Polynomial approximation of regions of attraction via occupation measures: an application to a biological autonomous system

In this work we analyze the problem of computing the regions of attraction of a well-acknowledged model in the framework of diabetes modeling and control, the model by Topp et al. Despite the importance of this pioneering model in the literature of mathematical models of diabetes progression, to the best of our knowledge a clear representation of the regions of attraction of specific target sets under suitable conditions appears to be lacking. We address this problem by means of a method employing moment-sum-of-squares (moment-SOS) hierarchy that we exploit to assess the validity of a general computation of the regions of attraction performed through a Monte Carlo simulation. Addressing the problem of the knowledge of certain region of attraction, this work paves the way to future research aimed at exploiting a polynomial version of diabetes progression models to leverage optimal control problem design via occupation measures and momentSOS hierarchy.