A mathematical model describing the antiretroviral therapy of Enfuvirtide on HIV-1 patients is developed. The effect of Enfuvirtide （formerly called T-20） by impulsive differential equations is modeled by two different drug elimination kinetics, the first-order elimination kinetics and the Michaelis-Menten elimination kinetics. The model is a non-autonomous system of differential equations. For a time-dependent system, the disease-free equilibrium is mainly studied. Its stability, when the therapy is taken with perfect adherence, is obtained. To ensure the disease-free equilibrium remains stable, the analytical thresholds for dosage and dosing intervals are determined. The effects of super- vised treatment interruption are also explored. It is shown that the supervised treatment interruption can be worse than no therapy at all.
Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infected- susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert （BA） scale-free networks are in good agreement with the analytical results.
