  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 is a viscosity
solution of 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.
