J. Phys. I France
Volume 1, Numéro 12, December 1991
Page(s) 1709 - 1713
DOI: 10.1051/jp1:1991228
J. Phys. I France 1 (1991) 1709-1713

On a discrete approach to cell dynamics in context to immune response against HIV

R. B. Pandey

Department of Physics and Astronomy, University of Southern Mississippi, Hattiesburg, MS 39406-5046, U.S.A.

(Received 23 August 1991, accepted in final form 2 September 1991)

A network model of interacting cellular elements, such as macrophages, viruses, T4 cells, and T8 cells, is introduced to study the evolution of cell population in an early HIV infection in a cell mediated response. The mean field treatment leads to two fixed points (describing "immunocompetence" and "immunodeficiency") and a limit cycle in infected states of period two. Using a cellular automata rule for the nearest neighbour interaction, the growth of the cellular population is studied as a function of their initial concentration p; on increasing p, a crossover from an immunodeficient to an immunocompetent state occurs at a characteristic value $p_{\rm c}$.

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