Experimental and computational analyses reveal that environmental restrictions shape HIV-1 spread in 3D cultures

Here, using an integrative experimental and computational approach, Imle et al. show how cell motility and density affect HIV cell-associated transmission in a three-dimensional tissue-like culture system of CD4+ T cells and collagen, and how different collagen matrices restrict infection by cell-free virions

Mathematical modelling of internal HIV dynamics

We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper

Modeling long-term longitudinal HIV dynamics with application to an AIDS clinical study

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiretroviral (ARV) therapies in AIDS clinical trials. This marker can be used to assess the ARV potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. HIV dynamic studies have significantly contributed to the understanding of HIV pathogenesis and ARV treatment strategies. However, the models of these studies are used to quantify short-term HIV dynamics ($<$ 1 month), and are not applicable to describe long-term virological response to ARV treatment due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. Long-term therapy with ARV agents in HIV-infected patients often results in failure to suppress the viral load. Pharmacokinetics (PK), drug resistance and imperfect adherence to prescribed antiviral drugs are important factors explaining the resurgence of virus. To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy. The models directly incorporate drug concentration, adherence and drug susceptibility into a function of treatment efficacy and, hence, fully integrate virologic, PK, drug adherence and resistance from an AIDS clinical trial into the analysis. A Bayesian nonlinear mixed-effects modeling approach in conjunction with the rescaled version of dynamic differential equations is investigated to estimate dynamic parameters and make inference. In addition, the correlations of baseline factors with estimated dynamic parameters are explored and some biologically meaningful correlation results are presented. Further, the estimated dynamic parameters in patients with virologic success were compared to those in patients with virologic failure and significantly important findings were summarized. These results suggest that viral dynamic parameters may play an important role in understanding HIV pathogenesis, designing new treatment strategies for long-term care of AIDS patients.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS192 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Global dynamics of cell mediated immunity in viral infection models with distributed delays

In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection $R_{0}$ and for CTL response $R_{1}$ such that $R_{1}<R_{0}$. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if $R_{0}\leq1$, an infected equilibrium without immune response is globally asymptotically stable if $R_{1}\leq1<R_{0}$ and an infected equilibrium with immune response is globally asymptotically stable if $R_{1}>1$. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if $R_{1}>1$.Comment: 16 pages, accepted by Journal of Mathematical Analysis and Application

Hybrid spreading mechanisms and T cell activation shape the dynamics of HIV-1 infection

HIV-1 can disseminate between susceptible cells by two mechanisms: cell-free infection following fluid-phase diffusion of virions and by highly-efficient direct cell-to-cell transmission at immune cell contacts. The contribution of this hybrid spreading mechanism, which is also a characteristic of some important computer worm outbreaks, to HIV-1 progression in vivo remains unknown. Here we present a new mathematical model that explicitly incorporates the ability of HIV-1 to use hybrid spreading mechanisms and evaluate the consequences for HIV-1 pathogenenesis. The model captures the major phases of the HIV-1 infection course of a cohort of treatment naive patients and also accurately predicts the results of the Short Pulse Anti-Retroviral Therapy at Seroconversion (SPARTAC) trial. Using this model we find that hybrid spreading is critical to seed and establish infection, and that cell-to-cell spread and increased CD4+ T cell activation are important for HIV-1 progression. Notably, the model predicts that cell-to-cell spread becomes increasingly effective as infection progresses and thus may present a considerable treatment barrier. Deriving predictions of various treatments' influence on HIV-1 progression highlights the importance of earlier intervention and suggests that treatments effectively targeting cell-to-cell HIV-1 spread can delay progression to AIDS. This study suggests that hybrid spreading is a fundamental feature of HIV infection, and provides the mathematical framework incorporating this feature with which to evaluate future therapeutic strategies