A new emerging disease QQ has created an epidemic in South America. Everyone in the population is susceptible and no one is vaccinated for the disease. The World Health Organization (WHO) has calculated the reproduction rate of disease to be an R0 of 5. What percentage of the population should be vaccinated to create a herd immunity threshold, and stop the spread?

Question

BlackTom AI · Accepted Answer

To tackle this question, I’ll walk through what herd immunity threshold means and how it relates to R0 before evaluating each option.
Option a: 75% — This would correspond to a herd immunity level of 0.75. However, with an R0 of 5, the theoretical threshold is higher, since more transmission needs to be blocked to prevent outbreaks. Therefore, 75% is too low.
Option b: 20% — A herd immunity threshold of 20% implies that only a small fraction needs immunity to stop spread. This contradicts the basic epidemiological relation where higher R0 requires a substantially larger protected fraction; 20% is not plausible for an R0 as high as 5.
Option c: 45% — This option suggests a moderate level of population immunity. Yet, using the standard herd immunity calculation (1 - 1/R0), an R0 of 5 yields a threshold around 0.8 or 80%. 45% falls short of what is needed to halt transmission.
Option d: 80% — This aligns with the commonly used herd immunity formula: HIT = 1 - 1/R0. Substituting R0 = 5 gives HIT = 1 - 1/5 = 4/5 = 0.8, i.e., 80%. This means about four-fifths of the population would need immunity to stop the spread in a completely susceptible population with no vaccination.
In summary, the key idea is that herd immunity threshold rises with R0, and for an R0 of 5 the required vaccination coverage is around 80%. The alternative options either underestimate or misinterpret the relationship between R0 and the necessary immune fraction, leading to incorrect conclusions about the epidemic's control point.

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