Modelling and Simulation of the Immune Process at Viral Hepatitis C

Authors

  • I. Edisonov Bulgarian Academy of Sciences, Institute of Mechanics, “Acad. G.Bonchev” St., Bl. 4, 1113 Sofia, Bulgaria
  • S. Ranchev Bulgarian Academy of Sciences, Institute of Mechanics, “Acad. G.Bonchev” St., Bl. 4, 1113 Sofia, Bulgaria

DOI:

https://doi.org/10.53555/ms.v5i7.1021

Keywords:

mathematical modeling, viral hepatitis C, kinetic variables, simulation

Abstract

Mathematical model at viral hepatitis C is proposed as nonlinear system from ordinary differential equations. Based on clinical data of the immune process at viral Hepatitis C a numerical simulation is carried out.  As a result of the simulation such values of the parameters in the kinetic model are obtained at which the experimental clinical values are maximal near to the theoretical results.

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References

. Tami, J.A., Parr, M.D., and Thompson, J.S. (1992). The immune system. Bull. Math. Biol. 54(4), 649-672.

. Seeff, LB. (2002). Natural history of chronic hepatitis C. Hepatology 36, S35-S46.

. Chang, K. M., Rehermann, B., and Chisari, F. V. (1997). Immunopathology of hepatitis C. Springer Semin Immunopathol 19, 57–68.

. Cooper, S., Erickson, A. L., Adams, E. J., Kansopon, J., Weiner, A. J., Chien, D. Y., Houghton, M., Parham, P., and Walker, C. M. (1999). Analysis of a successful immune response against hepatitis C virus. Immunity 10, 439–449.

. de Araujo, E. S., Cavalheiro Nde, P., Cubero Leitao, R. M., Borges Tosta, R. A., and Barone, A. A. (2002). Hepatitis C viral load does not predict disease outcome: going beyond numbers. Rev Inst Med Trop Sao Paulo 44, 71–78.

. Einav, S., and Koziel, M. J. (2002). Immunopathogenesis of hepatitis C virus in the immunosuppressed host. Transpl Infect Dis 4, 85–92.

. Farci, P. (2001). Hepatitis C virus. The importance of viral heterogeneity. Clin Liver Dis 5, 895–916.

. Farci, P., Shimoda, A., Coiana, A., et al.(2000). The outcome of acute hepatitis C predicted by the evolution of the viral quasispecies. Science 288, 339–344.

. Forns, X., Purcell, R. H., and Bukh, J. (1999). Quasispecies in viral persistence and pathogenesis of hepatitis C virus. Trends Microbiol 7, 402–410.

. Hoofnagle, J. H. (1999). Management of hepatitis C: current and future perspectives. J Hepatol 31, 264–268.

. Morel, P.A. (1998). Mathematical modeling of immunological reactions. Front. Biosci. 3, d338-347.

. Marchuk, G.I. (1983). Mathematical models in immunology. Springer-Verlag, New York.

. Perelson, A.S. (2002). Modelling viral and immune system dynamics, Nature Rew. Immunol. 2, 28-36.

. Novak, M.A., and May, R.M. (2000). Virus dynamics: Mathematical principles of immunology and virology. Oxford University Press, New York.

. Perelson, A.S. (1999). Viral kinetics and mathematical models. Amer. J. Med. 107 (6B), 49S-52S.

. Layden, T.J., Layden, J.E., Ribeiro, R.M., and Perelson, A.S. (2003). Mathematical modeling of viral kinetics: A tool to understand and optimize therapy. Clinics in Liver Disease 7, 163-178.

. Weinand, R.G., and Conrad, M. (1988). Maturation of the immune response: a computational model. J. Theor. Biol. 133(4), 409-428.

. Layden, T. J., Lam, N. P., and Wiley, T. E. (1999). Hepatitis C viral dynamics. Clin Liver Dis 3, 793–810.

. Layden, T. J., Mika, B., and Wiley, T. E. (2000). Hepatitis C kinetics: mathematical modeling of viral response to therapy. Semin Liver Dis 20, 173–183.

. Zeuzem, S. (1999). Clinical implication of hepatitis C viral kinetics. J. Hepatol. 31, 61-64.

. Herrmann, E., Neumann, AU., Schmidt, JM., et al. (2000). Hepatitis C virus kinetics. Antivir. Ther. 5, 85-90.

. Law, MG., Dore, GJ., Bath, N., et al. (2003). Modelling C virus incidence, prevalence and long-term sequelae in Australia, 2001. Int. J. Epidemol. 32, 717-724.

. Deuffic, S., Buffat, L., Poynard, T., and Valleron, AJ. (1999). Modelling the hepatitis C virus epidemic in France. Hepatology 29, 1596-1601.

. Neumann, A.U., Lam, N.P., Dahari, H., Gretch, D.R., Wiley, T.E., Layden, T.J., and Perelson, A.S. (1998). Hepatitis C virus dynamics in vivo and antiviral effiacy of interferon- alpha therapy. Science 282, 103-107.

. Edissonov, I. (1996). Fuzzy modelling of the L-lysin biosynthesis process during periodical cultivation of Brevibacterium flavum type microbial population. Fuzzy Sets and Systems 78, 271-278.

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Published

2019-07-31

How to Cite

Edisonov, I., & Ranchev, S. (2019). Modelling and Simulation of the Immune Process at Viral Hepatitis C. International Journal For Research In Mathematics And Statistics, 5(7), 01–09. https://doi.org/10.53555/ms.v5i7.1021