I am interested in monitoring patients in remission from cancer, the goal being to detect their relapse as quickly as possible, as well as the type of relapse, in order to give them the appropriate treatment as efficiently as possible. To this effect, we study the level of cancerous cells in the blood, a continuous process measured with noise at discrete intervals. This process is modelled by a piecewise deterministic Markov process (PDMP). Several decisions must be made based on these incomplete and noisy observations.
In the work presented here, I will seek to control the process, by authorising treatments that influence the level of cancer cells, and I will also want to determine the optimal dates for the next visits. This work, carried out with Benoîte de Saporta, is motivated by real data on multiple myeloma.

No pre-requisite on PDMPs is required, I will spend some time on the mathematical modelisation choice and the technical difficulties in solving our optimisation framework, but I will hide the ugly computations.
I will then describe two resolution strategies, one based on discretising the process, and from which we can derive error bounds, the other purely based on simulations, a promising approach that can scale up to more complex problems.