2.1 Herd immunity threshold

In section 1, we discussed disease susceptibility and the proportion of the population who are susceptible. This value is designated by a variable ‘S’. In the illustrated example (Figure 5a) in a population of 12 individuals 9 are resistant and 3 are susceptible.

S = 3/12 = 0.25 and the proportion resistant = 1 –S = 0.75

Figure 5 Diagrammatic representation of herd immunity threshold for a disease where R0 = 4. An infective (purple) is introduced into a population (a) where three individuals are susceptible (yellow) and nine are resistant (green). Potentially the infective could infect 4 individuals (arrows) but 3/4 of these contacts are resistant, so there is only one new case of infection (purple dot), ie RE =1.

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Part (a) shows one infective surrounded by12 individuals of which 3 are susceptible. In part (b), the infective makes contacts with four of the individuals, as shown by arrows, but transmits the infection to only 1 of them since three of the potential contacts are resistant. Blocked transmission is indicated by a cross on the contact arrows.

Figure 5 Diagrammatic representation of herd immunity threshold for a disease where R0 = 4. An infective (purple) is introduced into a ...

Recall that if R_TT =1. The value can be calculated from the basic reproduction number R₀.

HIT = 1 – 1/R₀

Let us consider how this works for a disease with R₀ = 4

HIT = 1 -1/4 = 0.75

If this is now expressed as the percentage of the population that must be resistant to stop a disease from spreading:

HIT = 0.75 x100 = 75%.

For a diagrammatic representation of this example, see Figure 5(b). In this case R₀=4 and there is only one secondary infection (R_E =1), because 3 of the 4 potential effective contacts are resistant.

There is some simplification in the calculation of HIT, since it assumes that a person is either completely susceptible or totally resistant. In practice resistance develops over time following infection or vaccination, and the level of resistance can wane. Nevertheless, considering individuals to be susceptible or resistant is useful for modelling epidemics and planning vaccination programmes.