SEIR

The Susceptible-Exposed-Infected-Recovered model. Extends SIR with an exposed (latent) period before individuals become infectious.

Compartments

Susceptible: individuals who can be infected
Exposed: individuals who are infected but not yet infectious (latent period)
Infected: individuals who are currently infectious
Recovered: individuals who have recovered and are immune

Transitions

Susceptible → Exposed: mediated by transmission_rate and the number of Infected individuals
Exposed → Infected: spontaneous at incubation_rate
Infected → Recovered: spontaneous at recovery_rate

Parameters

Some parameters can be provided in multiple forms. For example, you can pass R0 instead of transmission_rate, incubation_period instead of incubation_rate, or infectious_period instead of recovery_rate, and they are automatically converted. If both forms are supplied, the rate form wins and the source is dropped silently. See calculated parameters for the conversion machinery.

Parameter	Status	Default	Description
`transmission_rate`	Default	`0.3`	$\beta$ . Per-contact transmission rate.
`R0`	Alternative to `transmission_rate`	unset	Basic reproduction number. When passed, `transmission_rate = R0 * recovery_rate / CONTACT_MATRIX_EIGENVALUE_ALL`.
`incubation_rate`	Default	`0.2`	E → I rate.
`incubation_period`	Alternative to `incubation_rate`	unset	Days from exposure to infectiousness. When passed, `incubation_rate = 1 / incubation_period`.
`recovery_rate`	Default	`0.1`	I → R rate.
`infectious_period`	Alternative to `recovery_rate`	unset	Days infectious. When passed, `recovery_rate = 1 / infectious_period`.

Examples

Both examples below seed 0.1% of the population as Exposed at t=0 via an explicit initial_conditions block; the rest of the population starts in Susceptible. See Initial Conditions for other seeding options.

Rate form

curl -X POST https://epyscenario-api.isi.it/api/v1/simulations \
-H "Content-Type: application/json" \
-d '{
  "model": {
    "preset": "SEIR",
    "parameters": {"transmission_rate": 0.3, "incubation_rate": 0.2, "recovery_rate": 0.1}
  },
  "population": {"name": "United_States"},
  "simulation": {"start_date": "2024-01-01", "end_date": "2024-06-01", "Nsim": 10},
  "initial_conditions": {
    "method": "percentage",
    "initial_percentages": {"Exposed": 0.1}
  }
}'

Using `R0` and period forms

curl -X POST https://epyscenario-api.isi.it/api/v1/simulations \
-H "Content-Type: application/json" \
-d '{
  "model": {
    "preset": "SEIR",
    "parameters": {"R0": 2.5, "incubation_period": 5.0, "infectious_period": 10.0}
  },
  "population": {"name": "United_States"},
  "simulation": {"start_date": "2024-01-01", "end_date": "2024-06-01", "Nsim": 10},
  "initial_conditions": {
    "method": "percentage",
    "initial_percentages": {"Exposed": 0.1}
  }
}'

Compartments​

Transitions​

Parameters​

Examples​

Rate form​

Using R0 and period forms​