Abstract: In this paper, the authors present a model illustrateing the interactions between the two HIV-1 phenotypes and cytokines. By introducing the important cytokines, IL-2 and CAF, in the HIV-1 dynamics model, the authors study the evolution of the two different HIV-1 phenotypes: the M-tropic (NSI) and the T-cell-tropic (SI). Using the type K_m monotone system theory, the authors obtain two results. First, the number of steady states of the system is odd, the odd indexed equilibria are asymptotically stable, and the even ones are unstable. Secondly, some detailed information about the bases of attraction of these steady states has been obtained. These results indicate that the two phenotypes will coexist in the infected patient for long time. Moreover, all these results can be explained by the pathogenesis of AIDS and are consistent with the results of clinical studies.

Key words: HIV-1, NSI phenotype, SI phenotype, IL-2, CAF, Type K_mmonotone system