Herd Immunity for Smallpox

initial fraction immune

0.05

final time

60.

A population has "herd immunity" when the immune population is high enough so that if an infection is introduced, it dies out without building up. You can see this by sliding the initial immune fraction until the red graph does not increase in the illustration for smallpox.

The limit

lim

t∞

s(t)

represents the fraction of the population left susceptible after an epidemic. You can see this by sliding the final time until

i(t)

is effectively zero.

This Demonstration shows the spread of smallpox in a large fixed population with contact number

c=5.2

, infectious period

1/b=16

, and daily contact rate,

a=0.325

.