Relationships between antiviral treatment effects and biphasic viral decay rates in modeling HIV dynamics

Recently, potent combination antiviral therapies consisting of reverse transcriptase inhibitor (RTI) drugs and protease inhibitor (PI) drugs, have been developed which can rapidly suppress HIV below the limit of detection. Two phases of plasma viral decay after initiation of treatment have been observed in clinical studies. Some researchers have suggested that the viral decay rates may reflect the potency (efficacy) of antiviral therapies. In this paper we model the effect of RTI drugs and PI drugs as inhibition rates of cell infection and infectious virus production, respectively, based on the biological mechanisms of these two different types of drugs. Through rigorous mathematical derivation, we show that the two viral decay rates are monotone functions of the treatment effects of these antiviral therapies. We derive approximation formulas for the relationships between viral decay rates and treatment effects. Computer simulations show that the approximation formulas approximate the true values very well. These formulas may be used to study what factors really affect the viral decay rates. The results in this paper provide a theoretical justification for using both viral decay rates for evaluation of the treatment efficacy of antiviral therapies.