Search

This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an ordinary differential equation is schemed to consist of three components such as untainted CD4+ T-cells, tainted CD4+ T-cells (HIV) and CTL. A discrete time delay is ushered to the formulated model in order to account for vital components, such as intracellular delay and HIV latency which were missing in previous works but have been advocated for future research. It was divested that when the reproductive number was less than unity, the disease free equilibrium of the model was asymptotically stable. Hence the adopted model with or without the delay component articulates less production of virions as per the decline rate. Therefore CD4+ T-cells in the blood remains constant at δ 1 / δ 3 , hence declining the virions level in the blood. As per the adopted model, the best STI practice is intimated for compliance. [ABSTRACT FROM AUTHOR]

It is widely accepted that the primary immune system contains a subpopulation of cells, known as regulatory T cells whose function is to regulate the immune response. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and turn into immune promoting cells. In this paper, we develop mathematical models to investigate the effects of regulatory T cell switching on the immune response. Depending on environmental conditions, regulatory T cells may transition, becoming effector T cells that are immunostimulatory rather than immunoregulatory. We consider this mechanism both in the context of a simple, ordinary differential equation (ODE) model and in the context of a more biologically detailed, delay differential equation (DDE) model of the primary immune response. It is shown that models that incorporate such a mechanism express the usual characteristics of an immune response (expansion, contraction, and memory phases), while being more robust with respect to T cell precursor frequencies. We characterize the affects of regulatory T cell switching on the peak magnitude of the immune response and identify a biologically testable range for the switching parameter. We conclude that regulatory T cell switching may play a key role in controlling immune contraction. [ABSTRACT FROM AUTHOR]

The currently accepted paradigm for the primary T cell response is that effector T cells commit to autonomous developmental programs. This concept is based on several experiments that have demonstrated that the dynamics of a T cell response is largely determined shortly after antigen exposure and that T cell dynamics do not depend on the level and duration of antigen stimulation. Another experimental study has also shown that T cell responses are robust to variations in antigen-specific precursor frequency. Various mathematical models have corroborated the first result that programmed T cell responses are insensitive to the level of antigen stimulation. However, this paper proposes that programmed responses do not entirely explain the robustness of T cell dynamics to variations in precursor frequency. This work studies the hypothesis that the dynamics of a T cell response may also be governed by a feedback loop involving adaptive regulatory cells rather than by intrinsic developmental programs. We formulate two mathematical models based on T cell developmental programs. In one model, effector cells undergo a fixed number of divisions before dying. In the second model, effector cells live for a fixed time during which they may divide. The study of these models suggests that developmental programs are not sufficiently robust as they produce an immune response that directly scales with precursor frequencies. Consequently, we derive a third model based on the principle that adaptive regulatory T cells develop in the course of an immune response and suppress effector cells. Our simulations show that this feedback mechanism responds robustly over a range of at least four orders of magnitude of precursor frequencies. We conclude that the proliferation program paradigm does not entirely capture the observed robustness of T cell responses to variations in precursor frequency. We propose an alternative mechanism by which the primary T cell response is governed by an emergent group dynamic and not by individual T cell programs. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected cells are incorporated into the models. The models consider multiple discrete or distributed delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The existence and global stability of the steady states are determined by the basic reproduction number. The global stability analysis of the steady states is performed using Lyapunov method. We solve the system of delay differential equations numerically to support the theoretical results. [ABSTRACT FROM AUTHOR]