Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

Arunachalam Selvam; Sriramulu Sabarinathan; Beri Venkatachalapathy Senthil Kumar; Haewon Byeon; Kamel Guedri; Sayed M Eldin; Muhammad Ijaz Khan; Vediyappan Govindan

doi:10.1038/s41598-023-35624-4

Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

Sci Rep. 2023 Jun 2;13(1):9012. doi: 10.1038/s41598-023-35624-4.

Authors

Arunachalam Selvam¹, Sriramulu Sabarinathan², Beri Venkatachalapathy Senthil Kumar³, Haewon Byeon⁴, Kamel Guedri⁵, Sayed M Eldin⁶, Muhammad Ijaz Khan⁷, Vediyappan Govindan⁸

Affiliations

¹ Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur, Tamilnadu, 603 203, India.
² Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulthur, Tamilnadu, 603 203, India. ssabarimaths@gmail.com.
³ Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamilnadu, 602 105, India.
⁴ Department of Digital Anti-Aging Healthcare (BK21), Inje University, Gimhae, 50834, Republic of Korea.
⁵ Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah, 21955, Saudi Arabia.
⁶ Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo, 11835, Egypt. sayed.eldin22@fue.edu.eg.
⁷ Laboratry of Systems Ecology and Sustainability Science College of Engineering, Peking University, Beijing, China.
⁸ Department of Mathematics, DMI St John The Baptist University Central Mangochi-409, Cental Africa, Malawi.

Abstract

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

COVID-19*
Coinfection*
Fractals
Humans
Intention