Applications of control theory to mathematical biology are numerous. The study of control strategies happens most often in the context of optimal resource allocation or investigation of asymptotic convergence of solutions to equilibria with specific properties. The study of solutions of controlled systems which must respect some specific constraints has been pursued to a lesser extent. The ODE-based models I will present are subject to constraints on both the control and one or more phase variables. The mathematical task is to describe and compute the viability kernel associated to the constraints. This kernel is the set of those initial states for which viable solutions of the system exist, i.e. solutions that respect these constraints for all future times. The viability kernel can be characterised in the phase space as a sub-zero level set of a value function that solves an equation of Hamilton-Jacobi-Bellman type. I will discuss some examples in the field of anti-mosquito measures for vector-borne diseases and cancer therapy, where the value function has been approximated numerically.
11. April 2024, 13:00-14:00