DIVERSITY AND VIRULENCE THRESHOLDS IN AIDS

We propose a model for the interaction between human immunodeficiency virus and the immune system. Two differential equations describe the i nteractions between one strain of virus and one clone of T lymphocytes . We use the model to generalize earlier results pertaining to the AID S diversity threshold [Nowak, M.A., Anderson, R.M., McLean, A. R., Wol fs, T. F. W., Goudsmit, J. and May, R. M. (1991) Science 254, 963-969] . Our model has (i) a stable steady state corresponding to the ''contr olled'' persistence of the virus and (ii) a region corresponding to AI DS. The separatrix between the two regimes is formed by the stable man ifold of a saddle point. We define a dimensionless ''virulence'' param eter which combines the infectivity and antigenicity of a virus strain . We derive analytically two parameter conditions involving virulence. The first corresponds to a saddle-node bifurcation which causes AIDS due to the loss of the stable equilibrium. The second corresponds to a global bifurcation which causes AIDS due to a change in the basins of attraction. Incorporating diversity into the model, we derive a diver sity threshold corresponding to the saddle-node bifurcation. In this t hreshold condition diversity and virulence have an equivalent effect. By studying the effect of diversity on the critical virulence that is required for a new mutant to cause AIDS, we again establish that diver sity and virulence are equivalent parameters. Because in our model inc reasing diversity decreases the critical virulence, the strain that ev entually causes AIDS need not be a virulent one.