A dynamic programming approach for controlled fractional SIS models

We investigate a susceptible-infected-susceptible (SIS) epidemic model based on the Caputo–Fabrizio operator. After performing an asymptotic analysis of the system, we study a related finite horizon optimal control problem with state constraints. We prove that the corresponding value function satisfies in the viscosity sense a dynamic programming equation. We then turn to the asymptotic behavior of the value function, proving its convergence to the solution of a stationary problem, as the planning horizon tends to infinity. Finally, we present some numerical simulations providing a qualitative description of the optimal dynamics and the value functions involved.