ELLIS against Covid-19

Learning the Dynamic SIR Model: An Optimal Control Approach

ellis 22 April 2020 - 22 April 2020
22 April 2020 • 13:45 - 13:55

(University of Siena)

The problem of parameter estimation for an epidemic model is crucial for the forecasting of the infection spread. We discuss an approach for learning the time-variant parameters of the dynamic SIR model from data. We formulate the problem in terms of a functional risk that depends on the learning variables through the solutions of the dynamic SIR. The resulting variational problem is then solved using a gradient flow on a suitable, regularized, functional. We show preliminary results on the estimates performed on COVID-19 data relative to some Italian regions.


Question & Answers

Link to the recording of the live Questions & Discussion session for this talk. 


  • Q: How do you handle with very non-exponential distributions of time-to-death? It appears it is bimodal (some people die quickly, others after a couple of weeks).

    • A: We initially focussed on the dynamic SIR model to have the simplest possible model that could in principle approximate multimodal distributions through the time varying coefficients. The interesting point is that our approach does not depend (up to a certain extent) on the underlying model for the estimation of the deceases. Indeed we are currently trying to extend the plain dynamic SIR model by assuming that the rate of change of the removed is estimated through a convolution of a distribution (object of the learning) and the number of infected exactly to take more explicitly into account the kind of behaviour you described in your question.

  • Q: How is the found model validated (e.g. how do you assure there is no overfitting to training)?

    • A: We do not have a proper validation of our model; however we split the data into a set from which we perform training  and we keep a final temporal window for the testing our prediction. Moreover we control overfitting adding to the problem a regularisation either by explicitly adding a momentum term in the gradient flow update or by adding a derivative regularisation directly in te functional we optimise.

      The first question  (Q1) has been already answered live during the discussion (here I have summed up what I said). Lastly they asked for the slides of the presentation; in attachment you can find the PDF with my slides (I’ve already sent the slides to the person that asked for them explicitly).


Thumb ticker marco gori
(University of Siena)
Thumb ticker alessandro betti
(University of Siena)