Branching process models for HIV-1 drug resistant mutants
Drug therapy for human immunodeficiency virus type 1 (HIV-1) infection often fails because of the appearance of resistant viral mutants. Thus knowledge on the abundance of resistant mutants prior to treatment is essential for optimizing drug therapy to avoid resurgence of resistant mutants. A simple multitype continuous-time branching process model is developed and investigated for the generation of resistant viral mutants during HIV-1 infection. The growth of mutant populations is characterized by means, variances and marginal distributions from the start of acute infection to equilibrium in the chronic stage. The expressions for the equilibrium frequencies of mutants are derived and their dependence on mutation rates and mutant fitness explored. The model suggests that mutants with three or more point mutations are unlikely to occur prior to treatment. A similar branching process model is also used to compute the number of resistant mutants that are generated de novo during treatment. Then the two possible causes of resistance-related treatment failure are discriminated by characterizing the ratio of the amount of resistant mutants produced de novo to the number of preexisting resistant mutants. The ratio is determined by the fitness of mutants prior to treatment and the fitness of the wild-type virus and intermediate mutants during treatment.