These models are a type of aggregated or compartmental model, which is described by a system of initial value problems (IVP) given by stochastic differential equations (SDE). In MEmilio, they are implemented as an ODE-based model with an additional function to compute the random noise, as can be seen :doc:`here <sde_creation>`. Hence, for the most part, SDE models are used exactly like ODE-based models. They mostly differ in how they are simulated, see the :ref:`Simulation SDE` section below. For everything else, check out the page on :doc:`ODE-based model usage <ode>`.

The class used for implementing SDE models is called StochasticModel. It is derived from a CompartmentalModel (or optionally a FlowModel) for the representation of the deterministic part of the model equations. Check out :doc:`SDE model creation <sde_creation>` for more details.

Once the model is set up, one can run a simple simulation from time t0 to tmax with an initial step size dt using the mio::simulate_stochastic() function. This will run a simulation of type StochasticSimulation that saves the sizes of each compartment over time. The simulation uses an Euler-Maruyama scheme by default, so the step size does not change over time.

Flow information cannot be obtained even when the StochasticModel is defined using a FlowModel, as the integrator may need to rescale results with respect to compartments to avoid negative values.

.. toctree::
    :titlesonly:

    models/ssir
    models/ssirs
    models/sseir