Question

"Polio has a basic reproduction number (R0) = 5. The vaccine is very good; in fact, polio vaccine is 99% effective when two follow up booster shots are given. What proportion of a population needs to be vaccinated in order for herd immunity to be effective? Be sure to enter your answer as a decimal, not as a percentage."

Answer 1

0.81

Explanation:

Herd immunity or community immunity is the immunity seen after vaccination of a population wherein the large portion of the population becomes immune to the pathogen. It depends on vaccine efficacy and vaccination rate.

The reproduction number R_o is a factor indicating the number of people that can be infected by the person with the disease. If Ro=5 then one infected person can infect 5 people with Polio virus.

V_c= q_c/E

V_c= Vaccine coverage

q_c= herd immunity threshold

E= Vaccine efficacy= 99%=0.99

`q_c=1-1/R_o= 1-1/5=0.8`

V_c= q_c/E

V_c= 0.8/0.99= 0.808= 0.81

Thus, 81% coverage or vaccination for Polio is required to stop spread of Polio in the population.