Table 1.
An overview of the parameters and variables.
Fig 1.
Simulations of the multiple-reactivation model.
(A) Graphical representation of Eq 1. The gray lines indicate the exponential growth curves of individual clones that originated from a single successful reactivation from the latent reservoir. The blue curve represents the total VL, i.e. the sum of the gray lines. (B) Comparison between the expectation of the process Vt (in black) and realizations sampled from this process (in blue). The mean ± standard deviation (sd) of Vt is shown as a gray band. The dashed thick curve corresponds to the approximation with t0 = 1/λd. Parameters: g = 0.5 d−1, λ = 1.0 d−1, and v0 = 0.1 copies mL−1
Fig 2.
Comparison between the approximation for the time-to-rebound distribution and simulated rebound times.
The simulated empirical distributions are shown in color, and our approximation is shown in black. (A) The probability density function (PDF; defined by Eq 6). (B) The survival function (i.e. the fraction of subjects S(t) that do not have a detectable VL at time t). For the top, middle, and bottom panels different values of λ are used (λ = 5 d−1, 1 d−1, and 0.2 d−1 respectively). Notice the different time scale on the horizontal axes. For the remaining parameters, we used the values: g = 0.5 d−1, v0 = 0.1 copies mL−1, LoD ℓ = 50 copies mL−1.
Fig 3.
Representative examples of the fits of the mixed-effects model to the VL rebound time series.
(A) The top panels show the VL data (black dots connected by black lines, with red dots for left-censored observations; the grey dots are ignored) taken from macaques where ART was started at different days post infection (DPI), and the model prediction (blue lines: posterior mean; dark blue band: 50% credible interval (CrI), light blue band: 50% posterior predictive interval). The estimated time-to-rebound (τ) is given by the vertical black line (gray band: 50% CrI). (B) The bottom panels show posterior predictive distributions of the time-to-rebound. The green distributions (c) are conditioned on the estimated time of the initial recrudescence event, the purple distributions (u) are unconditional. Model fits and posterior predictive distributions for all 25 macaques are shown in S1 Fig.
Fig 4.
Estimates of recrudescence and growth rates from the SIV rebound data and the percentage of the variance of the time-to-rebound.
(A) Point estimates (posterior modes; red) and 50% CrIs (black) of λ for each macaque as a function of the time ART was initiated. (B) Estimates of g. The cyan markers denote estimates of the growth rate for acute infections of 13 of the 25 macaques. These acute VL growth rates cluster around 2 d−1. (C) Proportion of the total variance due to secondary reactivation events. The heat map shows Var[τ1]/Var[τ0] ⋅ 100%, where τi ≔ inf{t : Vt ≥ ℓ, V0 = i ⋅ v0} is the rebound time (i = 0) or the time between the first successful reactivation and rebound (i = 1). Additional parameters are v0 = 0.1 copies mL−1 and ℓ = 50 copies mL−1. The markers indicate the estimates from macaque SIV rebound experiments in which the macaques were treated, starting tART days after infection, with tART equal to 1 day (●), 2 days (+), 3 days (▲), 7 days (★), 10 days (×), or 14 days (♦).
Table 2.
Prior distributions of the Bayesian mixed-effects model.
Fig 5.
Sensitivity of the multiple-reactivation model to misspecification.
(A) A misspecified initial viral load v0 can lead to a biased estimate of the recrudescence rate λ. Rebound data sets (n = 200) were simulated by sampling from the viral load process (Eq 1) using different values of the recrudescence rate λ (horizontal dashed lines), and different assumed values of v0 (horizontal axis). The ground truth value of v0 equals 0.1 copies mL−1 (vertical dashed lines). Shown are the 95% CrIs of the estimate of λ (black bars) and the posterior medians (red). (B) Intra-host variation in the exponential growth rate of the VL can lead to a biased estimate of the recrudescence rate λ. Data sets of rebound time series were now simulated from a viral load process with within-host variability of the growth rate Gi (Eq S12 in S1 Text, S5 Fig), using different values of the recrudescence rate and the standard deviation of the viral growth rate (σG, horizontal axis), ranging from 0% to 20% of the most likely growth rate g = 0.5.