Submit to Mathematical BiosciencesRelationships between Antiviral TreatmentE ects and

Recently potent combination antiviral therapies, which consist of reverse transcriptase inhibitor (RTI) drugs and protease inhibitor (PI) drugs, can rapidly suppress HIV below the limit of detection. Two phases of plasma viral decay after initiation of treatment were observed from clinical studies. Some researchers have suggested that the viral decay rates may reeect the potency (eecacy) of antiviral therapies. In this paper we model the eeect 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 diierent types of drugs. Through rigorous mathematical derivation, we show that the two viral decay rates are monotone functions of the treatment eeects of these antiviral therapies. Approximation formulas for the relationships between viral decay rates and treatment eeects are constructed. Computer simulations show that the approximation formulas approximate the true values very well. These formulas may be used to study what factors really aaect the viral decay rates. The results in this paper provide a theoretical justiication for using both viral decay rates for evaluation of treatment eecacy of antiviral therapies.