Coexistence and competition in HIV infections.

In this paper we extend our explanation of a model for the dynamics of the interaction between HIV and the cells of the immune system (Nowak et al., 1990). We show that the Simpson index of viral diversity is a Lyapunov function for a simplified version of this model. We also present a more general mathematical characterization of the nature of the diversity threshold exhibited by the model, including for the first time heterogeneity in parameters like virus replication rate, cytopathicity and antigenicity. The more general diversity threshold condition includes the different contributions of strains with higher replication rates and cytopathicities or strains that are only weakly recognized by the immune system. This leads to some new insights and a more detailed understanding of why the viral diversity falls once the diversity threshold is exceeded.