Occupation measure methods for modelling and analysis of biological hybrid systems

Abstract

Mechanistic models in biology often involve numerous parameters about which we do not have direct experimental information. The traditional approach is to fit these parameters using extensive numerical simulations (e.g. by the Monte-Carlo method), and eventually revising the model if the predictions do not correspond to the actual measurements. In this work we propose a methodology for hybrid system model revision, when new types of functions are needed to capture time varying parameters. To this end, we formulate a hybrid optimal control problem with intermediate points as successive infinite-dimensional linear programs (LP) on occupation measures. Then, these infinite-dimensional LPs are solved using a hierarchy of semidefinite relaxations. The whole procedure is applied on a recent model for haemoglobin production in erythrocytes.