# Effect of ACE2 receptor and CTL response on within-host dynamics of SARS-CoV-2 infection

Volume 33, Issue 3, pp 298--325
Publication Date: January 24, 2024 Submission Date: October 17, 2023 Revision Date: November 23, 2023 Accteptance Date: December 13, 2023
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### Authors

A. M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia. A. S. Alsulami - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia. A. D. Hobiny - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

### Abstract

Since the end of 2019, scientists and researchers have intensified their efforts to comprehend the within-host dynamics of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes coronavirus illness 2019 (COVID-19). The dynamics and progression of the SARS-CoV-2 inside the body may be understood with the use of mathematical modeling. In this study, we develop a mathematical model for characterizing the within-host dynamics of SARS-CoV-2 infection under the effect of ACE2 receptor and cytotoxic T lymphocytes (CTL) response. Latently and actively (productively) epithelial infected cells are represented in the model as two distinct classes. We take into account three distributed delays, including (i) the formation of latently infected cells, (ii) the activation of latently infected cells, and (iii) the maturation of newly released virions. We first prove that the model is well-posed, then find all possible equilibria. To determine if an equilibrium exists and is globally asymptotically stable, we derive two threshold parameters: the basic reproduction number ($\Re_{0}$) and CTL response activation number ($\Re_{1}$). We demonstrate the global asymptotic stability for all equilibria by constructing the relevant Lyapunov functions and employing LaSalle's invariance principle. To illustrate the theoretical findings, we run numerical simulations. We do sensitivity analysis and determine the most vulnerable parameters. It is discussed how CTL response and ACE2 receptors affect the kinetics of the SARS-CoV-2. Even though $\Re_{0}$ is independent of CTL response characteristics, it is shown that significant CTL immune activation can impede viral replication. Moreover, we found that, $\Re_{0}$ is influenced by the rates of ACE2 receptor growth and degradation, and this may offer valuable guidance for the creation of potential receptor-targeted vaccinations and medications. The impact of time delays and the latent period on SARS-CoV-2 infection is finally examined.

### Share and Cite

##### ISRP Style

A. M. Elaiw, A. S. Alsulami, A. D. Hobiny, Effect of ACE2 receptor and CTL response on within-host dynamics of SARS-CoV-2 infection, Journal of Mathematics and Computer Science, 33 (2024), no. 3, 298--325

##### AMA Style

Elaiw A. M., Alsulami A. S., Hobiny A. D., Effect of ACE2 receptor and CTL response on within-host dynamics of SARS-CoV-2 infection. J Math Comput SCI-JM. (2024); 33(3):298--325

##### Chicago/Turabian Style

Elaiw, A. M., Alsulami, A. S., Hobiny, A. D.. "Effect of ACE2 receptor and CTL response on within-host dynamics of SARS-CoV-2 infection." Journal of Mathematics and Computer Science, 33, no. 3 (2024): 298--325

### Keywords

• SARS-CoV-2
• ACE2 receptor
• COVID-19
• CTL response
• Lyapunov function
• global stability

•  34D08
•  92C60
•  92D30
•  34D20

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