<Dd> R 0 ⋅ S = 1 . (\ displaystyle \ R_ (0) \ cdot S = 1 .) </Dd> <P> S can be rewritten as (1 - p) because p is the proportion of the population that is immune and p + S equals one . Then, the equation can be rearranged to place p by itself as follows: </P> <Dl> <Dd> R 0 ⋅ (1 − p) = 1, (\ displaystyle \ R_ (0) \ cdot (1 - p) = 1,) → 1 − p = 1 R 0, (\ displaystyle 1 - p = (\ frac (1) (R_ (0))),) → p c = 1 − 1 R 0 . (\ displaystyle p_ (c) = 1 - (\ frac (1) (R_ (0))).) </Dd> </Dl> <Dd> R 0 ⋅ (1 − p) = 1, (\ displaystyle \ R_ (0) \ cdot (1 - p) = 1,) → 1 − p = 1 R 0, (\ displaystyle 1 - p = (\ frac (1) (R_ (0))),) → p c = 1 − 1 R 0 . (\ displaystyle p_ (c) = 1 - (\ frac (1) (R_ (0))).) </Dd>

How herd immunity is responsible for the eradication of smallpox