SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study

Amar Nath Chatterjee; Fahad Al Basir; Muqrin A Almuqrin; Jayanta Mondal; Ilyas Khan

doi:10.1016/j.rinp.2021.104260

SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study

Results Phys. 2021 Jul:26:104260. doi: 10.1016/j.rinp.2021.104260. Epub 2021 May 21.

Authors

Amar Nath Chatterjee¹, Fahad Al Basir², Muqrin A Almuqrin³, Jayanta Mondal⁴, Ilyas Khan⁵

Affiliations

¹ Department of Mathematics, K.L.S. College, Nawada, Magadha University, India.
² Department of Mathematics, Asansol Girls' College, West Bengal 713304, India.
³ Department of Mathematics, Faculty of Science in Zulfi, Majmaah University, 11952, Kingdom of Saudi Arabia.
⁴ Department of Mathematics, Diamond Hurbour Women's University, West Bengal 743368, India.
⁵ Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia.

Abstract

In this research article, we establish a fractional-order mathematical model to explore the infections of the coronavirus disease (COVID-19) caused by the novel SARS-CoV-2 virus. We introduce a set of fractional differential equations taking uninfected epithelial cells, infected epithelial cells, SARS-CoV-2 virus, and CTL response cell accounting for the lytic and non-lytic effects of immune responses. We also include the effect of a commonly used antiviral drug in COVID-19 treatment in an optimal control-theoretic approach. The stability of the equilibria of the fractional ordered system using qualitative theory. Numerical simulations are presented using an iterative scheme in Matlab in support of the analytical results.

Keywords: Fractional calculus; Lytic and nonlytic effect; Mathematical model; Optimal control; SARS-CoV-2.