Question

formula 3 points
when a critical proportion of the population becomes immune, the disease may no longer persist in the population. this is called herd immunity threshold (hit), and it can be calculated as: ( pc = 1 - (1/r_0) ).
what would be the hit for a disease with an ( r_0 ) of 5.9? remember that this value represents the proportion of the population that needs to become immunized to stop the spread of the disease. please enter your value in percentile (%). enter 1 decimal place only, without units.
answer

Explanation:

Step1: Recall the HIT formula

The formula for Herd Immunity Threshold (HIT) is \( pc = 1 - \frac{1}{R_0} \), where \( R_0 \) is the basic reproduction number.

Step2: Substitute \( R_0 = 5.9 \) into the formula

First, calculate \( \frac{1}{R_0} = \frac{1}{5.9} \approx 0.1695 \). Then, \( pc = 1 - 0.1695 = 0.8305 \).

Step3: Convert to percentage and round to 1 decimal place

Multiply by 100 to get the percentage: \( 0.8305\times100 = 83.05\% \), which rounds to \( 83.1\% \).

Answer:

83.1