Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Liu, Xuan; Arfan, Muhammad; ur Rahman, Mati; Fatima, Bibi
• Is Part Of: Computer methods in biomechanics and biomedical engineering. Volume 26:Issue 1(2023)
• Page Start: 98
• Page End: 112
• Publication Date: 2023-01-02
• Subjects: Fractional SIQR model -- Atangana-Baleanu-Caputo derivative -- existence theory; Biomechanics -- Data processing -- Periodicals; Biomedical engineering -- Periodicals; Biomechanics -- Periodicals; Biomedical Engineering -- methods -- Periodicals; Computing Methodologies -- Periodicals; 612.7
• DOI: 10.1080/10255842.2022.2047954
• Languages: English
• ISSNs: 1025-5842

Abstract

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.