Science has once again stepped in to show the value of herd immunity. In a theoretical study in PLoS One, Guy Katriel and Lewi Stone look at the effect of herd immunity on pandemics. They demonstrate that the probability of a pandemic increases non-linearly as immunity levels in a population decline.
In particular, we note the dramatic nonlinear increase in attack rate as
a function of the percentage of susceptibles initially present in the
population.
Small decreases in herd immunity have potentially large consequences in terms of disease.
Assuming, the attack rate (continuous line) is plotted as a
function of the initial fraction of susceptiblesin the population. An epidemic will not trigger
unless the initial susceptibles are greater than, due to herd immunity. The dashed line shows the
naive prediction for the attack rate, obtained by extrapolating linearly
from theattack rate for
, which can be well below the theoretical estimate.









