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

Abstract

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.

Keywords: HIV viral decay; Infected cell lifespan; Modified Gompertz model; SHIV; Stochastic modeling; Uncertainty quantification.

Figure 1:

Initial dynamics of SHIV.C.CH505 viral load in infant rhesus macaques. Treatment is initiated at the vertical line, and viral load below the LOD (horizontal line) indicates that that measurement was below the LOD (60 copies/mL). The first measurement below the LOD is taken as the LOD/2 (30 copies/mL) for plotting purposes. Figure adapted from [16, 17].

Figure 2:

Example trajectories for one subject for each virus using the MG and TSD models. Note that the MG model captures the decay behavior of SHIV in rhesus macaques more effectively than the TSD model.

Figure 3:

Distribution of the normalized viral load produced by V₂(t), the productively infected cells present at the time of ART initiation for each infant rhesus macaque starting from the time of ART initiation till 12 weeks post ART initiation.