Abstract
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.
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Cacace, S., Lai, A.C. & Loreti, P. A dynamic programming approach for controlled fractional SIS models. Nonlinear Differ. Equ. Appl. 30, 20 (2023). https://doi.org/10.1007/s00030-022-00832-w
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DOI: https://doi.org/10.1007/s00030-022-00832-w