SIR

The Susceptible-Infected-Recovered model. A basic epidemic model where recovered individuals gain permanent immunity.

Compartments

• Susceptible: individuals who can be infected
• Infected: individuals who are currently infectious
• Recovered: individuals who have recovered and are immune

Transitions

• Susceptible → Infected: mediated by transmission_rate and the number of Infected individuals
• 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, 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.
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

Rate form

curl -X POST https://epyscenario-api.isi.it/api/v1/simulations \
-H "Content-Type: application/json" \
-d '{
  "model": {
    "preset": "SIR",
    "parameters": {"transmission_rate": 0.3, "recovery_rate": 0.1}
  },
  "population": {"name": "United_States"},
  "simulation": {"start_date": "2024-01-01", "end_date": "2024-04-01", "Nsim": 10}
}'

Using R0 and infectious_period

curl -X POST https://epyscenario-api.isi.it/api/v1/simulations \
-H "Content-Type: application/json" \
-d '{
  "model": {
    "preset": "SIR",
    "parameters": {"R0": 2.5, "infectious_period": 10.0}
  },
  "population": {"name": "United_States"},
  "simulation": {"start_date": "2024-01-01", "end_date": "2024-04-01", "Nsim": 10}
}'

Seeding initial conditions (percentage)

Seed 0.1% of the population as Infected. The remainder goes to the first compartment (Susceptible). Values in initial_percentages are percentages, not fractions.

curl -X POST https://epyscenario-api.isi.it/api/v1/simulations \
-H "Content-Type: application/json" \
-d '{
  "model": {
    "preset": "SIR",
    "parameters": {"R0": 2.5, "infectious_period": 10.0}
  },
  "population": {"name": "United_States"},
  "simulation": {"start_date": "2024-01-01", "end_date": "2024-04-01", "Nsim": 10},
  "initial_conditions": {
    "method": "percentage",
    "initial_percentages": {"Infected": 0.1}
  }
}'