  In this paper we extend the Celada-Seiden (CS) model of the humoral immune
response to include infectious virus and cytotoxic T lymphocytes (cellular
response). The response of the system to virus involves a competition between
the ability of the virus to kill the host cells and the host's ability to
eliminate the virus. We find two basins of attraction in the dynamics of this
system, one is identified with disease and the other with the immune state.
There is also an oscillating state that exists on the border of these two
stable states. Fluctuations in the population of virus or antibody can end the
oscillation and drive the system into one of the stable states. The
introduction of mechanisms of cross-regulation between the two responses can
bias the system towards one of them. We also study a mean field model, based on
coupled maps, to investigate virus-like infections. This simple model
reproduces the attractors for average populations observed in the cellular
automaton. All the dynamical behavior connected to spatial extension is lost,
as is the oscillating feature. Thus the mean field approximation introduced
with coupled maps destroys oscillations.
