Separate solver from Model class in IDE model

[annawendler]

Currently, the solver of the IDE-SECIR model is implemented directly in the Model class and can only be applied to a SECIR-type model. We want to separate the IDE solver from the model and make it more general so that it can also be applied to models with different infection dynamics, e.g. an SIR model. In the future, we can then also apply different solvers to the same model.

The following steps are necessary:

• Create a new file in math folder and move the simulation functions there.
• Generalize the solver such that is is not restricted to the SECIR infection dynamics .This could be done by tagging the relevant InfectionStates or InfectionTransitions that are relevant for the solver, e.g. the Dead compartment or the infectious compartments and adapt the simulation functions accordingly.

Possible issues:

• When implementing additional solvers, different initial conditions might be needed and the user needs to provide different types of input. The starting conditions are provided to the constructor of Model. Maybe we can provide different constructors and depending on the used constructor, the appropriate solver is chosen. Note that this would also mean that different equations are solved since the starting conditions are not identical. This is a somehow vague issue as an additional solver is still in work and the necessary starting conditions still need to be defined/investigated.

To discuss:

• In MEmilio, an IDE-SEIR model was implemented with a specific solver for the respective infection dynamics. How do we proceed with this? We could allow this solver when setting up a SEIR model but not for other infection dynamics.