This paper examines the numerical and functional consequences of various stimuli on antiviral CD8+ T-cell memory using a mathematical model. The model is based upon biological evidence from the murine model of infection with lymphocytic choriomeningitis virus (LCMV) that the phenotype of immunological memory represents low-level responses driven by various stimuli, and the memory CTL population is partitioned between resting, cycling and effector cells. These subpopulations differ in their lifespan, their potential to mediate antiviral protection and in the stimuli needed for their maintenance. Three types of maintenance stimuli are examined: non-antigen-specific (bystander) stimulation, persisting antigen stimulation and reinfection-mediated stimulation. The modelling predicts that: (i) stable persistence of CTL memory requires the presence of either bystander or antigen-specific stimulation above a certain threshold depending on the sensitivity of memory CTL to stimulation and their life-span; (ii) a relatively low level of stimuli (approximately 10(4) fold less on a per CTL basis compared to acute infection) is needed to stabilize the expanded memory CTL population; (iii) the presence of CTL subsets in the memory pool of different activation states and lifespans ensures the robustness of memory persistence in the face of temporal variation in the low-level stimuli and; (iv) an 'optimal' population structure of the memory CTL pool, in terms of immediate protection, requires the presence of both activated cycling and effector CTL. For this, persisting antigen alone or synergistically with bystander signals provide the appropriate stimulation, so that the stimuli equivalent to approximately 30 p.f.u. of LCMV in the spleen are sufficient to maintain approximately 10(5)-10(6) specific CTL in the memory pool. These observations are relevant both to our understanding of natural protective immunity and to vaccine design.