We propose a model for the interaction between human immunodeficiency virus and the immune system. Two differential equations describe the interactions between one strain of virus and one clone of T lymphocytes. We use the model to generalize earlier results pertaining to the AIDS diversity threshold [Nowak, M. A., Anderson, R. M., McLean The development of AIDS is associated with the selective depletion of the most crucial cell type of the immune system: the CD4+ helper T cell. The human immunodeficiency virus (HIV) infects helper T cells by binding the gpl20 virus envelope glycoprotein to CD4+ molecules (1). The selective infection and death of CD4+ T cells provides a simple explanation for the impairment of the immune system (2, 3). This explanation, however, is widely debated (4-7).One hallmark of HIV infection is the long and variable incubation period. Although the processes of infection and immune activation have a short time scale, a typical time scale for the incubation period is 10 years (8). Another hallmark of HIV is its enormous genetic diversity. The dominant surface antigen for the immune response is the V3 loop of gpl20 (9,10). This V3 loop is hypervariable: virus isolates from one infected individual have genetically different V3 loops (11, 12). Since HIV accumulates one point mutation per genome during an average replication cycle (12,13), the genetic variability will grow exponentially. However, antigenic variability is not unique to HIV: several pathogens possess antigenic variability which lets them "run ahead" of the immune response.A recent model (14-17) combines these two hallmarks of AIDS in that it attributes the long and variable incubation period to genetic variability. The authors of the model coinedThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. the term "diversity threshold" for the critical variability beyond which the immune system is no longer capable of controlling the virus. The diversity threshold emerges mathematically from their simple and quite reasonable model. The diversity threshold (14-17) is a generic property of a wide variety of models. (See refs. 17 and 18 for recent reviews of mathematical models for the various pathogenic effects of HIV.)The virus quasispecies (19) not only increases in diversity but also evolves physiologically different strains. Virus strains evolve different replication rates, cytotrophisms, and antigenicities (20)(21)(22). Here we develop a model that allows us to study the relation between the diversity of the virus quasispecies and the "virulence" of each virus strain. We derive a dimensionless virulence parameter and show that it is involved in well-known local and global bifurcations.
Models of the Immune Response to HIVOur models describe the interactions between one strain of virus vj, where j is the strain number, and the clone(s) of CD4+ T cells tj that recognizes thi...