Questions: Infectious Disease Epidemiology

Question 1

A pathogen has a basic reproduction number R₀ = 4. Approximately what fraction of the population must be immune to achieve herd immunity?

• A. 25%
• B. 50%
• C. 75%
• D. 90%

Answer: (C)

The herd immunity threshold is 1 − 1/R₀. For R₀ = 4: 1 − 1/4 = 0.75, or 75%. This is the fraction of the population that must be immune (through vaccination or prior infection) to reduce the effective reproduction number below 1 and cause the outbreak to die out. A common error is confusing R₀ itself with the threshold — R₀ = 4 does NOT mean 40% immunity suffices.

Question 2

R₀ is a fixed biological property of a pathogen that remains constant regardless of the population in which it spreads.

• T. True
• F. False

Answer: False

R₀ depends on both pathogen biology AND population characteristics: contact rates, population density, behavior, prior immunity, and environmental factors. SARS-CoV-2, for example, had dramatically different estimated R₀ values across countries and across time periods as behavior changed. Treating R₀ as a fixed constant leads to incorrect predictions about outbreak dynamics and intervention thresholds.

Question 3

A disease has a case fatality rate of only 0.1% but an R₀ of 8. A second disease has a case fatality rate of 10% but an R₀ of 1.1. Which is likely to cause more total deaths in a large naive population, and why?

Model answer: The first disease (R₀ = 8, CFR 0.1%) would likely cause more total deaths because total deaths = total infections × CFR. With R₀ = 8, the high-transmissibility disease infects a much larger fraction of the population, and even 0.1% of a very large number can exceed 10% of a small number.

Total mortality is driven by both transmissibility and lethality. A highly transmissible pathogen infects a huge proportion of the population before herd immunity is reached. For R₀ = 8, the final epidemic size is roughly 98% of the population; for R₀ = 1.1, it may infect only a few percent. Multiplying those totals by the respective CFRs often reverses intuitions about which disease is more dangerous.