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

Volume 33, Issue 3, pp 298--325 https://dx.doi.org/10.22436/jmcs.033.03.08

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.

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Keywords

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

MSC

•  34D08
•  92C60
•  92D30
•  34D20

References

• [1] P. Abuin, A. Anderson, A. Ferramosca, E. A. Hernandez-Vargas, A. H. Gonzalez, Characterization of SARS-CoV-2 dynamics in the host, Annu. Rev. Control, 50 (2020), 457–468
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] A. Addeo, A. Friedlaender, Cancer and COVID-19: unmasking their ties, Cancer Treat. Rev., 88 (2020), 7 pages
  • View Article
  • Google Scholar


• [3] I. Al-Darabsah, K.-L. Liao, S. Portet, A simple in-host model for COVID-19 with treatments: model prediction and calibration, J. Math. Biol., 86 (2023), 36 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] A. E. S. Almoceraa, G. Quiroz, E. A. Hernandez-Vargas, Stability analysis in COVID-19 within-host model with immune response, Commun. Nonlinear Sci. Numer. Simul., 95 (2021), 15 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] N. Bairagi, D. Adak, Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay, Appl. Math. Model., 38 (2014), 5047–5066
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] A. N. Chatterjee, F. Al Basir, A model for SARS-CoV-2 infection with treatment, Comput. Math. Methods Med., 2020 (2020), 11 pages
  • View Article
  • Google Scholar


• [7] B. Chhetri, V. M. Bhagat, D. K. K. Vamsi, V. S. Ananth, D. B. Prakash, R. Mandale, S. Muthusamy, C. B Sanjeevi, Within-host mathematical modeling on crucial inflammatory mediators and drug interventions in COVID-19 identifies combination therapy to be most effective and optimal, Alex. Eng. J., 60 (2021), 2491–2512
  • View Article
  • Google Scholar


• [8] A. Danchin, O. Pagani-Azizi, G. Turinici, G. Yahiaoui, COVID-19 adaptive humoral immunity models: weakly neutralizing versus antibody-disease enhancement scenarios, Acta Biotheor., 70 (2022), 1–24
  • View Article
  • Google Scholar


• [9] B. Dariya, G. P. Nagaraju, Understanding novel COVID-19: its impact on organ failure and risk assess- ment for diabetic and cancer patients, Cytokine Growth Factor Rev., 53 (2020), 43–52
  • View Article
  • Google Scholar


• [10] H. M. Dobrovolny, Quantifying the effect of remdesivir in rhesus macaques infected with SARS-CoV-2, Virology, 550 (2020), 61–69
  • View Article
  • Google Scholar


• [11] S. Q. Du, W. Yuan, Mathematical modeling of interaction between innate and adaptive immune responses in COVID-19 and implications for viral pathogenesis, J. Med. Virol., 92 (2020), 1615–1628
  • View Article
  • Google Scholar


• [12] A. M. Elaiw, A. J. Alsaedi, A. D. Hobiny, S. Aly, Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response, Phys. A, 616 (2023), 34 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] F. Fatehi, R. J. Bingham, E. C. Dykeman, P. G. Stockley, R. Twarock, Comparing antiviral strategies against COVID-19 via multiscale within-host modelling, Royal Soi. Open Sci., 8 (2021), 1–17
  • View Article
  • Google Scholar


• [14] I. Ghosh, Within host dynamics of SARS-CoV-2 in humans: modeling immune responses and antiviral treatments, SN Comput. Sci., 2 (2021), 1–12
  • View Article
  • Google Scholar


• [15] A. Gonc¸alves, J. Bertrand, R. Ke, E. Comets, X. de Lamballerie, D. Malvy, A. Pizzorno, O. Terrier, M. R. Calatrava, F. Mentr´e, P. Smith, A. S. Perelson, J. Guedj, Timing of antiviral treatment initiation is critical to reduce SARS-CoV-2 viral load, CPT: Pharmacomet. Syst. Pharmacol., 9 (2020), 509–514
  • View Article
  • Google Scholar


• [16] J. K. Hale, S. M. Verduyn Lunel, Introduction to functional differential equations, Springer-Verlag, New York (1993)
  • View Article
  • MathSciNet
  • Google Scholar


• [17] K. Hattaf, N. Yousfi, Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response, Math. Biosci. Eng., 17 (2020), 5326–5340
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] E. A. Hernandez-Vargas, J. X. Velasco-Hernandez, In-host mathematical modelling of COVID-19 in humans, Annu. Rev. Control, 50 (2020), 448–456
  • View Article
  • Google Scholar


• [19] G. Huang, Y. Takeuchi, W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. App. Math., 70 (2010), 2693–2708
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] C. B. Jackson, M. Farzan, B. Chen, H. Choe, Mechanisms of SARS-CoV-2 entry into cells, Nat. Rev. Mol. Cell Biol., 23 (2020), 3–20
  • View Article
  • Google Scholar


• [21] A. L. Jenner, R. A. Aogo, S. Alfonso, V. Crowe, X. Deng, A. P. Smith, P. A. Morel, C. L. Davis, A. M. Smith, M. Craig, COVID-19 virtual patient cohort suggests immune mechanisms driving disease outcomes, PLoS Pathog., 17 (2021), 1–33
  • View Article
  • Google Scholar


