Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative

TL;DR

This paper develops an optimal control framework for a fractional reaction-diffusion SEIR epidemiological model using Caputo-Fabrizio derivatives, aiming to minimize infections and costs through vaccination strategies.

Contribution

It introduces a novel fractional PDE model with Caputo-Fabrizio derivatives and applies optimal control theory to determine effective vaccination policies.

Findings

Optimal vaccination control reduces infection spread.

Dynamic graphs illustrate control effectiveness.

Model provides a new approach for epidemic management.

Abstract

In this work we study a fractional SEIR biological model of a reaction-diffusion, using the non-singular kernel Caputo-Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is considered a control variable. Our study aims to identify the ideal control pair that reduces the number of infected/infectious people and the associated vaccine and treatment costs over a limited time and space. Moreover, by using the forward-backward algorithm, the approximate results are explained by dynamic graphs to monitor the effectiveness of vaccination.