A dynamic programming approach for controlled fractional SIS models
Analysis of PDEs
2021-07-29 v1
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 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.
Keywords
Cite
@article{arxiv.2107.13316,
title = {A dynamic programming approach for controlled fractional SIS models},
author = {Simone Cacace and Anna Chiara Lai and Paola Loreti},
journal= {arXiv preprint arXiv:2107.13316},
year = {2021}
}