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# Prevalence, incidence and duration

- Concept

How many people are ill depends on how many fall ill and how long the illness lasts: P ≈ I × D.

Updated Nov 5, 2026

## Key points

- In a steady state with low prevalence: P ≈ I × D (incidence times mean duration).
- Units must match: incidence per person-year and duration in years.
- A treatment that prolongs survival without cure raises prevalence even when incidence is unchanged.
- A short acute illness (a cold) can have high incidence and low prevalence.
- A long chronic disease (diabetes) accumulates cases: high prevalence with moderate incidence.

On this page

- The basics Key points
- What it is
- Key facts
- Worked example
- Examples of incidence and duration combined
- Markers
- In practice
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

Prevalence behaves like the water level in a tank: incidence is the tap filling it, and cure or death is the drain. When the situation is stable and the disease is uncommon, prevalence is roughly incidence multiplied by mean duration. This explains why a treatment that prolongs life without curing raises prevalence, and why short illnesses have low prevalence even when they are common.

## Key facts

- Exact steady-state form: P/(1 − P) = I × D; when P is small, P/(1 − P) ≈ P.
- Knowing two of the three values gives the third: D ≈ P / I.
- The relation does not hold during an outbreak or a fast-changing epidemic (no steady state).

## Worked example

- Data: a chronic disease has an incidence of 4 per 1,000 person-years and lasts 5 years on average; the situation is stable.
- Prevalence ≈ I × D = 0.004 per year × 5 years = 0.02, that is 2% (20 per 1,000).
- A treatment arrives that does not cure but extends mean duration to 8 years; incidence stays at 4 per 1,000.
- New prevalence ≈ 0.004 × 8 = 0.032, that is 3.2% (32 per 1,000).
- Reading: more people are living with the disease because they live longer, not because more people fall ill.

## Examples of incidence and duration combined

| Situation | Incidence | Duration | Prevalence |
| --- | --- | --- | --- |
| Brief respiratory infection | High | Days | Low |
| Incurable chronic disease | Moderate | Decades | High |
| Highly lethal acute disease | Moderate | Very short (death) | Low |
| Treatment that prolongs life without cure | Unchanged | Longer | Rises |

## Markers

- P ≈ I × D

## In practice

- Wider antiretroviral treatment raised the prevalence of people living with HIV because survival improved.
- A programme that finds and cures an infection earlier shortens its duration and lowers prevalence.

## Common pitfalls

- Reading a rise in prevalence as a rise in new cases.
- Mixing units (incidence per year with duration in months).
- Using P ≈ I × D when prevalence is high, without the P/(1 − P) correction.

## Memory aid

The bathtub: incidence is the tap, cure and death are the drain; plug the drain and the water rises even if the tap is unchanged.

## Test yourself

Think of the answer, then tap the question to see it.

## Incidence 2 per 1,000 person-years and mean duration 10 years, in a steady state. What is the approximate prevalence?

P ≈ 0.002 × 10 = 0.02, that is 2% (20 per 1,000).

## What happens to prevalence if a drug cures the disease faster, with the same incidence?

It falls, because each case lasts a shorter time.

## Why can seasonal influenza have high incidence and low prevalence?

Each episode lasts only days: many cases appear, but few overlap at any one moment.

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## Connections

## Related 4

- [Prevalence](https://durgical.com/en/epidemiology/prevalence/)
- [Incidence](https://durgical.com/en/epidemiology/incidence/)
- [Incidence rate and person-time](https://durgical.com/en/epidemiology/incidence-rate-and-person-time/)
- [Natural history of disease](https://durgical.com/en/epidemiology/natural-history-of-disease/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [Principles of Epidemiology | Lesson 3 - Section 2](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html) (Centers for Disease Control and Prevention, 2012); [Principles of Epidemiology | Lesson 3 - Section 1](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section1.html) (Centers for Disease Control and Prevention, 2012).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/prevalence-incidence-and-duration/