Global stability of infection-free state and endemic infection state of a modified human immunodeficiency virus infection model

Anti-viral drug treatment of infections with the human immunodeficiency virus type I (HIV-1) usually leads to a rapid decline in the abundance of plasma virus. The effect of single drug therapy, however, is often only short-lived as the virus readily develops drug-resistant mutants. In this paper we provide analytic approximations for the rate of emergence of resistant virus. We study the decline of wildtype virus and the rise of resistant mutant virus in different compartments of the virus population such as free plasma virus, cells infected with actively replicating virus, long-lived infected cells and cells carrying defective provirus. The model results are compared with data on the rise of drug-resistant virus in three HIV-1 infected patients treated with neverapine (NVP). We find that the half-life of latently infected cells is between 10 and 20 days, whereas the half-life of cells with defective provirus is about 80 days. We also provide a crude estimate for the basic reproductive ratio of HIV-1 during NVP therapy.

There are many biological steps between viral infection of CD4(+) T cells and the production of HIV-1 virions. Here we incorporate an eclipse phase, representing the stage in which infected T cells have not started to produce new virus, into a simple HIV-1 model. Model calculations suggest that the quicker infected T cells progress from the eclipse stage to the productively infected stage, the more likely that a viral strain will persist. Long-term treatment effectiveness of antiretroviral drugs is often hindered by the frequent emergence of drug resistant virus during therapy. We link drug resistance to both the rate of progression of the eclipse phase and the rate of viral production of the resistant strain, and explore how the resistant strain could evolve to maximize its within-host viral fitness. We obtained the optimal progression rate and the optimal viral production rate, which maximize the fitness of a drug resistant strain in the presence of drugs. We show that the window of opportunity for invasion of drug resistant strains is widened for a higher level of drug efficacy provided that the treatment is not potent enough to eradicate both the sensitive and resistant virus.