Global dynamics for a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed delays

Abstract

In this paper, a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed infection delays is proposed. The drug-sensitive strain could mutate and become drug-resistant strain during the process of reverse transcription (i.e., SR conversion in short). The nonnegativity and boundedness of solutions are discussed, by introducing two kinds of principle reproduction numbers, i.e., Rs (the reproduction number induced by drug-sensitive strain of HIV virus) and Rr (the reproduction number induced by drug-resistant strain of HIV virus), the existence of equilibria is also acquired. Using the linearization method and constructing the suitable Lyapunov functionals, the criteria are established on the local and global stability of equilibria (including infection-free, drug-sensitive strain, drug-resistant strain and endemic) based on the composite effects of Rs and Rr. We find that there exist competitive exclusion and coexistence phenomenon between drug-sensitive and drug-resistant strains without SR conversion, while uniform persistence between the two kinds of strains with SR conversion. The theoretical results are illustrated by numerical simulations.