Prevalence Bathtub: Incidence × Duration

Inflow & Duration

Incidence rate 40 new cases / week

Average illness duration 14 days

Case-fatality proportion 6%

Simulation speed 1.0×

Live Readouts

Current prevalence

Steady-state I × D

Cumulative deaths

Cumulative recoveries

Observed case-fatality

0.0%

Sim days elapsed

Active case (in the prevalence pool)

Recovered — exits left

Died — exits right

How it works

Prevalence is a stock: a population of currently-ill people sitting in a pool. Two flows change it — incidence (new cases entering) and resolution (cases leaving, by recovery or death). This is exactly the "bathtub" analogy used across epidemiology and queueing theory:

Steady-state Prevalence  P  ≈  Incidence rate (I)  ×  Average duration (D)

  (an epidemiological instance of Little's Law, L = λW,
   valid whenever the inflow and outflow rates have settled)

Each case here carries an age since entry. With an exponential (memoryless) duration model, a case in the pool leaves during a small time step dt with probability dt / D — so the mean time in the pool is D regardless of how long it has already been there, matching how recovery/removal is modelled in standard compartmental epidemic models (SIR/SEIR). When a case leaves, it becomes a death with probability equal to the case-fatality proportion, otherwise a recovery.

Incidence rate — how many brand-new cases join the pool per week; drives the inflow pipe at the top of the tank.
Average illness duration — the mean number of days a case stays in the pool before resolving; longer duration inflates prevalence even if incidence is flat.
Case-fatality proportion — the share of resolving cases that exit as deaths (red, right chute) rather than recoveries (green, left chute).
Watch current prevalence drift toward the dashed steady-state I × D line — a low-incidence, long-duration disease (like a chronic condition) can sustain the same pool size as a high-incidence, short-duration one (like a common cold), which is exactly why prevalence and incidence answer different questions in real surveillance data.

Prevalence pool Recovery exit Death exit

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