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.
Table of Contents
Introduction -- Background and literature review -- Mathematical models -- Model analysis -- Simulations -- Discussion and future work
Degree
M.S.