Cellular automata approach to interacting cellular network models for the dynamics of cell population in an early HIV infection

In order to understand the evolution of cell population in an early HIV infection (AIDS), a network model of interacting cellular elements, such as macrophages, viruses, T4 cells, and T8 cells, is introduced for a cell mediated response. In a simplified discrete representation of binary cells, boolean expressions are used to describe their interactions and concentrations. Two different interaction models are considered and flows of configurations are studied in their configurational phase space. In the mean field (or infinite range interacting network) treatment, one interaction gives two fixed points describing the extreme limits of “immuno-competence” and “immunodeficiency”; in addition, it gives rise to a periodic cycle consisting of an “infected”, a “severely infected”, and a “susceptible” state. The other interaction leads to seven fixed points, two of which are the same as those in the first. The third fixed point represents a “severely infected” state, and the remaining four describe “susceptible” states of varying order. Growth and decay of cellular elements are then studied on a simple cubic lattice where nearest neighbor interactions are treated by inhomogeneous cellular automata using computer simulations. In order to take into account the sporadic growth of virions, an interaction latency parameter B is introduced, and the decline of immunocompetence as a function of B is discussed. A detail study is presented for the crossover between an immunodeficient and an immunocompetent state as a function of the initial concentration of the host cells and latency/dilution.