Spline Example: A Modulating Input Function

Summary

In this example, it is demonstrated how a continuous input function can be estimated that modulates the right-hand side of an ODE in a time-dependent manner. The model used for demonstration purpose is an SEIR model. These models are frequently applied for modelling of the dynamics of diseases in a population. The example shows how the modulation of the infection rate can be estimated. Such a modulation might originate from political actions that aim containment, i.e. reduction of the infection rate.

In particular, instead of a commont rate or reaction

Susceptibles -> Exposed CUSTOM "b * Infectious * Susceptibles" "description"

it might be desired to have time dependent b, e.g.

Susceptibles -> Exposed CUSTOM "b * b_time_dependence * Infectious * Susceptibles" "description"

The aim of this example is not having a realistic model and a common parametrization from literature. Instead, the model is rather simple for demonstrating capabilities of D2D in input estimation.