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Emergence of HIV-1 drug resistance during antiretroviral treatment.

  • Libin Rong
  • Zhilan Feng
  • Alan S Perelson
Bull. Math. Biol. 2007; 69 (6): 2027-2060
Abstract
Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4(+) T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. In this paper, we use a simple mathematical model to study the mechanism of the emergence of drug resistance during therapy. The model includes two viral strains: wild-type and drug-resistant. The wild-type strain can mutate and become drug-resistant during the process of reverse transcription. The reproductive ratio [Symbol: see text](0) for each strain is obtained and stability results of the steady states are given. We show that drug-resistant virus is more likely to arise when, in the presence of antiretroviral treatment, the reproductive ratios of both strains are close. The wild-type virus can be suppressed even when the reproductive ratio of this strain is greater than 1. A pharmacokinetic model including blood and cell compartments is employed to estimate the drug efficacies of both the wild-type and the drug-resistant strains. We investigate how time-varying drug efficacy (due to the drug dosing schedule and suboptimal adherence) affects the antiviral response, particularly the emergence of drug resistance. Simulation results suggest that perfect adherence to regimen protocol will well suppress the viral load of the wild-type strain while drug-resistant variants develop slowly. However, intermediate levels of adherence may result in the dominance of the drug-resistant virus several months after the initiation of therapy. When more doses of drugs are missed, the failure of suppression of the wild-type virus will be observed, accompanied by a relatively slow increase in the drug-resistant viral load.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 1.0
Id Name Initial quantity Compartment Fixed
T 1000000.0 default
Trr 0.0 default
Ts 0.0 default
Vr 0.0 default
Vs 0.000001 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 ∅ = T

lambda
v10 ∅ = Vr

delta*Nr*Trr
v11 Vr = ∅

c*Vr
v2 T = ∅

d*T
v3 T = Ts

ks*T*Vs
v4 T = Trr

kr*T*Vr
v5 Ts = Trr

ks*mu*T*Vs
v6 Ts = ∅

delta*Ts
v7 ∅ = Vs

delta*Ns*Ts
v8 Vs = ∅

c*Vs
v9 Trr = ∅

delta*Trr

Global parameters

Id Value
Nr 2000.0
Ns 3000.0
SumVsr 0.0
TmicroL 0.0
c 23.0
d 0.01
delta 1.0
kr 0.00000002
ks 0.000000024
lambda 10000.0
mu 0.00003

Local parameters

Id Value Reaction

Assignment rules

Definition
TmicroL = T/1000.0
SumVsr = Vr + Vs

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments