Modeling the Effects of Drugs of Abuse on HIV Infections with Two Viral Species

Abstract

Injection drug use is one of the greatest risk factors associated with contracting human immunodeficiency virus (HIV), and drug abusers infected with HIV suffer from a higher viral load and rapid pathogenesis. Replication of HIV may result in a large number of mutant viruses that can escape recognition of the hosts immune response. Experimental results have shown that the presence of morphine can decrease the viral mutation rate and cellular immune responses. This thesis presents a mathematical model to determine if the decrease in mutation and cellular immune response in the presence of morphine can account for the increased viral load. Two viral species are considered: a wild-type and a mutant. The morphine-altered mutation rate and cellular immune response is shown to allow the wild-type virus to out compete the mutant, resulting in a higher set point viral load. Calculation of the basic reproduction number for each species shows that the dominant species is determined by a threshold morphine concentration, with the mutant dominating below the threshold and the wild-type dominating above. Stability analysis is performed on the infection free and mutant only equilibria of the system and numerical simulations reflect the increased viral load associated with morphine use.