SDE-based models ================ 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 `. 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 `. 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 ` for more details. .. _Simulation SDE: Simulation ---------- 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. List of models -------------- .. toctree:: :titlesonly: models/ssir models/ssirs models/sseir