The aim of this work is the construction, calibration, and comparative analysis of mathematical models of the evolution of the human immunodeficiency virus (HIV) in the course of infection when the models are based on deterministic principles of the quasispecies theory (Eigen-Schuster) and on stochastic approaches of genetic algorithms (Holland). The models take into account the replication of viral genomes and selection of descendants according to their fitness, point mutations, multi-infection of target cells and recombination of genomes at the stage of formation of proviral DNA. The processes of diversification of the virus population under the action of the antiviral drug azidothymidine (AZT) that blocks reverse transcription of the virus are simulated. A four-letter alphabet is used in the stochasticmodel for description of nucleotide sequences. The parameters of the model are estimated using original data on the degree of adaptation of the HIV mutants that are partly or completely resistant to this drug. The influence of parameters of infection on the characteristics of viral mutants population diversity is studied