A disease has a per-contact transmission probability of 0.30 and a contact rate of 5 contacts per day with infectious individuals. A researcher claims the force of infection is therefore 0.30. What is wrong with this claim?
AThe force of infection equals R₀ divided by the infectious period, not the per-contact probability
BForce of infection is not the per-contact transmission probability; it integrates contact rate, per-contact probability, and current prevalence of infection in the population
CThe force of infection must be dimensionless, so it cannot equal a probability
DThe per-contact probability of 0.30 should first be converted to an odds ratio
In the standard SIR model, force of infection λ = β × I/N, where β combines the contact rate and per-contact transmission probability, and I/N is the current prevalence. The per-contact probability (q = 0.30) is only one component. Even with the same per-contact probability, λ will be high when many people are currently infected (high I/N) and low when few are (e.g., late in the epidemic or with high vaccine coverage). The researcher has confused a fixed biological parameter (q) with a population-level, time-varying rate (λ).
Question 2 Multiple Choice
A cross-sectional seroprevalence survey finds that antibody positivity to a childhood virus rises steeply between ages 1–5 and plateaus near 95% by age 8. What does this pattern most directly reveal about the force of infection?
AThe force of infection increases with age — older children are at higher risk than younger ones
BThe force of infection is high in early childhood, concentrating most transmission among young children
CThe attack rate is 95%, implying this is a highly lethal infection
DThe virus was introduced into the population approximately 8 years ago
Under a catalytic model with constant force of infection λ, the proportion susceptible at age a is e^(-λa) — an exponential decay. A steep rise in seroprevalence during ages 1–5 means the probability of remaining susceptible falls quickly in those years, which requires a high λ in that age range. Near-complete seropositivity by age 8 means almost all susceptibles have been infected by then. This pattern is characteristic of diseases transmitted mainly in daycare and school settings (measles, varicella before vaccination), where young children have high contact rates. The pattern directly informs the optimal age for vaccination.
Question 3 True / False
The force of infection λ remains constant throughout the course of an epidemic in the classic SIR model.
TTrue
FFalse
Answer: False
In the SIR model, λ = βI/N. As the epidemic progresses, I — the number of currently infectious individuals — rises to a peak and then falls as infected individuals recover. λ therefore rises from near zero (early epidemic, few infectious individuals), peaks at the epidemic peak, and declines as the pool of susceptibles is depleted and infectious individuals recover. This dynamic trajectory of λ over time is precisely what produces the characteristic bell-shaped incidence curve. A constant λ would produce an exponential rise in cases with no natural peak.
Question 4 True / False
The force of infection can be estimated from age-seroprevalence data using the catalytic model, in which the probability of remaining susceptible at age a is approximately e^(−λa) under a constant force of infection.
TTrue
FFalse
Answer: True
The catalytic model treats infection as a continuous hazard process: a susceptible person faces a constant rate λ of becoming infected per unit time. Survival analysis gives the probability of escaping infection to age a as e^(-λa). Equivalently, the expected proportion seropositive at age a is 1 − e^(-λa). Fitting this curve to observed seroprevalence data by age yields a maximum-likelihood estimate of λ. The rate at which the seroprevalence curve rises with age directly reflects the force of infection. This approach is widely used for estimating pre-vaccination transmission intensity of measles, rubella, and other childhood infections.
Question 5 Short Answer
Explain the distinction between force of infection (λ), per-contact transmission probability (q), and the basic reproduction number (R₀), and why correctly distinguishing them matters for vaccine program design.
Think about your answer, then reveal below.
Model answer: Per-contact transmission probability (q) is a biological parameter: the chance of transmission given a single contact between an infectious and a susceptible individual. Force of infection (λ) is a population-level hazard rate: the instantaneous per-capita rate at which susceptibles become infected, which depends on q, the contact rate, and current disease prevalence. R₀ is a threshold parameter at epidemic start in a fully susceptible population: the average number of secondary cases from one case. For vaccine design, λ matters most: because λ varies by age (reflecting age-specific contact rates), age-seroprevalence curves reveal which age groups face the highest infection hazard and therefore benefit most from vaccination — guiding decisions about target age, booster timing, and coverage needed for herd immunity.
Confusing these quantities leads to policy errors. Using q (per-contact risk) as a proxy for λ ignores how prevalence and contact patterns shift the actual infection rate. Using R₀ alone obscures age structure entirely. Estimating λ from serological data is the empirically grounded approach that directly measures who is getting infected and at what rate — the input the vaccine program actually needs.