Study of the stability for Drug Delivery Models
Résumé
In this work, mathematical models of drug delivery are presented. We are particularly interested in studying the stability of these models to release the drug in a polymer matrix and detect its transfer to the overall biological tissue. These results are illustrated on two models. In order to gain protocol treatment, instead of using the optimal control theory, Lyapunov's stability theorem is used to study the stability of the first nonlinear system. For the second, we proceed by establishing the properties of the equilibrium point (which is strongly related to the stability of the nonlinear system) by modifying the system into a canonical equation and studying the spectrum of its Jacobian matrix to show that the system is stable.