Global Properties of a Discrete SARS-CoV-2/HIV Co-Dynamics Model

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M. A. Alshaikh, A. K. Aljahdali


Coronavirus disease 2019 (COVID-19), which is caused by the virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a respiratory disease. In this paper, we analyze the global stability of a discrete SARS-CoV-2/HIV co-dynamics model. We create the discrete model by applying a nonstandard finite difference (NSFD) method. We demonstrate that NSFD retains essential solution properties, including positivity and boundedness. We determine the fixed points and identify their existence conditions. We investigate the global stability of these fixed points through the application of the Lyapunov method. To complement our analytical findings, we present numerical simulations.

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  1. Z. Bakouny, J.E. Hawley, T.K. Choueiri, S. Peters, B.I. Rini, J.L. Warner, C.A. Painter, COVID-19 and Cancer: Current Challenges and Perspectives, Cancer Cell. 38 (2020), 629–646.
  2. Z. Varga, A.J. Flammer, P. Steiger, M. Haberecker, R. Andermatt, A.S. Zinkernagel, M.R. Mehra, R.A. Schuepbach, F. Ruschitzka, H. Moch, Endothelial Cell Infection and Endotheliitis in COVID-19, The Lancet 395 (2020), 1417–1418.
  3. N. Evans, E. Martinez, N. Petrosillo, J. Nichols, E. Islam, K. Pruitt, S. Almodovar, SARS-CoV-2 and Human Immunodeficiency Virus: Pathogen Pincer Attack, HIV/AIDS - Res. Pall. Care. 13 (2021), 361–375.
  4. P. Ssentongo, E.S. Heilbrunn, A.E. Ssentongo, S. Advani, V.M. Chinchilli, J.J. Nunez, P. Du, Epidemiology and Outcomes of COVID-19 in HIV-Infected Individuals: A Systematic Review and Meta-Analysis, Sci. Rep. 11 (2021), 6283.
  5. K.S. Sharov, HIV/SARS-CoV-2 Co-Infection: T Cell Profile, Cytokine Dynamics and Role of Exhausted Lymphocytes, Int. J. Infect. Dis. 102 (2021), 163–169.
  6. J. Ambrosioni, J.L. Blanco, J.M. Reyes-Urueña, M.A. Davies, O. Sued, et al. Overview of SARS-CoV-2 Infection in Adults Living With HIV, Lancet HIV. 8 (2021), e294–e305.
  7. O.N. Kanwugu, P. Adadi, HIV/SARS-CoV-2 Coinfection: A Global Perspective, J. Med. Virol. 93 (2020), 726–732.
  8. WHO, COVID-19 Vaccines, World Health Organization, (2021).
  9. A.M. Elaiw, A.D. Al Agha, S.A. Azoz, E. Ramadan, Global Analysis of Within-Host SARS-CoV-2/HIV Coinfection Model With Latency, Eur. Phys. J. Plus 137 (2022), 174.
  10. S.A. Pasha, Y. Nawaz, M.S. Arif, On the Nonstandard Finite Difference Method for Reaction-diffusion Models, Chaos Solitons Fractals 166 (2023), 112929.
  11. R.E. Mickens, Nonstandard Finite Difference Models of Differential equations, World Scientific, Singapore, 1994.
  12. A. Korpusik, A Nonstandard Finite Difference Scheme for a Basic Model of Cellular Immune Response to Viral Infection, Commun. Nonlinear Sci. Numer. Simul. 43 (2017), 369–384.
  13. Y. Geng, J. Xu, J. Hou, Discretization and Dynamic Consistency of a Delayed and Diffusive Viral Infection Model, Appl. Math. Comput. 316 (2018), 282-295.
  14. J. Xu, Y. Geng, Stability Preserving NSFD Scheme for a Delayed Viral InfectionModelWith Cell-to-Cell Transmission and General Nonlinear Incidence, J. Differ. Equ. Appl. 23 (2017), 893–916.
  15. K. Manna, A Non-Standard Finite Difference Scheme for a Diffusive HBV Infection Model With Capsids and Time Delay, J. Differ. Equ. Appl. 23 (2017), 1901–1911.
  16. S. Vaz, D.F.M. Torres, Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Response, arXiv:2205.02199, (2022).
  17. S.M. Salman, A Nonstandard Finite Difference Scheme and Optimal Control for an HIV Model with BeddingtonDeAngelis Incidence and Cure Rate, Eur. Phys. J. Plus 135 (2020), 808.
  18. X.L. Liu, C.C. Zhu, A Non-Standard Finite Difference Scheme for a Diffusive HIV-1 Infection Model with Immune Response and Intracellular Delay, Axioms. 11 (2022), 129.
  19. A.M. Elaiw, M.A. Alshaikh, Global Stability of Discrete Virus Dynamics Models With Humoural Immunity and Latency, J. Biol. Dyn. 13 (2019), 639–674.
  20. A.M. Elaiw, M.A. Alshaikh, Stability Analysis of a General Discrete-Time Pathogen Infection Model With Humoral Immunity, J. Differ. Equ. Appl. 25 (2019), 1149–1172.
  21. A.M. Elaiw, M.A. Alshaikh, Stability Preserving Nsfd Scheme for a General Virus Dynamics Model With Antibody and Cell-Mediated Responses, Chaos Solitons Fractals. 138 (2020), 109862.
  22. A.M. Elaiw, A.K. Aljahdali, A.D. Hobiny, Dynamical Properties of Discrete-Time HTLV-I and HIV-1 within-Host Coinfection Model, Axioms. 12 (2023), 201.
  23. A.M. Elaiw, A.K. Aljahdali, A.D. Hobiny, Discretization and Analysis of HIV-1 and HTLV-I Coinfection Model with Latent Reservoirs, Computation. 11 (2023), 54.
  24. R.E. Mickens, Application of Nonstandard Finite Difference Scheme, World Scientific, Singapore, (2000).
  25. P. Shi, L. Dong, Dynamical Behaviors of a Discrete Hiv-1 Virus Model With Bilinear Infective Rate, Math. Meth. Appl. Sci. 37 (2013), 2271–2280.