For many viral diseases, the immune system's "killer" T cells, the cytotoxic T lymphocytes (CTLs), efficiently clear virus from the host. The human immunodeficiency virus (HIV), by contrast, inevitably establishes a chronic infection. Are HIV-specific CTLs defective in some way? The question drew renewed interest after vaccines against infection by a simian immunodeficiency virus (SIV)-HIV combination succeeded in lowering the viral load in monkeys by an amount previously achieved in patients only by triple-combinations of drugs. But one of the monkeys later died of AIDS when its virus escaped from CTL recognition. In this Project, new mathematical tools for comparing theories of CTL and vaccine action will be developed and new studies to test the theories proposed. The predictions of competing "CTL-defect" scenarios will be evaluated, the estimates of CTL killing action improved, and the strategies for delaying escape from CTLs explored. A "double-labeling" experiment can reveal important CTL kinetic parameters and support or rule out CTL-defect theories. Collaborations between modelers, statisticians, laboratory scientists, and clinical investigators will facilitate these studies in HIV-infected subjects or SIV-infected animals, which moreover may contribute to existing programs to develop a CTL-directed HIV vaccine.