Vol 5 No 7 (2019): International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662)


Published July 28, 2019
  • mathematical modeling,
  • viral hepatitis C,
  • kinetic variables,
  • simulation
How to Cite
I. EDISSONOV, & S. RANCHEV. (2019). MODELLING AND SIMULATION OF THE IMMUNE PROCESS AT VIRAL HEPATITIS C. International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662), 5(7), 01-09. Retrieved from https://gnpublication.org/index.php/ms/article/view/1021


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.


Download data is not yet available.


  1. . Tami, J.A., Parr, M.D., and Thompson, J.S. (1992). The immune system. Bull. Math. Biol. 54(4), 649-672.
  2. . Seeff, LB. (2002). Natural history of chronic hepatitis C. Hepatology 36, S35-S46.
  3. . Chang, K. M., Rehermann, B., and Chisari, F. V. (1997). Immunopathology of hepatitis C. Springer Semin Immunopathol 19, 57–68.
  4. . 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.
  5. . 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.
  6. . Einav, S., and Koziel, M. J. (2002). Immunopathogenesis of hepatitis C virus in the immunosuppressed host. Transpl Infect Dis 4, 85–92.
  7. . Farci, P. (2001). Hepatitis C virus. The importance of viral heterogeneity. Clin Liver Dis 5, 895–916.
  8. . 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.
  9. . Forns, X., Purcell, R. H., and Bukh, J. (1999). Quasispecies in viral persistence and pathogenesis of hepatitis C virus. Trends Microbiol 7, 402–410.
  10. . Hoofnagle, J. H. (1999). Management of hepatitis C: current and future perspectives. J Hepatol 31, 264–268.
  11. . Morel, P.A. (1998). Mathematical modeling of immunological reactions. Front. Biosci. 3, d338-347.
  12. . Marchuk, G.I. (1983). Mathematical models in immunology. Springer-Verlag, New York.
  13. . Perelson, A.S. (2002). Modelling viral and immune system dynamics, Nature Rew. Immunol. 2, 28-36.
  14. . Novak, M.A., and May, R.M. (2000). Virus dynamics: Mathematical principles of immunology and virology. Oxford University Press, New York.
  15. . Perelson, A.S. (1999). Viral kinetics and mathematical models. Amer. J. Med. 107 (6B), 49S-52S.
  16. . 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.
  17. . Weinand, R.G., and Conrad, M. (1988). Maturation of the immune response: a computational model. J. Theor. Biol. 133(4), 409-428.
  18. . Layden, T. J., Lam, N. P., and Wiley, T. E. (1999). Hepatitis C viral dynamics. Clin Liver Dis 3, 793–810.
  19. . 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.
  20. . Zeuzem, S. (1999). Clinical implication of hepatitis C viral kinetics. J. Hepatol. 31, 61-64.
  21. . Herrmann, E., Neumann, AU., Schmidt, JM., et al. (2000). Hepatitis C virus kinetics. Antivir. Ther. 5, 85-90.
  22. . 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.
  23. . Deuffic, S., Buffat, L., Poynard, T., and Valleron, AJ. (1999). Modelling the hepatitis C virus epidemic in France. Hepatology 29, 1596-1601.
  24. . 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.
  25. . Edissonov, I. (1996). Fuzzy modelling of the L-lysin biosynthesis process during periodical cultivation of Brevibacterium flavum type microbial population.
  26. Fuzzy Sets and Systems 78, 271-278.