Mathematical Modelling of Enfuvirtide and Protease Inhibitors as Combination Therapy for HIV

Abstract Enfuvirtide (formerly T20) is an injectable fusion inhibitor that has established effective antiretroviral activity and excellent tolerability in extensively pretreated patients. This fusion inhibitor does not affect the metabolism of other co-administrated drugs for metabolic drug interactions involving enfuvirtide. Few mathematical models have considered co-administration of antiretroviral drugs. We develop a mathematical model to study the effect of enfuvirtide upon this process in combination with protease inhibitors (PIs) using impulsive differential equations. We divide the T cells into several classes to describe the drug activity. Analytical results show that a combination of enfuvirtide and PIs gives a better outcome than single drug activity; furthermore, use of enfuvirtide clearly outranks PIs if only one class of drugs were to be used. We determine the threshold value for the dosage and dosing intervals to ensure the stability of the disease-free state and illustrate our results with numerical simulations. We recommend that use of enfuvirtide, in combination with PIs, be expanded beyond salvage therapy.