A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques

The dynamics of HIV viral load following the initiation of antiretroviral therapy is not well-described by simple, single-phase exponential decay. Several mathematical models have been proposed to describe its more complex behavior, the most popular of which is two-phase exponential decay. The underlying assumption in two-phase exponential decay is that there are two classes of infected cells with different lifespans. However, with the exception of CD4⁺ T cells, there is not a consensus on all of the cell types that can become productively infected, and the fit of the two-phase exponential decay to observed data from SHIV.C.CH505 infected infant rhesus macaques was relatively poor. Therefore, we propose a new model for viral decay, inspired by the Gompertz model where the decay rate itself is a dynamic variable. We modify the Gompertz model to include a linear term that modulates the decay rate. We show that this simple model performs as well as the two-phase exponential decay model on HIV and SIV data sets, and outperforms it for the infant rhesus macaque SHIV.C.CH505 infection data set. We also show that by using a stochastic differential equation formulation, the modified Gompertz model can be interpreted as being driven by a population of infected cells with a continuous distribution of cell lifespans, and estimate this distribution for the SHIV.C.CH505-infected infant rhesus macaques. Thus, we find that the dynamics of viral decay in this model of infant HIV infection and treatment may be explained by a distribution of cell lifespans, rather than two distinct cell types.