 = 4 (b) The initial infective transmits the infection to an average of RE others; RE = 2 because the two contacts who might have been infected (blue crosses) are resistant.

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Part (a) shows one infective surrounded by nine susceptibles. In part (b), the infective make contacts with four of the susceptibles, as shown by arrows, and transmit the infection to them; so there are now five infectives in the population. Three of the five dots are green in both (a) and (b). 2 of the lines in part (b) have the + sign on them.

Figure 3 Diagrammatic representation of the effective reproduction number RE . (a) A single infected person (the purple dot) is ...

Notice that R_E will never be greater than R₀ and will usually be less than R₀ because of the level of resistance or immunity in the population.

Another point is that R_E can tell us something about whether an infection will develop into an epidemic or just die out. If R_E is >1 then the number of infections will gradually increase over time. Exactly how quickly an epidemic will develop depends partly on the value of R_E, and partly on how long it takes before each infected person becomes infectious themselves, ie the time-course of infection.

Conversely if R_E <1 then the infection is self-limiting, because the number of infected people gradually decreases over time.