Open Access

ARTICLE

Optimal Control Model for the Transmission of Novel COVID-19

Isa Abdullahi Baba^1,*, Bashir Ahmad Nasidi¹, Dumitru Baleanu^2,3,4
1 Department of Mathematical Sciences, Bayero University Kano, Nigeria
2 Department of Mathematics, Cankaya University, Ankara, 06530, Turkey
3 Institute of Space Sciences, Bucharest, Romania
4 Department of Medical Research, China Medical University Hospital, Taichung, Taiwan
* Corresponding Author: Isa Abdullahi Baba. Email:
(This article belongs to this Special Issue: Mathematical aspects of the Coronavirus Disease 2019 (COVID-19): Analysis and Control)

Computers, Materials & Continua 2021, 66(3), 3089-3106. https://doi.org/10.32604/cmc.2021.012301

Received 24 June 2020; Accepted 06 October 2020; Issue published 28 December 2020

Abstract

As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u₁(t) (isolation of the susceptible communities), u₂(t) (contact track measure by which susceptible individuals with contact history are quarantined), u₃(t) (contact track measure by which infected individualsare quarantined), u₄(t) (control effort of hospitalizing the infected I₁) and u₅(t) (control effort of hospitalizing the infected I₂). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.

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Keywords

COVID-19; optimal control; Pontryaging maximum principle; mathematical model; existence of control; stability analysis

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Citations