Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models

Abstract

We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with consideration of pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand the effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics.

Fig. 1

Simulation of typical solutions of drug on-off state systems (3.4) and (3.5) with C^TH = 700ul⁻¹, C_TH = 200ul⁻¹. (A) Time trajectory of total CD4+ T cell population; (B) Time trajectory of health CD4+ T cell population (dashed line) and infected CD4+ T cell population (solid line); (C) Durations of drug on and drug off for each drug on-off switch; (D) Phase plane plot of health CD4+ T cell and infected CD4+ T cell populations.

Fig. 2

Numerical simulations of solutions of drug on-off state systems (3.4) and (3.5) with different low and upper threshold values. Case 2: (A–B) Blue cure for the solution with C^TH = 1300ul⁻¹, C_TH = 350ul⁻¹, pink curve for the solution with C^TH = 1400ul⁻¹, C_TH = 350ul⁻¹; Case 3: (C–D) Blue cure for the solution with C^TH = 1300ul⁻¹, C_TH = 150ul⁻¹, pink curve for the solution with C^TH = 1400ul⁻¹, C_TH = 350ul⁻¹, and green curve for the solution with C^TH = 1300ul⁻¹, C_TH = 100ul⁻¹; Case 4: (E–F) Blue cure for the solution with C^TH = 700ul⁻¹, C_TH = 150ul⁻¹, and green curve for the solution with C^TH = 700ul⁻¹, C_TH = 100ul⁻¹.