Theory in Biosciences

, Volume 121, Issue 2, pp 237–245 | Cite as

Effects of viral mutation on cellular dynamics in a monte carlo simulation of HIV immune response model in three dimensions

  • R. Mannion
  • H. J. Ruskin
  • R. B. Pandey


The cellular dynamics of HIV interaction with the immune system is explored in three-dimensions using a direct Monte Carlo simulation. Viral mutation with probability, Pmut, is considered with immobile and mobile cells. With immobile cells, the viral population becomes larger than that of the helper cells beyond a latency period Tcrit and above a mutation threshold Pcrit. That is at Pmut ≥ Pcrit, {\({\rm T}_{crit} \propto \left( {{\rm P}_{mut} - {\rm P}_{crit} } \right)^{ - \gamma } \)}, with γ ⋍ 0.73 in three dimensions and γ ⋍ 0.88 in 2-D. Very little difference in Pcrit is observed between two and three dimensions. With mobile cells, no power-law is observed for the period of latency, but the difference in Pcrit between two and three dimensions is increased. The time-dependency of the density difference between Viral and Helper cell populations (ρV − ρH) is explored and follows the basic pattern of an immune response to infection. This is markedly more defined than in the 2-D case, where no clear pattern emerges.

Key words

Monte Carlo HIV mobility mutation latency 


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  1. Ahmed, E. (1996). Fuzzy Cellular Automata Models in Immunology. J. Stat. Phys 85, 291.CrossRefGoogle Scholar
  2. Castiglione, F., Bernaschi, M. & Succi, S. (1997). Simulating the Immune Response on a Distributed Parallel Computer. Int. J. Mod. Phys. C 8, 527.CrossRefGoogle Scholar
  3. Chowdhury, D., Sahimi, M. & Stauffer, D. (1991). A discrete model for immune surveillance, tumor immunity, and cancer J. Theor. Bio. 152, 263.CrossRefGoogle Scholar
  4. Dayan, I., Stauffer, D. & Havlin, S. (1988). Cellular Automata Generalization of the Weisbuch-Atlan Model for Immune Response J. Phys. A 21, 2473.CrossRefGoogle Scholar
  5. De Oliveira, S., De Oliveira, P. M. C. & Stauffer, D. (1999). “Evolution, Money, War and Computers”, Teubner (Stuttgart and Leipzig) Chapter 3.Google Scholar
  6. Fauci, A. S., Pantaleo, G., Stanley, S. & Weissmann, D. (1996). Immunopathogenic mechanisms of HIV infection. Ann. Internal Medic. 124, 654.Google Scholar
  7. Hershberg U., Louzoun, Y., Atlan, H. & Solomon, S. (2001). HIV time hierarchy: winning the war while losing all the battles. Physica A, 289, 178.CrossRefGoogle Scholar
  8. Kaneko, K., (1997). Coupled maps with growth and death: An approach to cell differentiation. Physica D 103, 505 and references therein.CrossRefGoogle Scholar
  9. Mannion, R., Ruskin, H. J. & Pandey, R. B. (2000)(a). Effect of Mutation on Helper T cells and Viral Population: A computer Simulation Model for HIV. Theor. Biosci. 119, 10.CrossRefGoogle Scholar
  10. Mannion, R., Ruskin, H. J., & Pandey, R. B. (2000)(b). A Monte Carlo Approach to Population Dynamics of Cells in an HIV Immune Response Model. Theor. Biosci. 119, 145.CrossRefGoogle Scholar
  11. Mielke, A. & Pandey, R. B. (1998). A Computer Simulation Study of Cell Population in a Fuzzy Interaction Model for Mutating HIV. Physica A 251, 430.CrossRefGoogle Scholar
  12. Pandey, R. B. (1991). Cellular automata approach to interacting cellular network models for the dynamics of cell population in an early HIV infection. Physica A 179, 442.CrossRefGoogle Scholar
  13. Pandey, R. B. (1996). A Cellular Automata Approach to Modelling the Immune Response: HIV, in “Scientific Computing in Europe, SCE 1996”, Sept. 2–4, 1996, Dublin, Ireland, edited by H.J. Ruskin, R. O’Connor, and Y. Feng.Google Scholar
  14. Pandey, R. B. (1998). A Stochastic Cellular Automata Approach to Cellular Dynamics for HIV: Effect of Viral Mutation. Theor. Biosci. 117, 32.Google Scholar
  15. Perelson, A. S. & Weisbuch, G. (1997). Immunology for Physicists. Rev. Mod. Phys. 69(4), 1219–1267.CrossRefGoogle Scholar
  16. Stauffer, D. & Pandey, R. B. (1992). Immunologically motivated simulation of cellular automata. Computers in Physics 6, 404.Google Scholar
  17. Zorzenon Dos Santos, R. M. (1999). Immune Responses: Getting close to experimental results with cellular automata models. Ann. Rev. Comp. Phys. vol. VI, edited by D. Stauffer, World Scientific Singapore, p. 159.Google Scholar
  18. Zorzenon Dos Santos, R. M. & Coutinho. (2000). On the dynamics of the evolution of the HIV Infection. cond-mat/0008081.Google Scholar

Copyright information

© Urban & Fischer Verlag 2002

Authors and Affiliations

  • R. Mannion
    • 1
  • H. J. Ruskin
    • 1
  • R. B. Pandey
    • 2
  1. 1.Department of Physics and AstronomySchool of Computer Applications, Dublin City UniversityDublin 9Ireland
  2. 2.Department of Physics and AstronomyUniversity of Southern MississippiHattiesburgUS

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