Mathematical Analysis of Age‐Structured HIV‐1 Dynamics with Combination Antiretroviral Therapy

Abstract

Various classes of antiretroviral drugs are used to treat HIV infection, and they target different stages of the viral life cycle. Age‐structured models can be employed to study the impact of these drugs on viral dynamics. We consider two models with age‐of‐infection and combination therapies involving reverse transcriptase, protease, and entry/fusion inhibitors. The reproductive number ${\cal R}$ is obtained, and a detailed stability analysis is provided for each model. Interestingly, we find in the age‐structured model a different functional dependence of ${\cal R}$ on $\epsilon_{RT}$, the efficacy of a reverse transcriptase inhibitor, than that found previously in nonage‐structured models, which has significant implications in predicting the effects of drug therapy. The influence of drug therapy on the within‐host viral fitness and the possible development of drug‐resistant strains are also discussed. Numerical simulations are performed to study the dynamical behavior of solutions of the models, and the effects of different combinations of antiretroviral drugs on viral dynamics are compared.