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DYNAMIC ANALYSIS FOR DELAYED HCV INFECTION IN VIVO WITH ANTI-RETRO VIRAL TREATMENT

  • Krishnapriya, P. (Department of Mathematics, Mary Matha College of Arts and Science) ;
  • Hyun, Ho Geun (Department of Mathematics Education, Kyungnam University)
  • Received : 2021.01.02
  • Accepted : 2021.04.05
  • Published : 2021.09.15

Abstract

In this paper, we study a within-host mathematical model of HCV infection and carry out mathematical analysis of the global dynamics and bifurcations of the model in different parameter regimes. We explore the effect of reverse transcriptase inhibitors (RTI) on spontaneous HCV clearance. The model can produce all clinically observed patient profiles for realistic parameter values; it can also be used to estimate the efficacy and/or duration of treatment that will ensure permanent cure for a particular patient. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

Keywords

References

  1. P. Krishnapriya, M. Pitchaimani and Tarynn M. Witten, Mathematical analysis of an influenza A epidemic model with discrete delay, J. Comput. and Appl. Math., 324 (2017), 155-172. https://doi.org/10.1016/j.cam.2017.04.030
  2. P. Krishnapriya and M. Pitchaimani, Analysis of time delay in viral infection model with immune impairment, J. Appl. Math. Comput., 55 (2017), 421-453. https://doi.org/10.1007/s12190-016-1044-5
  3. P. Krishnapriya and M. Pitchaimani, Modeling and bifurcation analysis of a viral infection model with time delay and immune impairment, Japan J. Indust. Appl. Math., 34(1) (2017), 99-139. https://doi.org/10.1007/s13160-017-0240-5
  4. P. Krishnapriya and M. Pitchaimani, Optimal control of mixed immunotherapy and chemotherapy of tumours with discrete delay, Int. J. Dynam. Cont., 5(3) (2017), 872-892. https://doi.org/10.1007/s40435-015-0221-y
  5. M.C. Maheswari, P. Krishnapriya, K. Krishnan and M. Pitchaimani, A mathematical model of HIV-1 infection within host cell to cell viral transmissions with RTI and discrete delays, J. Appl. Math. Comput., 56(1) (2018), 151-178. https://doi.org/10.1007/s12190-016-1066-z
  6. M. Pitchaimani, P. Krishnapriya and C. Monica Mathematical modeling of intra-venous glucose tolerance test model with two discrete delays, J. Bio. Syst., 23(4) (2015), 631-660.
  7. N.S. Ravindran, M. Mohamed Sheriff and P. Krishnapriya Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control, J. Bio. Dyna., 11(1) (2017), 480-503. https://doi.org/10.1080/17513758.2017.1381280
  8. R.Nagarajan, K.Krishnan and P. Krishnapriya, Optimal control of HIV-1 infection model with logistic growth using discrete delay, Nonlinear Funct. Anal. Appl., 22(2) (2017), 301-309.
  9. P. Krishnapriya and M. Pitchaimani, Analysis of HIV-1 Model: Within Host Cell to Cell Viral Transmission with ART, Nonlinear Funct. Anal. Appl., 21(4) (2016), 597-612.
  10. A.S. Perelson, A.U. Neumann, M. Markowitz, J.M. Leonard and D.D. Ho HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, 271(5255) (1996), 1582-1586. https://doi.org/10.1126/science.271.5255.1582
  11. X. Wei, S.K. Ghosh, M.E. Taylor, V.A. Johnson, E.A. Emini, P. Deutsch, J.D. Lifson, S. Bonhoeffer, M.A. Nowak, B.H. Hahn et. al., Viral dynamics in human immunodeficiency virus type 1, infection, Nature, 373(6510) (1995), 117-122. https://doi.org/10.1038/373117a0
  12. A.U. Neumann, N.P. Lam, H. Dahari, D.R. Gretch, T.E. Wiley, T.J. Layden and A.S. Perelson, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy, Science, 282(5386) (1998), 103-107. https://doi.org/10.1126/science.282.5386.103
  13. A.S. Perelson, E. Herrmann, F. Micol and S. Zeuzem, New kinetic models for the hepatitis C virus, Hepatology, 42(4) (2005), 749-754. https://doi.org/10.1002/hep.20882
  14. H. Dahari, M. Major, X. Zhang, K. Mihalik, C.M. Rice, A.S. Perelson, S.M. Feinstone and A.U. Neumann, Mathematical modeling of primary hepatitis C infection: noncytolytic clearance and early blockage of virion production, Gastroenterology, 128(4) (2005), 1056-1066. https://doi.org/10.1053/j.gastro.2005.01.049
  15. H. Dahari, A. Lo, R.M. Ribeiro and A.S. Perelson, Modelling hepatitis C virus dynamics: liver regeneration and critical drug efficacy, J. Theor. Biol., 247(2) (2007), 371-381. https://doi.org/10.1016/j.jtbi.2007.03.006
  16. H. Dahari, R.M. Ribeiro and A.S. Perelson, Triphasic decline of hepatitis C virus RNA during antiviral therapy, Hepatology, 46(1) (2007), 16-21. https://doi.org/10.1002/hep.21657
  17. M.A. Nowak and R.M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, New York, 2000.
  18. A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41(1) (1999), 3-44. https://doi.org/10.1137/S0036144598335107
  19. Ruthie Birger, Roger Kouyos, Jonathan Dushoff and Bryan Grenfell, Modeling the effect of HIV coinfection on clearance and sustained virologic response during treatment for hepatitis C virus, Epidemics, 12 (2015), 1-10. https://doi.org/10.1016/j.epidem.2015.04.001
  20. N. MacDonald, Biological Delay Systems: Linear Stability Theory, Cambridge University, Cambridge, 1989.
  21. J. Hale, Theory of Functional differential equations, Springer, New York, 1997.
  22. Y. Kuang, Delay differential equations with applications in population dynamics, Math. Sci. Eng., Academic Press, Boston, 1993.
  23. E. Avila-Vales, Noe Chan-Chi, Gerardo E. Garcia-Almeida a and Cruz Vargas-De-Leon, Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission, Appl. Math. Comput., 259 (2015), 293-312. https://doi.org/10.1016/j.amc.2015.02.053
  24. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33(5) (2002), 1144-1165. https://doi.org/10.1137/S0036141000376086
  25. J. Hale and S.V. Lunel, Introduction to Functional Differential Equations, SpringerVerlag, New York, 1993.
  26. H. Smith and X. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47(9) (2001), 6169-6179. https://doi.org/10.1016/S0362-546X(01)00678-2
  27. X. Lai and X. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl., 426(1) (2015), 563-584. https://doi.org/10.1016/j.jmaa.2014.10.086
  28. K.A. Pawelek, S. Liu, F. Pahlevani and L. Rong, A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data, Math. Biosci., 235(1) (2012), 98-109. https://doi.org/10.1016/j.mbs.2011.11.002