A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models. Author Summary: While on successful drug treatment, routine testing does not usually detect virus in the blood of an HIV patient. However, more sensitive techniques can detect extremely low levels of virus. Occasionally, routine blood tests show “viral blips”: short periods of elevated, detectable viral load. We explore the hypothesis that residual low-level viral load can be largely explained by re-activation of cells that were infected before the initiation of treatment, and that viral blips can be viewed as occasional statistical events. To do this, we propose a mathematical model of latently-infected cells, activated cells, and virus. The model captures random fluctuations of the system as well as the mean behaviour. We estimate the time it takes for all the latently-infected cells to be eradicated. Eradication of these cells is considered a major hurdle in eliminating infection. We predict a wide range of eradication times, highlighting the importance of studying latently-infected cells. We also estimate the frequency and duration of viral blips, and find qualitative agreement with clinical studies. By refining our models, we hope to find guidelines that can be used in practise to distinguish between clinically insignificant statistical blips, and instances of drug failure.