• [22] R. Ke, C. Zitzmann, D. D. Ho, R. M. Ribeiro, A. S. Perelson, In vivo kinetics of SARS-CoV-2 infection and its relationship with a person’s infectiousness, Proc. Natl. Acad. Sci. USA, 118 (2021), 1–9
  • View Article
  • MathSciNet
  • Google Scholar


• [23] T. Keyoumu, W. Ma, K. Guo, Existence of positive periodic solutions for a class of in-host MERS-CoV infection model with periodic coefficients, AIMS Math., 7 (2022), 3083–3096
  • View Article
  • MathSciNet
  • Google Scholar


• [24] T. Keyoumu, K. Guo, W. Ma, Periodic oscillation for a class of in-host MERS-CoV infection model with CTL immune response, Math. Biosci. Eng., 19 (2022), 12247–12259
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] T. Keyoumu,W. Ma, K. Guo, Global stability of a MERS-CoV infection model with CTL immune response and intracellular delay, Mathematics, 11 (2023), 1–26
  • View Article
  • Google Scholar


• [26] H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall,, Upper Saddle River (2002)
  • View Article


• [27] A. Khan, R. Zarin, G. Hussain, N. A. Ahmad, M. H. Mohd, A. Yusuf, Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan), Results Phys., 20 (2021), 17 pages
  • View Article
  • Google Scholar


• [28] A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879–883
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, Boston (1993)
  • View Article
  • Google Scholar


• [30] C. Leon, A. Tokarev, A. Bouchnita, V. Volpert, Modelling of the innate and adaptive immune response to SARS viral infection, cytokine storm and vaccination, Vaccines, 11 (2023), 1–30
  • View Article
  • Google Scholar


• [31] C. Li, J. Xu, J. Liu, Y. Zhou, The within-host viral kinetics of SARS-CoV-2, Math. Biosci. Eng., 17 (2020), 2853–2861
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [32] J. Lv, W. Ma, Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein, Appl. Math. Lett., 142 (2023), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [33] S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theoret. Biol., 254 (2008), 178–196
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [34] J. Mondal, P. Samui, A. N. Chatterjee, Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic, Eur. Phys. J. Spec. Top., 231 (2022), 3357–3370
  • View Article
  • Google Scholar


• [35] B. J. Nath, K. Dehingia, V. N. Mishra, Y.-M. Chu, H. K. Sarmah, Mathematical analysis of a within-host model of SARS-CoV-2, Adv. Difference Equ., 2021 (2021), 11 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [36] N. N´eant, G. Lingas, Q. Le Hingrat, J. Ghosn, I. Engelmann, Q. Lepiller, A. Gaymard, V. Ferr´e, C. Hartard, J.-C. Plantier, , V. Thibault, J. Marlet, B. Montes, K. Bouiller, F.-X. Lescure, J.-F. Timsit, E. Faure, J. Poissy, C. Chidiac, F. Raffi, A. Kimmoun, M. Etienne, J.-C. Richard, P. Tattevin, D. Garot, V. Le Moing, D. Bachelet, C. Tardivon, X. Duval, Y. Yazdanpanah, F. Mentr´e, C. Laou´enan, B. Visseaux, J. Guedj, Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort, Proc. Natl. Acad. Sci., 118 (2021),
  • View Article
  • Google Scholar


• [37] L. Pinky, H. M. Dobrovolny, SARS-CoV-2 coinfections: could influenza and the common cold be beneficial?, J. Med. Virol., 92 (2020), 2623–2630
  • View Article
  • Google Scholar


• [38] M. Sadria, A. T. Layton, Modeling within-host SARS-CoV-2 infection dynamics and potential treatments, Viruses, 13 (2021), 1–15
  • View Article
  • Google Scholar


• [39] T. Song, Y. Wang, X. Gu, S. Qiao, Modeling the within-host dynamics of SARS-CoV-2 infection based on antiviral treatment, Mathematics, 11 (2023), 1–19
  • View Article
  • Google Scholar


• [40] S. Tang, W. Ma, P. Bai, A novel dynamic model describing the spread of the MERS-CoV and the expression of dipeptidyl peptidase 4, Comput. Math. Methods Med., 2017 (2017), 6 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [41] M. Z. Tay, C. M., Poh, L. R´enia, P. A. MacAry, L. F. P. Ng, The trinity of COVID-19: immunity, inflammation and intervention, Nat. Rev. Immunol., 20 (2020), 363–374
  • View Article
  • Google Scholar


• [42] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [43] S. Wang, Y. Pan, Q. Wang, H. Miao, A. N. Brown, L. Rong, Modeling the viral dynamics of SARS-CoV-2 infection, Math. Biosci., 328 (2020), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [44] H. Yang, J.Wei, Analyzing global stability of a viral model with general incidence rate and cytotoxic T lymphocytes immune response, Nonlinear Dynam., 82 (2015), 713–722
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [45] P. Zhou, X.-L. Yang, X.-G. Wang, B. Hu, L. Zhang, W. Zhang, H.-R. Si, Y. Zhu, B. Li, C.-L. Huang, H.-D. Chen, J. Chen, Y. Luo, H. Guo, R.-D. Jiang, M.-Q. Liu, Y. Chen, X.-R. Shen, X. Wang, X.-S. Zheng, K. Zhao, Q.-J. Chen, F. Deng, L.-L. Liu, B. Yan, F.-X. Zhan, Y.-Y. Wang, G.-F. Xiao, Z.-L. Shi, A pneumonia outbreak associated with a new coronavirus of probable bat origin, Nature, 579 (2020), 270–273
  • View Article
  • Google Scholar