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Herd immunity

The basic reproduction number says how many people one infected person on average infects further in a population where everyone is susceptible. In the simple model the problems use, spread stops when the immune share is one minus one divided by this number. The infection then too often meets someone who is already immune. Those who cannot be vaccinated are protected indirectly. The threshold is a calculation in the model, not a guarantee for a particular disease, because infection is not always evenly spread and immunity can wane.

p=1−1R0p = 1 - \frac{1}{R_0}immune share in the simple model

Symbols

R0R_0new infections per case, without immunity
ppthreshold

Example

R0=5R_0 = 5: p=(1−1/5)⋅100=80p = (1 - 1/5) \cdot 100 = 80%.

R0=2R_0 = 2: p=(1−1/2)⋅100=50p = (1 - 1/2) \cdot 100 = 50%.

A higher R0 needs a higher immune share. Recalculate the threshold if the number changes.
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Part of Biology 2: The immune system.