SEIR Model

What is the SEIR Model?

A basic model for infectious diseases. The SEIR Model helps researchers to gain insights into how quickly these diseases spread, how these diseases are affecting different proportions of the population, how quickly those infected are able to recover, etc.

Basic Compartments of the Model

The SEIR Model separates the population into different compartments. They are:

Susceptible - Healthy and not infected, can become infected

Exposed - Exposed to disease by an infected person, may (or may not) become infected

Infected - Can infect susceptible portions of the population

Recovered - Was infected, cannot become infected again

The model produces the number of susceptible (S(t)), infected (I(t)), exposed (E(t)), and recovered (R(t)) on day t.

State Transitions

When running the simulation, the model will change from

Susceptible → Exposed → Infected → Recovered

Variables

Below are the most important and relevant variables:

• N: total population

• S(t): number of people susceptible on day t

• E(t): number of people exposed on day t

• I(t): number of people infected on day t

• R(t): number of people recovered on day t

• β: expected amount of people an infected person infects per day

• D: number of days an infected person has and can spread the disease

• γ: the proportion of infected recovering per day γ = (1/D)

• Ro: the total number of people an infected person infects (Ro = β/γ)

Change in Variables S(t), E(t), I(t), R(t)

It is necessary to compute the derivative of variables S(t), E(t), I(t), and R(t), so that the changes in these variables can be calculated per day, t. The differential equations are shown below: