Modeling of KSHV/HHV-8 and HIV-1 Co-Dynamics in Vivo

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-160
Published: Sep 16, 2024
Cite as:
E. A. Almohaimeed, A. M. Elaiw, A. D. Hobiny, Modeling of KSHV/HHV-8 and HIV-1 Co-Dynamics in Vivo, Int. J. Anal. Appl., 22 (2024), 160.

Main Article Content

E. A. Almohaimeed, A. M. Elaiw, A. D. Hobiny

Abstract

Human immunodeficiency virus kind 1 (HIV-1) compromises the immune system by infecting and damaging CD4+ T cells. Infection can progress to the ultimate stage, acquired immune deficiency syndrome (AIDS), if HIV-1 therapy is not received. People living with HIV/AIDS are more vulnerable to infections that they otherwise wouldn’t develop. Opportunistic infections or malignancies are the terms used to describe them. Kaposi sarcoma (KS) is an AIDSrelated malignancy caused by Kaposi’s sarcoma-associated herpesvirus (KSHV) (also known as human herpesvirus 8 (HHV-8)). HIV-1 and KSHV co-infection cases has been shown in several studies. Using a system of ODEs, we develop a new mathematical model to study the co-dynamics of HIV-1 and KSHV in vivo. The model includes interactions between healthy CD4+ T cells, HIV-1-infected CD4+ T cells, HIV-1 particles, healthy B cells, KSHV-infected B cells, and KSHV particles. By analyzing the boundedness and nonnegativity of the solutions, we prove the mathematical well-posedness and biological compatibility of the model. The existence and stability of the model’s steady states are established by four threshold values that we identify. We prove that steady states are globally asymptotically stable by using Lyapunov’s method and LaSalle’s invariance principle. Numerical simulations are used to display the results. For both basic reproduction ratios of HIV-1 mono-infection (R1) and KSHV mono-infection (R2), sensitivity analysis is carried out. A comparison between HIV-1 or KSHV mono-infections and co-infections with HIV-1 and KSHV is given. Empirical evidence indicates that co-infection results in higher KSHV and HIV-1 concentrations compared to mono-infection cases. This result is in line with a number of findings found in the literature.

Article Details

References

  1. N. Dorratoltaj, R. Nikin-Beers, S.M. Ciupe, S.G. Eubank, K.M. Abbas, Multi-Scale Immunoepidemiological Modeling of Within-Host and Between-Host HIV Dynamics: Systematic Review of Mathematical Models, PeerJ 5 (2017), e3877. https://doi.org/10.7717/peerj.3877.
  2. P. Aavani, L.J.S. Allen, The Role of CD4 T Cells in Immune System Activation and Viral Reproduction in a Simple Model for HIV Infection, Appl. Math. Model. 75 (2019), 210–222. https://doi.org/10.1016/j.apm.2019.05.028.
  3. S.L. Swain, K.K. McKinstry, T.M. Strutt, Expanding Roles for CD4+ T Cells in Immunity to Viruses, Nat. Rev. Immunol. 12 (2012), 136–148. https://doi.org/10.1038/nri3152.
  4. D.Wodarz, D.N. Levy, Human Immunodeficiency Virus Evolution Towards Reduced Replicative Fitnessin Vivoand the Development of AIDS, Proc. R. Soc. B. 274 (2007), 2481–2491. https://doi.org/10.1098/rspb.2007.0413.
  5. P.L. Vernazza, J.J. Eron, S.A. Fiscus, M.S. Cohen, Sexual Transmission of HIV: Infectiousness and Prevention, AIDS 13 (1999), 155–166. https://doi.org/10.1097/00002030-199902040-00003.
  6. T.F. Schulz, Y. Chang, P.S. Moore, Kaposi’s Sarcoma-Associated Herpesvirus (Human Herpesvirus 8), in: D.J. McCance (Ed.), Human Tumor Viruses, ASM Press, Washington, DC, USA, 2014: pp. 87–134. https://doi.org/10.1128/9781555818289.ch3.
  7. Y. Chang, E. Cesarman, M.S. Pessin, F. Lee, J. Culpepper, D.M. Knowles, P.S. Moore, Identification of HerpesvirusLike DNA Sequences in AIDS-Sssociated Kaposi’s Sarcoma, Science 266 (1994), 1865–1869. https://doi.org/10.1126/science.7997879.
  8. S.M. Akula, F.Z. Wang, J. Vieira, B. Chandran, Human Herpesvirus 8 Interaction With Target Cells Involves Heparan Sulfate, Virology 282 (2001), 245–255. https://doi.org/10.1006/viro.2000.0851.
  9. S.J. Dollery, R.J. Santiago-Crespo, D. Chatterjee, E.A. Berger, Glycoprotein K8.1A of Kaposi’s Sarcoma-Associated Herpesvirus Is a Critical B Cell Tropism Determinant Independent of Its Heparan Sulfate Binding Activity, J. Virol. 93 (2019), 01876-18. https://doi.org/10.1128/jvi.01876-18.
  10. R.F. Kaondera-Shava, E. Lungu, B. Szomolay, A Novel Mathematical Model of AIDS-Associated Kaposi’s Sarcoma: Analysis and Optimal Control, Biosystems. 200 (2021), 104318. https://doi.org/10.1016/j.biosystems.2020.104318.
  11. M.J. Cannon, A.S. Laney, P.E. Pellett, Human Herpesvirus 8: Current issues, Clinic. Infect. Dis. 37 (2003), 82–87. https://doi.org/10.1086/375230.
  12. E. Rohner, N. Wyss, Z. Heg, Z. Faralli, S.M. Mbulaiteye, U. Novak, M. Zwahlen, M. Egger, J. Bohlius, HIV and Human Herpesvirus 8 Co-Infection Across the Globe: Systematic Review and Meta-Analysis, Int. J. Cancer. 138 (2015), 45–54. https://doi.org/10.1002/ijc.29687.
  13. L.C. Pierrotti, A. Etzel, L.M. Sumita, P.E. Braga, J. Eluf-Neto, V.A.U.F. de Souza, A.A.C. Segurado, Human Herpesvirus 8 (HHV-8) Infection in HIV/AIDS Patients from Santos, Brazil: Seroprevalence and Associated Factors, Sex. Transmitted Dis. 32 (2005), 57–63. https://doi.org/10.1097/01.olq.0000148300.33428.6e.
  14. M. Maskew, A.P. MacPhail, D. Whitby, M. Egger, C.L. Wallis, M.P. Fox, Prevalence and Predictors of Kaposi Sarcoma Herpes Virus Seropositivity: A Cross-Sectional Analysis of HIV-Infected Adults Initiating ART in Johannesburg, South Africa, Infect. Agents Cancer. 6 (2011), 22. https://doi.org/10.1186/1750-9378-6-22.
  15. M. Masiá, C. Robledano, V. Ortiz de la Tabla, P. Antequera, B. Lumbreras, I. Hernández and F. Gutiérrez, Coinfection With Human Herpesvirus 8 Is Associated With Persistent Inflammation and Immune Activation in Virologically Suppressed HIV-Infected Patients, PLoS ONE. 9 (2014), e105442. https://doi.org/10.1371/journal.pone.0105442.
  16. D. Oktafiani, N.L. Megasari, E. Fitriana, N. Nasronudin, M.I. Lusida, S. Soetjipto, Detection of Human Herpesvirus8 Antigen in HIV-Infected Patients in East Java, Indonesia, Afr. J. Infect. Dis. 12 (2018), 43–46. https://doi.org/10.21010/ajid.v12i2.7.
  17. D. Watanabe, S. Iida, K. Hirota, T. Ueji, T. Matsumura, Y. Nishida, T. Uehira, H. Katano, T. Shirasaka, Evaluation of Human Herpesvirus-8 Viremia and Antibody Positivity in Patients with HIV Infection With Human Herpesvirus8-related Diseases, J. Med. Virol. 95 (2023), e29324. https://doi.org/10.1002/jmv.29324.
  18. H. Lambarey, M.J. Blumenthal, A. Chetram, W. Joyimbana, L. Jennings, C. Orrell, G. Schäfer, Reactivation of Kaposi’s Sarcoma-Associated Herpesvirus (KSHV) by SARS-CoV-2 in Non-hospitalised HIV-Infected Patients, eBioMedicine. 100 (2024), 104986. https://doi.org/10.1016/j.ebiom.2024.104986.
  19. M.A. Nowak, C.R.M. Bangham, Population Dynamics of Immune Responses to Persistent Viruses, Science. 272 (1996), 74–79. https://doi.org/10.1126/science.272.5258.74.
  20. A.V. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak, Viral Dynamics in Vivo: Limitations on Estimates of Intracellular Delay and Virus Decay, Proc. Nat. Acad. Sci. U.S.A. 93 (1996), 7247–7251. https://doi.org/10.1073/pnas.93.14.7247.
  21. R.V. Culshaw, S. Ruan, A Delay-Differential Equation Model of HIV Infection of CD4+ T-Cells, Math. Biosci. 165 (2000), 27–39. https://doi.org/10.1016/s0025-5564(00)00006-7.
  22. P.W. Nelson, A.S. Perelson, Mathematical Analysis of Delay Differential Equation Models of HIV-1 Infection, Math. Biosci. 179 (2002), 73–94. https://doi.org/10.1016/s0025-5564(02)00099-8.
  23. Z. Li, X.Q. Zhao, Global Dynamics of a Time-Delayed Nonlocal Reaction-Diffusion Model of Within-Host Viral Infections, J. Math. Biol. 88 (2024), 38. https://doi.org/10.1007/s00285-024-02052-5.
  24. J. Lin, R. Xu, X. Tian, Threshold Dynamics of an Hiv-1 Virus Model With Both Virus-to-Cell and Cell-to-Cell Transmissions, Intracellular Delay, and humoral immunity, Appl. Math. Comp. 315 (2017), 516–530. https://doi.org/10.1016/j.amc.2017.08.004.
  25. Y. Gao, J. Wang, Threshold Dynamics of a Delayed Nonlocal Reaction-Diffusion HIV Infection Model With Both Cell-Free and Cell-to-Cell Transmissions, J. Math. Anal. Appl. 488 (2020), 124047. https://doi.org/10.1016/j.jmaa.2020.124047.
  26. Z. Zhu, R. Wu, Y. Yang, Y. Xu, Modelling HIV Dynamics With Cell-to-cell Transmission and CTL Response, Math. Methods Appl. Sci. 46 (2022), 6506–6528. https://doi.org/10.1002/mma.8921.
  27. J. Li, X. Wang, Y. Chen, Analysis of an Age-Structured HIV Infection Model With Cell-to-Cell Transmission, Eur. Phys. J. Plus 139 (2024), 78. https://doi.org/10.1140/epjp/s13360-024-04873-1.
  28. R. Xu, C. Song, Dynamics of an HIV Infection Model With Virus Diffusion and Latently Infected Cell Activation, Nonlinear Anal.: Real World Appl. 67 (2022), 103618. https://doi.org/10.1016/j.nonrwa.2022.103618.
  29. A.S. Perelson, P. Essunger, Y. Cao, M. Vesanen, A. Hurley, K. Saksela, M. Markowitz, D.D. Ho, Decay Characteristics of HIV-1-Infected Compartments During Combination Therapy, Nature 387 (1997), 188–191. https://doi.org/10.1038/387188a0.
  30. K. Hattaf, H. Dutta, Modeling the Dynamics of Viral Infections in Presence of Latently Infected Cells, Chaos Solitons Fractals. 136 (2020), 109916. https://doi.org/10.1016/j.chaos.2020.109916.
  31. Y. Wang, Y. Zhou, F. Brauer, J.M. Heffernan, Viral Dynamics Model With CTL Immune Response Incorporating Antiretroviral Therapy, J. Math. Biol. 67 (2012), 901–934. https://doi.org/10.1007/s00285-012-0580-3.
  32. D. Wodarz, R.M. May, M.A. Nowak, The Role of Antigen-Independent Persistence of Memory Cytotoxic T Lymphocytes, Int. Immunol. 12 (2000), 467–477. https://doi.org/10.1093/intimm/12.4.467.
  33. Z. Xie, X. Liu, Global Dynamics in an Age-Structured HIV Model With Humoral Immunity, Int. J. Biomath. 14 (2021), 2150047. https://doi.org/10.1142/s1793524521500479.
  34. D. Wodarz, Hepatitis C Virus Dynamics and Pathology: The Role of CTL and Antibody Responses, J. Gen. Virol. 84 (2003), 1743–1750. https://doi.org/10.1099/vir.0.19118-0.
  35. P. Dubey, U.S. Dubey, B. Dubey, Modeling the Role of Acquired Immune Response and Antiretroviral Therapy in the Dynamics of HIV Infection, Math. Comp. Simul. 144 (2018), 120–137. https://doi.org/10.1016/j.matcom.2017.07.006.
  36. Z. Zhang, Y. Chen, X. Wang, L. Rong, Dynamic Analysis of a Latent HIV Infection Model With CTL Immune and Antibody Responses, Int. J. Biomath. 17 (2023), 2350079 https://doi.org/10.1142/s1793524523500791.
  37. G. Huang, X. Liu, Y. Takeuchi, Lyapunov Functions and Global Stability for Age-Structured HIV Infection Model, SIAM J. Appl. Math. 72 (2012), 25–38. https://doi.org/10.1137/110826588.
  38. J. Wang, J. Lang, X. Zou, Analysis of an Age Structured HIV Infection Model With Virus-to-Cell Infection and Cell-to-Cell Transmission, Nonlinear Anal.: Real World Appl. 34 (2017), 75–96. https://doi.org/10.1016/j.nonrwa.2016.08.001.
  39. L. Rong, A.S. Perelson, Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-Infected Patients on Potent Therapy, PLoS Comp. Biol. 5 (2009), e1000533. https://doi.org/10.1371/journal.pcbi.1000533.
  40. A. Mojaver, H. Kheiri, Mathematical Analysis of a Class of HIV Infection Models of CD4+ T-Cells With Combined Antiretroviral Therapy, Appl. Math. Comp. 259 (2015), 258–270. https://doi.org/10.1016/j.amc.2015.02.064.
  41. B.J. Nath, K. Sadri, H.K. Sarmah, K. Hosseini, An Optimal Combination of Antiretroviral Treatment and Immunotherapy for Controlling HIV Infection, Math. Comp. Simul. 217 (2024), 226–243. https://doi.org/10.1016/j.matcom.2023.10.012.
  42. O.M. Chimbola, E.M. Lungu, B. Szomolay, Optimal Control Application to a Kaposi’s Sarcoma Treatment Model, Int. J. Biomath. 15 (2022), 2150081. https://doi.org/10.1142/s1793524521500819.
  43. F. Nani, M. Jin, Dynamics of HIV-1 Associated Kaposi Sarcoma during HAART Therapy, Math and Computer Science Faculty Working Papers, 20, (2011).
  44. F. Nani, M. Jin, Analysis of Dynamics of HIV-1 Associated Kaposi Sarcoma during HAART and ACI, Br. J. Math. Comp. Sci. 19 (2016), 1–22. https://doi.org/10.9734/bjmcs/2016/20358.
  45. B. Szomolay, E.M. Lungu, A Mathematical Model for the Treatment of Aids-Related Kaposi’s Sarcoma, J. Biol. Syst. 22 (2014), 495–522. https://doi.org/10.1142/s0218339014500247.
  46. O.M. Chimbola, E.M. Lungu, B. Szomolay, Effect of Innate and Adaptive Immune Mechanisms on Treatment Regimens in an Aids-Related Kaposi’s Sarcoma Model, J. Biol. Dyn. 15 (2021), 213–249. https://doi.org/10.1080/17513758.2021.1912420.
  47. A.S. Perelson, D.E. Kirschner, R. De Boer, Dynamics of HIV Infection of CD4+ T Cells, Math. Biosci. 114 (1993), 81–125. https://doi.org/10.1016/0025-5564(93)90043-a.
  48. M.M. Hadjiandreou, R. Conejeros, V.S. Vassiliadis, Towards a Long-Term Model Construction for the Dynamic Simulation of HIV Infection, Math. Biosci. Eng. 4 (2007), 489–504. https://doi.org/10.3934/mbe.2007.4.489.
