Question

R_{o = rate of transmission}

Probability of infection = R_o /N

Herd Immunity Threshold = 1 – 1/R_o

1a) In some flu seasons Influenza has an R_o = 2. If 100 people are exposed to an individual that is infected, what is the probability that one of them becomes infected?

1b) What percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the R_o is less than 1?

1c) Currently, with an estimated R_o of around 4 for COVID-19 What percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the R_o is less than 1?

Answer 1

a) Given,

Ro = rate of transmission =2

N =100

The probability that one of them becomes infected i.e.

Probability of infection = Ro /N = 2/ 100 = 1/50 = 0.02

b) The percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the Ro is less than 1.

Suppose 0<Ro <1.

Herd Immunity Threshold = 1 – 1/Ro = 1 - 1/0.999999999 00 and in terms of percentage it beocmes 99.9999%.In other words, 100 people can need to be vaccinated.

c) Currently, with an estimated Ro of around 4 for COVID-19 What percentage of the 100 people would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the Ro is less than 1?

Ro 4

Herd Immunity Threshold = 1 – 1/4 = 3/4 = 0.75 i.e. 75 %

Out of 100 people, 75 would need to be vaccinated to reach the Herd Immunity Threshold (HIT) in which the Ro is less than 1.