Piecewise HIV virus dynamic model with CD4+ T cell count-guided therapy: I

Abstract

The strategies of structured treatment interruptions (STIs) of antiretroviral therapies have been proposed for clinical management of HIV infected patients, but clinical studies on STIs failed to achieve a consistent conclusion for this strategy. To evaluate the STI strategies, in particular, CD4+ T cell count-guided STIs, and explain these controversial conclusions from different clinical studies, in this paper we propose to use piecewise HIV virus dynamic models to quantitatively explore the STI strategies and investigate their dynamic behaviors. Our analysis results indicate that CD4+ T cell counts can be maintained above a safe level using the STI with a single threshold or a threshold window. Numerical simulations show that the CD4+ T cell counts either fluctuate or approach a stable level for a patient, depending on the prescribed upper or lower threshold values. In particular, the CD4+ T cell counts can be stabilized at a desired level if the threshold policy control is applied. The durations of drug-on and drug-off are very sensitive to the prescribed upper or lower threshold levels, which possibly explains why the on-off strategy with fixed schedule or a STI strategy with frequent switches is associated with the high rate of failure. Our findings suggest that it is critical to carefully choose the thresholds of CD4+ T cell count and individualize the STIs for each individual patient based on initial CD4+ T cell counts.

Modelling the regulatory system for diabetes mellitus with a threshold window

“…is called a threshold window of treatment decision [18]. In this case, we can extend model (1.1) by replacing the impulsive injection of insulin by lower and upper thresholds, which can be written as the following two states.…”

“…In this case the models (1.2) and (1.3) can be rewritten as a Filippov system, a model which has been applied widely in many fields of science and engineering. Furthermore, the theory of Filippov systems is being recognized as not only richer than the corresponding theory of continuous systems, but also as representing a more natural framework for the mathematical modelling of real-world phenomena [18][19][20][21][22][23][24][25][26][27][28][29].…”

Modelling pulsed immunotherapy of tumour–immune interaction

“…Mathematical models of tumour-immune dynamics not only help understanding of the involvement of immune cells and cancer cells and how they interact, but can also provide a useful tool to predict the results of immunotherapy and indicate improved treatment strategies. Many researchers have used ordinary differential equations (ODEs) to model populations of immune cells and tumour cells [28,14,5,20,19,8,21,35,38]. In these studies, the effects of the immune response and immunotherapy treatment on tumour growth and eradication have been studied in detail.…”

Hybrid on-Off Controls for an Hiv Model Based on a Linear Control Problem

“…These treatment strategies have received increasing attention in recent years, but their efficacy and safety have been controversial. Many studies have considered specific STI strategies involving different interruption intervals and decision rules for stopping and initiating therapy [17,20,23,28]. Tang et al [28] use a piecewise model of HIV dynamics to explore STI strategies guided by CD4+ T cell counts.…”

“…Many studies have considered specific STI strategies involving different interruption intervals and decision rules for stopping and initiating therapy [17,20,23,28]. Tang et al [28] use a piecewise model of HIV dynamics to explore STI strategies guided by CD4+ T cell counts. Palacios et al [20] examine the viral, immune, and clinical impacts of a STI program in three cycles of 12 weeks on and 4 weeks off on children infected with HIV.…”