Volume 6, Number 4, Winter 1998
ANALYSES OF AN ANTIVIRAL IMMUNE RESPONSE
MODEL WITH TIME DELAYS
KENNETH L. COOKE, YANG KUANG AND BINGTUAN LI
Abstract. This paper deals with the study of a model
of the response of the immune system within a human to an
invading virus. The model consists of three highly nonlinear
differential equations, some of which involve discrete delays.
The model was formulated in Tang et al. (21),where some
preliminary simulations were reported for a special case without
time delays. Here, among other things, we shall show that
the model is uniformly persistent in the sense that all positive
solutions eventually enter and stay in a compact set in the
interior of the positive cone. We also provide some numerical
simulation and bifurcation analyses.