Optimal neighboring infection control strategy on a multi-regions-based SIR epidemic model

Abstract

In this article, we consider a discrete-time multiregional SIR model that describes the evolution of an epidemic in several geographic areas believed to be linked by its population movement. Therefore, those affected can spread the disease by traveling from one region to another. In this work, we aim to define a new control (vaccination) strategy that is implemented in one patch (control source patch) and helps reduce infections and increase the number of individuals recovered in another patch (target patch), and this at an optimal cost. Optimal control problems are obtained based on a discrete version of Pontryagin's maximum principle, and then determined numerically using a discrete progressive-regressive scheme that converges as a result of a practical test related to the Forward-Backward Sweep Method (FBSM) on optimal control.