Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator

Xuan Liu; Muhammad Arfan; Mati Ur Rahman; Bibi Fatima

doi:10.1080/10255842.2022.2047954

Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator

Comput Methods Biomech Biomed Engin. 2023 Jan;26(1):98-112. doi: 10.1080/10255842.2022.2047954. Epub 2022 Mar 10.

Authors

Xuan Liu¹, Muhammad Arfan², Mati Ur Rahman³, Bibi Fatima⁴

Affiliations

¹ Department of Mathematics, Hanshan Normal University, Chaozhou, China.
² Department of Mathematics, Government Degree College Gulabad Dir (L), Khyber Pakhtunkhwa, Pakistan.
³ School of Mathematical Science, Shanghai Jiao Tong University, Shanghai, P.R. China.
⁴ Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan.

PMID: 35271386
DOI: 10.1080/10255842.2022.2047954

Abstract

In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible $(S),$ infectious $(I),$ quarantined $(Q)$ and recovered $(R)$ cases respectively. The fractional operator of Atangana-Baleanu-Caputo $(ABC)$ is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate $ζ,$ different simulations are performed to check the effect of it on the dynamics of COVID-19.

Keywords: Atangana-Baleanu-Caputo derivative; Fractional SIQR model; existence theory.