Control of COVID-19 dynamics through a fractional-order model

Samia Bushnaq,Tareq Saeed,Delfim F.M Torres,Anwar Zeb

doi:10.1016/j.aej.2021.02.022

Abstract

We investigate, through a fractional mathematical model, the effects of physical distance on the SARS-CoV-2 virus transmission. Two controls are considered in our model for eradication of the spread of COVID-19: media education, through campaigns explaining the importance of social distancing, use of face masks, etc., towards all population, while the second one is quarantine social isolation of the exposed individuals. A general fractional order optimal control problem, and associated optimality conditions of Pontryagin type, are discussed, with the goal to minimize the number of susceptible and infected while maximizing the number of recovered. The extremals are then numerically obtained.

Highlights

The availability of easy-to-use precise estimation models are essential to get an insight into the effects of transferable infectious diseases
Our control system is described by a fractional differential system (FDS) with a given/fixed initial condition as follows:
With the purpose to control the spread of the COVID-19 pandemic in the world, we use two control variables in the form of media campaigns, social distance, and use of masks — the control u1ðtÞ — applied to the susceptible class; and quarantine — the control u2ðtÞ — applied to the exposed class

Summary

Introduction

The availability of easy-to-use precise estimation models are essential to get an insight into the effects of transferable infectious diseases. Person to person spread of COVID-19 happens through close contact, up to six feet This group of viruses mainly affects the hepatic, neurological and respiratory systems [2,3,4]. All health organizations are trying to drive the most lethal infectious diseases towards eradication, using educational and enlightenment campaigns, vaccination, treatment, etc. Many of these infectious diseases will become eventually endemic because of interventions to mitigate the spread in time and lack of adequate policies.

The fractional model

Basics of fractional control theory

Cðm À aÞ

Fractional-order model with controls

Conclusion