SEIR Model
SEIR Model
Overview
Like the SIR model, the SEIR model is used to model how a condition spreads over a population. Also like the SIR model, the typical application of the SEIR model is modeling the spread of an infectious disease.
The SEIR model expands on the SIR model by adding a new state. In addition to being susceptible (S), infectious (I), recovered (R), and individual can be exposed (E). This allows the model to account for an incubation period during which the individual has been infected but does not yet infect others.
Parameters
The SEIR model typically uses the following parameters (most of which are already present in the simpler SIR model), often expressed as Greek letters:
beta ( β ): probability susceptible-infected contact results in a new exposure
gamma ( γ ): probability infected recovers
sigma ( σ ) or alpha ( α ): probability exposed person becomes infected
More complicated versions of the SEIR may add birth and death rates:
Lambda ( Λ ): birth rate
mu ( μ ): death rate
Underlying Math
For quants, the underlying math of the model:
Change in number of susceptible = Lambda - mu * number susceptible - beta * number susceptible * number infectious / total number of individuals
Change in number exposed = beta * number susceptible * number infectious / total number of individuals - mu * number exposed - alpha * number exposed
Change in number infection = alpha * number exposed - mu * number infectious - gamma * number infectious
Change in number recovered = gamma * number infectious - mu * number recovered
Basic Reproduction Number
Under the SEIR model, the basic reproduction number is (alpha / (alpha + mu)) * (beta / (gamma + mu)).
Recall the reproduction number on a high level represents the number of new cases of infection caused by a previous case on infection. Intuitively, a basic reproduction number less than 1 means the number of new cases is less than the number of previous cases, so infection is going down. Meanwhile, a value greater than 1 means there are more new cases than previous cases, so infection is growing. See the SIR model page for a more detailed explanation.
Related Research
The SEIR has been used in recent research on COVID-19. The SEIR model is especially relevant to the COVID-19 virus because we have observed some infected individuals do not exhibit noticeable symptoms, making the risk of spread greater than if infection were obvious.
The SEIR model published by the WHO on January 31 estimates a basic reproduction number of 2.68, predicting epidemics in large Chinese cities which have since come to pass (though at larger scale than predicted). Another SEIR model by Gartner of Johns Hopkins suggests the actual number of cases is much higher than reported, and estimates the following number of imported cases by country (at the time):
Contributors: Jason Jin, Michael Lin, Anmol Kapur, Austin Witt