Question

Imagine that a new, deadly coronavirus arises and starts a global pandemic. Experts are worried because the disease spreads easily, having a basic reproductive number, R₀​, of 6 . The good news is that an effective vaccine is quickly developed. What minimum proportion of the population, R₅​, would need to be vaccinated to ensure that the disease can no longer spread? Round your answer to two decimal places.

Answer 1

At least 83.33% of the population would need to be vaccinated against a new coronavirus with a basic reproductive number (R₀) of 6 to prevent the spread of the disease.

Step-by-step explanation:

To determine what minimum proportion of the population needs to be vaccinated against a new coronavirus with a basic reproductive number (R₀) of 6 to ensure that the disease can no longer spread, we apply the concept of herd immunity. The formula for herd immunity threshold (R₅) is R₅ = 1 - (1/R₀). Substituting the given R₀ of 6 into the formula, we get:

R₅ = 1 - (1/6)

R₅ = 1 - 0.1667

R₅ = 0.8333

This value then needs to be converted into a percentage by multiplying by 100, resulting in 83.33%. Therefore, at least 83.33% of the population would need to be vaccinated to stop the spread of the virus.

When we round the answer to two decimal places, we get R₅ ≈ 83.33%.