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SIR

dissmodel.models.sysdyn.sir.SIR

Bases: Model

Deterministic SIR epidemiological model.

Tracks the spread of an infectious disease through three compartments: susceptible, infected, and recovered. At each step, new infections and recoveries are computed based on contact rate, transmission probability, and disease duration.

Parameters:

Name Type Description Default
susceptible int

Initial number of susceptible individuals, by default 9998.

 required
infected int

Initial number of infected individuals, by default 2.

 required
recovered int

Initial number of recovered individuals, by default 0.

 required
duration int

Average number of steps an individual remains infectious, by default 2.

 required
contacts int

Average number of contacts per individual per step, by default 6.

 required
probability float

Probability of transmission per contact with an infected individual, by default 0.25.

 required
Notes

The @track_plot decorators register susceptible, infected, and recovered for automatic live plotting. Any :class:~dissmodel.visualization.Chart connected to the same environment will plot these variables at every step without any extra configuration.

The force of infection at each step is computed as:

.. math::

\alpha = contacts \times probability

\Delta I = I \times \alpha \times \frac{S}{N}

\Delta R = \frac{I}{duration}

Examples:

>>> from dissmodel.core import Environment
>>> env = Environment(end_time=30)
>>> sir = SIR()
>>> env.run()
Source code in dissmodel/models/sysdyn/sir.py 
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@track_plot("Susceptible", "green")
@track_plot("Infected", "red")
@track_plot("Recovered", "blue")
class SIR(Model):
    """
    Deterministic SIR epidemiological model.

    Tracks the spread of an infectious disease through three compartments:
    susceptible, infected, and recovered. At each step, new infections and
    recoveries are computed based on contact rate, transmission probability,
    and disease duration.

    Parameters
    ----------
    susceptible : int, optional
        Initial number of susceptible individuals, by default 9998.
    infected : int, optional
        Initial number of infected individuals, by default 2.
    recovered : int, optional
        Initial number of recovered individuals, by default 0.
    duration : int, optional
        Average number of steps an individual remains infectious,
        by default 2.
    contacts : int, optional
        Average number of contacts per individual per step, by default 6.
    probability : float, optional
        Probability of transmission per contact with an infected individual,
        by default 0.25.

    Notes
    -----
    The ``@track_plot`` decorators register ``susceptible``, ``infected``,
    and ``recovered`` for automatic live plotting. Any
    :class:`~dissmodel.visualization.Chart` connected to the same environment
    will plot these variables at every step without any extra configuration.

    The force of infection at each step is computed as:

    .. math::

        \\alpha = contacts \\times probability

        \\Delta I = I \\times \\alpha \\times \\frac{S}{N}

        \\Delta R = \\frac{I}{duration}

    Examples
    --------
    >>> from dissmodel.core import Environment
    >>> env = Environment(end_time=30)
    >>> sir = SIR()
    >>> env.run()
    """

    #: Number of susceptible individuals.
    susceptible: float

    #: Number of infected individuals.
    infected: float

    #: Number of recovered individuals.
    recovered: float

    #: Average number of steps an individual remains infectious.
    duration: int

    #: Average number of contacts per individual per step.
    contacts: int

    #: Probability of transmission per contact.
    probability: float

    def setup(
        self,
        susceptible: int = 9998,
        infected: int = 2,
        recovered: int = 0,
        duration: int = 2,
        contacts: int = 6,
        probability: float = 0.25,
    ) -> None:
        """
        Configure the model parameters.

        Parameters
        ----------
        susceptible : int, optional
            Initial number of susceptible individuals, by default 9998.
        infected : int, optional
            Initial number of infected individuals, by default 2.
        recovered : int, optional
            Initial number of recovered individuals, by default 0.
        duration : int, optional
            Average number of steps an individual remains infectious,
            by default 2.
        contacts : int, optional
            Average number of contacts per individual per step,
            by default 6.
        probability : float, optional
            Probability of transmission per contact, by default 0.25.
        """
        self.susceptible = susceptible
        self.infected    = infected
        self.recovered   = recovered
        self.duration    = duration
        self.contacts    = contacts
        self.probability = probability

    def execute(self) -> None:
        """
        Advance the model by one time step.

        Computes new infections and recoveries, then updates the
        susceptible, infected, and recovered compartments.
        """
        total = self.susceptible + self.infected + self.recovered
        alpha = self.contacts * self.probability

        new_infected  = self.infected * alpha * (self.susceptible / total)
        new_recovered = self.infected / self.duration

        self.susceptible -= new_infected
        self.infected    += new_infected - new_recovered
        self.recovered   += new_recovered

execute()

Advance the model by one time step.

Computes new infections and recoveries, then updates the susceptible, infected, and recovered compartments.

Source code in dissmodel/models/sysdyn/sir.py 
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def execute(self) -> None:
    """
    Advance the model by one time step.

    Computes new infections and recoveries, then updates the
    susceptible, infected, and recovered compartments.
    """
    total = self.susceptible + self.infected + self.recovered
    alpha = self.contacts * self.probability

    new_infected  = self.infected * alpha * (self.susceptible / total)
    new_recovered = self.infected / self.duration

    self.susceptible -= new_infected
    self.infected    += new_infected - new_recovered
    self.recovered   += new_recovered

setup(susceptible=9998, infected=2, recovered=0, duration=2, contacts=6, probability=0.25)

Configure the model parameters.

Parameters:

Name Type Description Default
susceptible int

Initial number of susceptible individuals, by default 9998.

 9998
infected int

Initial number of infected individuals, by default 2.

 2
recovered int

Initial number of recovered individuals, by default 0.

 0
duration int

Average number of steps an individual remains infectious, by default 2.

 2
contacts int

Average number of contacts per individual per step, by default 6.

 6
probability float

Probability of transmission per contact, by default 0.25.

 0.25
Source code in dissmodel/models/sysdyn/sir.py 
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def setup(
    self,
    susceptible: int = 9998,
    infected: int = 2,
    recovered: int = 0,
    duration: int = 2,
    contacts: int = 6,
    probability: float = 0.25,
) -> None:
    """
    Configure the model parameters.

    Parameters
    ----------
    susceptible : int, optional
        Initial number of susceptible individuals, by default 9998.
    infected : int, optional
        Initial number of infected individuals, by default 2.
    recovered : int, optional
        Initial number of recovered individuals, by default 0.
    duration : int, optional
        Average number of steps an individual remains infectious,
        by default 2.
    contacts : int, optional
        Average number of contacts per individual per step,
        by default 6.
    probability : float, optional
        Probability of transmission per contact, by default 0.25.
    """
    self.susceptible = susceptible
    self.infected    = infected
    self.recovered   = recovered
    self.duration    = duration
    self.contacts    = contacts
    self.probability = probability