We propose a novel model for the interaction between HIV and the immune system. Two differential equations describe the interactions between one strain of virus and one clone of T-lymphocytes. We employ the model to generalize earlier results on the AIDS diversity threshold (Nowak et al. 1990, Nowak et al. 1991). Virus diversity is implemented in the model by assuming that all virus strains and all T-cell clones are identical. Given this assumption, diversity is represented as a parameter.

First we confirm the earlier results by showing that our model has a diversity threshold corresponding to a saddle-node bifurcation. We derive an analytical expression for the local bifurcation point in terms of the parameters. This shows that the diversity threshold corresponds to a linear combination of the diversity, infectivity, and antigenicity of the virus quasi-species. The mechanism by which an increase in diversity causes AIDS is by increasing the total virus concentration.

Secondly we derive a ‘virulence’ threshold corresponding to a global bifurcation involving the basins of attraction. Here ‘virulence’ is defined as the infectivity and antigenicity of a virus strain. We derive an analytical expression for the global bifurcation point in terms of the parameters. A numerical study of the relation between the diversity and virulence thresholds suggests that the condition for the development of AIDS is a linear combination of diversity and virulence.