Susceptible-Exposed-Infected-Recovered (SEIR) Models

SEIR models are compartmental models of disease transmission that divide a population into people who are susceptible, exposed (infected but not yet infectious), infectious, and recovered, and then describe the flow of individuals between these compartments over time. By adding an exposed (latent) stage to the simpler SIR structure, the SEIR model captures the delay between infection and infectiousness that characterises many diseases, and it is one of the workhorse frameworks of infectious-disease epidemiology.

Definition

An SEIR model is a compartmental transmission model that partitions a population into susceptible, exposed (latent), infectious, and recovered classes and uses transition rates between these classes to describe how an epidemic evolves over time.

Scope

This entry explains the compartmental modelling idea, the meaning of the S, E, I, and R compartments and the transitions between them, the relationship of these models to the reproduction number, and the simplifying assumptions they make. It is a methodological reference topic, not clinical guidance.

Core questions

• What do the S, E, I, and R compartments represent, and how do individuals move between them?
• Why does adding an exposed compartment matter, and how does SEIR differ from SIR?
• How does the model's structure relate to the basic reproduction number?
• What assumptions, such as homogeneous mixing, do these models make?

Key concepts

• Susceptible compartment (S)
• Exposed / latent compartment (E)
• Infectious compartment (I)
• Recovered / removed compartment (R)
• Transition (transmission, progression, recovery) rates
• Homogeneous mixing assumption
• Relationship to R0 and the threshold

Key theories

Compartmental epidemic modelling

Kermack and McKendrick introduced the compartmental approach that represents an epidemic as flows between susceptible, infectious, and recovered classes, the framework that SEIR models extend by inserting a latent (exposed) compartment.

Next-generation derivation of R0 in compartmental models

Diekmann and colleagues showed how to derive the basic reproduction number directly from the structure of a compartmental model via its next-generation matrix, linking the SEIR transition rates to the model's threshold behaviour.

Mechanisms

In an SEIR model, susceptible individuals become exposed at a rate that depends on contact with infectious individuals; exposed individuals progress to the infectious class after a latent period; infectious individuals recover (or are removed) after an infectious period; and recovered individuals are typically assumed immune. These flows are written as transition rates, and the basic reproduction number emerges from their combination. The simplest forms assume homogeneous mixing, fixed rates, and a closed population, and these assumptions can be relaxed by adding compartments for age, spatial structure, or waning immunity. The SIR special case omits the exposed compartment when the latent period is negligible.

Clinical relevance

Compartmental models such as SEIR underpin how analysts project epidemic trajectories and explore, at the population level, how changes in contact or immunity would alter spread. They are a reference modelling framework that describes population dynamics and are not a basis for individual diagnostic or treatment decisions.

Epidemiology

SEIR and related compartmental models have been used to study a wide range of infections with a latent stage and to interpret outbreak data; their projections depend heavily on the assumed parameters and structure, so outputs are best read as scenario-dependent rather than precise forecasts.

History

The compartmental framework originates with Kermack and McKendrick in 1927. Over the following decades it was elaborated into the SIR and SEIR families and synthesised by Anderson and May, while the next-generation methods of Diekmann and colleagues clarified how the reproduction number follows from the compartmental structure.

Debates

How realistic must the model structure be?

Simple homogeneous-mixing SEIR models are transparent but can misstate dynamics when populations are strongly age- or contact-structured; how much heterogeneity to build in trades realism against tractability and identifiability, a recurring modelling judgement.

Key figures

• William Ogilvy Kermack
• Anderson Gray McKendrick
• Roy Anderson
• Robert May
• Odo Diekmann
• Matt Keeling

Seminal works

• kermack-mckendrick-1927
• diekmann-1990
• anderson-may-1991

Frequently asked questions

What is the difference between SIR and SEIR models?

An SEIR model adds an exposed (latent) compartment for individuals who are infected but not yet infectious, whereas a SIR model omits this stage and assumes individuals become infectious as soon as they are infected.

What does the 'exposed' compartment mean?

It represents people who have been infected but are still in the latent period and cannot yet transmit the agent; they later progress to the infectious compartment.