What is the commonly used relationship among prevalence, incidence, and average disease duration?

• A. Prevalence ≈ Incidence × Average duration
• B. Incidence ≈ Prevalence × Average duration
• C. Incidence × Prevalence = 1
• D. Prevalence + Incidence = 1

Answer: (A)

The situation assumes a stable, ongoing flow of new cases and a fairly constant time that people live with the disease. In that steady state, the number of people who have the disease at a given moment (the prevalence) is roughly the rate at which new cases occur (incidence) multiplied by how long people stay diseased on average. So, prevalence ≈ incidence × average duration.

Think of it this way: if 2% of the population develops the disease each year and, on average, people carry the disease for 5 years, you’d expect about 10% of the population to be living with the disease at any moment (ignoring deaths and recoveries that could alter the balance). This is an approximation that holds best when incidence is relatively constant and the disease duration doesn’t vary widely.

The other options don’t fit because they’d violate units or logical relationships. Incidence multiplied by duration makes sense dimensionally and conceptually for a steady state, while the alternatives would produce nonsensical units or imply an impossible fixed total when added or multiplied.