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 transmission_rate directly instead of the default R0, or a period such as incubation_period or infectious_period instead of its rate, which is converted automatically. If both forms are supplied, the rate form is used and the response includes a warning. See Preset conversions and precedence for details.

Parameter	Status	Default	Description
`R0`	Default	`2.5`	Basic reproduction number.
`transmission_rate`	Alternative to `R0`	derived	$\beta$ . Per-contact transmission rate. Default: `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`.

CONTACT_MATRIX_EIGENVALUE_ALL is the dominant eigenvalue of the chosen population's contact matrix, summed over layers. With the defaults, R0 stays at 2.5 and $\beta$ depends on the population: about 0.0178 for United_States and 0.0181 for United_States__Vermont. If you pass transmission_rate, it is used as given, so R0 is no longer fixed at 2.5. To see the effective transmission_rate, set output.include_parameters.

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​