  49. S.K. Sahani, Yashi, Effects of Eclipse Phase and Delay on the Dynamics of HIV Infection, J. Biol. Syst. 26 (2018), 421–454. https://doi.org/10.1142/s0218339018500195.
  50. O.M. Chimbola, Mathematical Model of Classical Kaposi’s Sarcoma, Appl. Math. 11 (2020), 579–600. https://doi.org/10.4236/am.2020.117040.
  51. H.L. Smith, P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, 1995.
  52. A. Korobeinikov, Global Properties of Basic Virus Dynamics Models, Bull. Math. Biol. 66 (2004), 879–883. https://doi.org/10.1016/j.bulm.2004.02.001.
  53. J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations, Springer, New York, (1993).
  54. H.K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, Upper Saddle River, (2002).
  55. M. Renardy, C. Hult, S. Evans, J.J. Linderman, D.E. Kirschner, Global Sensitivity Analysis of Biological Multiscale Models, Curr. Opinion Biomed. Eng. 11 (2019), 109–116. https://doi.org/10.1016/j.cobme.2019.09.012.
  56. Z. Zi, Sensitivity Analysis Approaches Applied to Systems Biology Models, IET Syst. Biol. 5 (2011), 336–346. https://doi.org/10.1049/iet-syb.2011.0015.
  57. V.M.S. de Morais, E.L.S. de Lima, G.G.d.M. Cahú, et al. MBL2 Gene Polymorphisms in HHV-8 Infection in People Living with HIV/AIDS, Retrovirology, 15 (2018), 75. https://doi.org/10.1186/s12977-018-0456-8.
  58. R. Minami, M. Yamamoto, S. Takahama, H. Ando, T. Miyamura, E. Suematsu, Human Herpesvirus 8 DNA Load in the Leukocytes Correlates with the Platelet Counts in HIV Type 1-Infected Individuals, AIDS Res. Human Retrovir. 25 (2009), 1–8. https://doi.org/10.1089/aid.2007.0260.
  59. R. Tedeschi, M. Enbom, E. Bidoli, A. Linde, P. De Paoli, J. Dillner, Viral Load of Human Herpesvirus 8 in Peripheral Blood of Human Immunodeficiency Virus-Infected Patients with Kaposi’s Sarcoma, J. Clin. Microbiol. 39 (2001), 4269–4273. https://doi.org/10.1128/jcm.39.12.4269-4273.2001.
  60. A. Caterino-de-Araujo, R.C.R. Manuel, R. Del Bianco, E. Santos-Fortuna, M.C. Magri, J.M.K. Silva, R. Bastos, Seroprevalence of Human Herpesvirus 8 Infection in Individuals From Health Care Centers in Mozambique: Potential for Endemic and Epidemic Kaposi’s Sarcoma, J. Med. Virol. 82 (2010), 1216–1223. https://doi.org/10.1002/jmv.21789.
  61. L.G. Chatlynne, D.V. Ablashi, Seroepidemiology of Kaposi’s Sarcoma-Associated Herpesvirus (KSHV), Semin. Cancer Biol. 9 (1999), 175–185. https://doi.org/10.1006/scbi.1998.0089.
  62. S.M. Mbulaiteye, R.M. Pfeiffer, D. Whitby, G.R. Brubaker, J. Shao, R.J. Biggar, Human Herpesvirus 8 Infection within Families in Rural Tanzania, J. Infect. Dis. 187 (2003), 1780–1785. https://doi.org/10.1086/374973.
  63. D. Burini, D.A. Knopoff, Epidemics and Society – a Multiscale Vision from the Small World to the Globally Interconnected World, Math. Models Methods Appl. Sci. 34 (2024), 1567–1596. https://doi.org/10.1142/s0218202524500295.
  64. N. Bellomo, D. Burini, N. Outada, Multiscale Models of Covid-19 with Mutations and Variants, Netw. Heterog. Media, 17 (2022), 293–310. https://doi.org/10.3934/nhm.2022008.
  65. N. Bellomo, K.J. Painter, Y. Tao, M. Winkler, Occurrence vs. Absence of Taxis-Driven Instabilities in a May–Nowak Model for Virus Infection, SIAM J. Appl. Math. 79 (2019), 1990–2010. https://doi.org/10.1137/19m1250261.