Constant drug dose in human immuno-deficiency virus-infected patients to induce long-term non-progressor status: bifurcation and controllability approach

Abstract

The authors propose a therapy consisting of a constant dosage of reverse transcription inhibitor and protease inhibitor to achieve long-term non-progressor (LTNP) status in human immuno-deficiency virus (HIV) patients. Based on the authors analyses of cytotoxic T lymphocyte precursor (CTLp) concentration at several equilibrium points and the bifurcation of these equilibrium points, they find that administration of drugs with an efficacy lower than a certain level induces a higher CTLp concentration. As a result, drug doses of moderate efficacy result in more patients with LTNP status than doses with high efficacy. In analyses of controllability, they show that a treatment of moderate efficacy is more efficient than one of very high efficacy in terms of controlling the immune system. Using simulations, they demonstrate that their proposed method results in LTNP status in HIV patients.

Fig. 1

HIV‐immune system

Fig. 2

Bifurcation diagram of the equilibrium points The solid and dotted lines represent stable and unstable equilibrium points, respectively

Fig. 3

Bifurcation diagrams of equilibrium points at various efficacies of RTI and PI The stable and physical equilibrium regions of points A, B, C and D are shaded a Point A b Point B c Point C d Point D

Fig. 4

Concentration of CTLp at stable equilibrium point C as the efficacies of RTI and PI are varied

Fig. 5

Simulation results for patients A and B treated with RTI monotherapy (η_RTI = 0.98 and η_PI = 0, and η_RTI = 0.85 and η_PI = 0) for 130 days, and then no treatment for the following 370 days a Patient A, η _RTI = 0.98 b Patient A, η _RTI = 0.85 c Patient B, η _RTI = 0.98 d Patient B, η _RTI = 0.85

Fig. 6

Controllabilities of patients A and B with the application of treatment (η_RTI = 0.98 and η_PI = 0, and η_RTI = 0.85 and η_PI = 0) for 130 days, and then no treatment for the following 370 days a Patient A with η_RTI = 0.98 and η _RTI = 0.85 b Patient B with η_RTI = 0.98 and η_RTI = 0.85

Fig. 7

Simulation results for patients A and B with treatment (η_RTI = 0.85 and η_PI = 0.85, and η_RTI = 0.85 and η_PI = 0.65) for 130 days, and then no treatment for the following 370 days a η _RTI = 0.85 and η _PI = 0.85 b η _RTI = 0.85 and η _PI = 0.65 c η _RTI = 0.85 and η _PI = 0.85 d η _RTI = 0.85 and η _PI = 0.65

Fig. 8

Controllabilities of patients A and B with the application of treatment (η_RTI = 0.85 and η_PI = 0.85, and η_RTI = 0.85 and η_PI = 0.65) for 130 days, and then no treatment for the following 370 days a Patient A with η _RTI = 0.85 and η _PI = 0.85, and η _RTI = 0.85 and η _PI = 0.65 b Patient B with η _RTI = 0.85 and η _PI = 0.85, and η _RTI = 0.85 and η _PI = 0.65

Fig. 9

Simulation results for patients A and B with RTI monotherapy (η_RTI = 0.85) for 130 days, and then no treatment for the following 370 days with the RTI drug‐resistant model (5) a Patient A, η _RTI = 0.85, β_m = 0.005 and m = 0.005 b Patient B, η _RTI = 0.85, β_m = 0.005 and m = 0.005 c Patient A, η _RTI = 0.85, β_m = 0.005 and m = 0.05 d Patient B, η _RTI = 0.85, β_m = 0.005 and m = 0.05 e Patient A, η _RTI = 0.85, β_m = 0.02 and m = 0.05 f Patient B, η _RTI = 0.85, β_m = 0.02 and m = 0.05