Estimation of Nucleation Parameters Using a Linear Optimal Control Problem

In this paper, we consider a Becker-Doring-type mathematical interaction model between Aβ monomers and Aβ proto-oligomers, which play an important role in Alzheimer's disease, with a given initial condition, but where the nucleation parameter is unknown. All of this work revolves around estimating the nucleation rate, which is not accessible experimentally. This estimation is made using techniques related to solving optimal control problems. We then propose a necessary and sufficient condition to ensure the existence and uniqueness of the solution, which should make it possible to estimate this parameter.