What Is the SEIR Model?
The SEIR model is the workhorse of infectious disease modeling. It divides a population into four compartments — Susceptible, Exposed (infected but not yet infectious), Infected, and Recovered — and tracks the flow of people between them over time. A susceptible person becomes exposed after contact with an infectious one. An exposed person becomes infectious after an incubation period. An infectious person becomes recovered (or deceased) after a recovery period.
This is a stub pillar page. The full guide will cover SEIR assumptions, extensions (SEIRD, age-structured SEIR, vaccinated compartments), limitations, and the spatial agent-based implementation. Use the browser simulators below to build intuition before reading the details.
The Core Flow
- S → E. Susceptible contacts an infectious person; transmission happens with probability β per contact.
- E → I. Exposed becomes infectious after the incubation period (1/σ).
- I → R. Infectious recovers (or dies) after the infectious period (1/γ). R₀ = β/γ.
Why SEIR and Not SIR
For diseases where the incubation period is short compared to the epidemic timescale, SIR is adequate. For everything else — COVID-19, measles, Ebola, many sexually transmitted infections — the lag between infection and infectiousness matters enormously. Skipping the E compartment makes the model predict faster-than-real dynamics because it assumes every newly infected person can immediately transmit.
From ODE to Agent-Based
The classic SEIR is a system of four ordinary differential equations. It assumes the population is well-mixed — every S has equal chance of encountering every I. This is wildly wrong in practice. An agent-based SEIR keeps the same compartments but places the agents on a grid or network, so transmission depends on proximity or contact structure. The curves look similar on average, but spatial SEIR produces wavefronts, refugia, and late-stage plateaus that the ODE model misses entirely.
Extensions That Matter
- SEIRD — adds a Deceased compartment. Required for mortality tracking.
- Age-structured SEIR — separate compartments by age band, with age-specific contact matrices and severity rates.
- SEIRV — adds a Vaccinated compartment that flows directly from S to R (or S to a protected version of S).
- Variant-aware SEIR — multiple I compartments for different variants, each with its own R₀ and cross-immunity coefficients.