Models of SIV rebound after treatment interruption that involve multiple reactivation events

In order to assess the efficacy of novel HIV-1 treatments leading to a functional cure, the time to viral rebound is frequently used as a surrogate endpoint. The longer the time to viral rebound, the more efficacious the therapy. In support of such an approach, mathematical models serve as a connection between the size of the latent reservoir and the time to HIV-1 rebound after treatment interruption. The simplest of such models assumes that a single successful latent cell reactivation event leads to observable viremia after a period of exponential viral growth. Here we consider a generalization developed by Pinkevych et al. and Hill et al. of this simple model in which multiple reactivation events can occur, each contributing to the exponential growth of the viral load. We formalize and improve the previous derivation of the dynamics predicted by this model, and use the model to estimate relevant biological parameters from SIV rebound data. We confirm a previously described effect of very early antiretroviral therapy (ART) initiation on the rate of recrudescence and the viral load growth rate after treatment interruption. We find that every day ART initiation is delayed results in a 39% increase in the recrudescence rate (95% credible interval: [18%, 62%]), and a 11% decrease of the viral growth rate (95% credible interval: [4%, 20%]). We show that when viral rebound occurs early relative to the viral load doubling time, a model with multiple successful reactivation events fits the data better than a model with only a single successful reactivation event.Author summary: HIV-1 persists during suppressive antiretroviral therapy (ART) due to a reservoir of latently infected cells. When ART is stopped, HIV generally rebounds within a few weeks. However, there is a small fraction of patients that do not rebound over a period of months or years. A variety of treatments are being tested for their ability to reduce the size of the latent reservoir, to induce effective immune responses against the virus, or to prevent or prolong the time to viral rebound after ART interruption. These novel treatments are typically first tested in SIV infected macaques, and the efficacy of the treatment assessed by interrupting ART and measuring the time to viral rebound. Here, we develop and test a mathematical and statistical model that describes the process of viral rebound. The model can be used for statistical inference of the efficacy of newly developed treatments. Importantly, the model takes into account that multiple recrudescence events can precede rebound. We test the model using data from early treated SIV infected macaques.