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There is a substantial interest in detailed models of viral infection and antiviral drug kinetics in order to optimize the treatment against viruses such as HIV. In this paper, we study within-viral dynamics under general intracellular distributed delays and periodic combination antiviral therapy. The basic reproduction number [Formula: see text] is established as a global threshold determining extinction versus persistence, and spectral methods are utilized for analytical and numerical computations of [Formula: see text]. We derive the critical maturation delay for virus and optimal phase difference between sinusoidally varying drug efficacies under various intracellular delays. Furthermore, numerical simulations are conducted utilizing realistic pharmacokinetics and gamma-distributed viral production delays for HIV. Our results demonstrate that the relative timing of the key viral replication cycle steps and periodic antiviral treatment schedule involving distinct drugs all can interact to critically affect the overall viral dynamics.

Floquet theory and perturbation techniques are used to analyze a classical within-host virus model with periodic drug treatment. Both single and multidrug treatment strategies are investigated. Specifically, the effects of both RT-inhibitors and P-inhibitors on the stability of the infection-free steady state are studied. It is found that when both classes of drugs have periodic drug efficacy functions, then shifting the phase of these functions can critically affect the stability of the infection-free steady state. A numerical study is conducted to illustrate the theoretical results and provide additional insights.