SIR Epidemiological Model¶

A deterministic compartmental model with dissmodel¶

The SIR model tracks the spread of an infectious disease through a population divided into three compartments:

• Susceptible — healthy individuals who can be infected
• Infected — individuals who carry and spread the disease
• Recovered — individuals who have recovered and gained immunity

Requirements — this notebook uses the SIR model from dissmodel-sysdyn, installed separately:

pip install "git+https://github.com/DisSModel/dissmodel-sysdyn.git"

How it works¶

At each time step, the model computes:

Variable	Formula	Description
α	contacts × probability	Force of infection
ΔI	I × α × (S / N)	New infections
ΔR	I / duration	New recoveries

Where N = S + I + R is the total population.

Imports¶

In [1]:

from dissmodel.core import Environment
from dissmodel_sysdyn.models import SIR
from dissmodel.visualization import Chart

from dissmodel.core import Environment from dissmodel_sysdyn.models import SIR from dissmodel.visualization import Chart

⚠️ Important: instantiation order¶

The Environment must always be created before any model (SIR, Chart). Models connect to the active environment automatically when instantiated — if no environment exists yet, the connection fails.

Environment  →  SIR  →  Chart
     ↑           ↑        ↑
  first       second    third

In [2]:

# 1. Environment must be created first
env = Environment()

# 1. Environment must be created first env = Environment()

Setting up the model¶

The SIR model accepts the following parameters:

Parameter	Description	Default
susceptible	Initial susceptible population	9998
infected	Initial infected population	2
recovered	Initial recovered population	0
duration	Steps an individual remains infectious	2
contacts	Average contacts per individual per step	6
probability	Transmission probability per contact	0.25

In [3]:

# 2. Model connects to the active environment automatically
SIR(
    susceptible=9998,
    infected=2,
    recovered=0,
    duration=2,
    contacts=6,
    probability=0.25,
)

# 2. Model connects to the active environment automatically SIR( susceptible=9998, infected=2, recovered=0, duration=2, contacts=6, probability=0.25, )

Out[3]:

<dissmodel_sysdyn.models.sir.SIR at 0x70e0542dffe0>

Visualization¶

The Chart model redraws the time series at every simulation step. It automatically tracks susceptible, infected, and recovered because the SIR class is decorated with @track_plot — no extra configuration needed.

In [4]:

# 3. Chart also connects to the active environment automatically
Chart(show_legend=True, show_grid=True, title="SIR Model")

# 3. Chart also connects to the active environment automatically Chart(show_legend=True, show_grid=True, title="SIR Model")

Out[4]:

<dissmodel.visualization.chart.Chart at 0x70e05430ba10>

Running the simulation¶

In [5]:

env.run(30)

env.run(30)

Try it yourself¶

Go back and experiment:

• Increase contacts to simulate a more contagious disease
• Increase duration to make the disease last longer
• Decrease probability to simulate a less transmissible disease
• Try starting with more infected individuals
• Change env.run(30) to run for more steps