Questions: Communicable Disease Epidemiology

Question 1

Measles has a basic reproduction number (R₀) of approximately 15. What fraction of the population must be immune to achieve herd immunity?

• A. About 50% — more than half is generally sufficient for herd immunity
• B. About 75% — high-R₀ diseases require three-quarters immune
• C. About 93% — derived from the formula 1 − 1/R₀
• D. 100% — diseases with R₀ above 10 require universal vaccination to interrupt transmission

Answer: (C)

Herd immunity threshold = 1 − 1/R₀ = 1 − 1/15 ≈ 0.933, or about 93%. This is why measles requires ~95% vaccination coverage (allowing some margin). Options A and B use rules of thumb unconnected to the actual formula. Option D is incorrect — herd immunity thresholds below 100% are what make vaccination campaigns feasible.

Question 2

Surveillance data in a city show influenza case counts declining consistently over three weeks. What does this most directly indicate about the effective reproduction number Re?

• A. Re > 1; the outbreak is still accelerating but slowing its pace
• B. Re equals R₀; the two values converge once an outbreak is established
• C. Re < 1; each case is on average producing fewer than one secondary case
• D. R₀ has decreased, probably due to viral mutation reducing pathogen fitness

Answer: (C)

Declining case counts mean the epidemic is shrinking — each generation of infection is smaller than the last. This is the definition of Re < 1. Re is the empirical, real-world reproduction number accounting for existing immunity and behavior; R₀ is a fixed property of the pathogen in a fully susceptible population. R₀ itself does not change week-to-week.

Question 3

Early in an epidemic, before significant population immunity has built up, the effective reproduction number Re is approximately equal to R₀.

• T. True
• F. False

Answer: True

Re = R₀ × (fraction of population still susceptible). At the very start of an outbreak in a naive population, almost everyone is susceptible, so that fraction is near 1, and Re ≈ R₀. As immunity accumulates through infection or vaccination, Re diverges downward from R₀.

Question 4

A pathogen with a higher R₀ will generally spread more rapidly through a population than one with a lower R₀.

• T. True
• F. False

Answer: False

R₀ describes spread in a fully susceptible population — a theoretical baseline. Real spread is governed by Re, which accounts for existing immunity and behavioral interventions. A pathogen with R₀ = 15 in a population with 94% immunity has Re < 1 and will not spread; a pathogen with R₀ = 3 in a fully naive population will spread rapidly. The common misconception is treating R₀ as a real-time indicator of spread.

Question 5

What three biological parameters combine to produce R₀, and why does understanding this decomposition matter for choosing interventions?

Model answer: R₀ = transmission probability per contact × contact rate × duration of infectiousness. The decomposition matters because different interventions target different components: masks and ventilation reduce transmission probability per contact; social distancing and isolation reduce contact rate; antivirals and supportive care reduce infectious duration. Knowing which parameter dominates for a given pathogen tells you where intervention effort will be most effective.

A single R₀ number can arise from very different parameter combinations — a highly transmissible pathogen with a short infectious period may have the same R₀ as a moderately transmissible one with a long period, but they require different control strategies. The decomposition makes the underlying biology visible and actionable.