A dynamic programming approach for controlled fractional SIS models

TL;DR

This paper develops a dynamic programming framework for a fractional SIS epidemic model with Caputo-Fabrizio operator, analyzing optimal control and asymptotic behavior through viscosity solutions and numerical simulations.

Contribution

It introduces a novel fractional SIS model with control, proves the viscosity solution property of the value function, and analyzes its asymptotic convergence.

Findings

Value function converges to stationary solution as horizon increases

Numerical simulations illustrate optimal epidemic control strategies

Viscosity solutions characterize the dynamic programming equation

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.