In a city of 600 000 people, a disease has R₀ = 10. A vaccine with 80 % efficacy is given to 70 % of the population. Assuming random mixing, calculate the additional percentage of the population that must already be immune (through prior infection or other measures) to achieve herd immunity.
Answer
34.0%
The correct answer is 34.0% — Express result as a percentage of total population: 34%.
Step-by-step solution
- Compute herd‑immunity threshold: 1-1/R₀ = 1-1/10 = 0.9 or 90%.
- Calculate immunity conferred by vaccination: coverage × efficacy = 0.70 × 0.80 = 0.56 or 56%.
- Determine remaining immunity required: 0.90 - 0.56 = 0.34 or 34%.
- Express result as a percentage of total population: 34%.
Common mistake: Using vaccine coverage instead of the product of coverage and efficacy
Concept tested: Herd immunity calculation with vaccine efficacy
Published · How this solution was prepared and checked
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