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 8 . The good news is that an effective vaccine is quickly developed. What minimum proportion of the population, Rc, would need to be vaccinated to ensure that the disease can no longer spread?

Round your answer to two decimal places. __________

Answer 1

To ensure that a new deadly coronavirus with a reproduction number of 8 can no longer spread, at least 87.5% of the population needs to be vaccinated, which rounds to 88% when expressed to two decimal places.

Step-by-step explanation:

In a hypothetical scenario where a new deadly coronavirus with a basic reproductive number (R₀) of 8 starts a global pandemic, scientists and medical professionals would need to quickly calculate the minimum proportion of the population that needs to be vaccinated to prevent the spread of the disease.

This proportion is known as the herd immunity threshold, Rc. The formula to calculate Rc in the context of vaccination is Rc = 1 - (1/R₀). Substituting the given R₀ value of 8 into this equation, we get Rc = 1 - (1/8), which simplifies to Rc = 7/8 or 0.875.

To achieve herd immunity, at least 87.5% of the population would need to be vaccinated. Due to the nature of rounding, we might express this as 0.88 or 88% when rounding to two decimal places.