Figure 3
Genomic biomarker dynamics over time. (A) GSI dynamics of 194 longitudinal and 252 single time point incident specimens along with the beta distribution model fit. Forty three subjects in Table S3 were serially followed from Fiebig stage I-V (circles with black solid lines) and 252 single time point incident specimens were collected at Fiebig stage I-V (circles), as presented in Table S2. The GSI varies between individuals, but in the majority of cases is close to one for new infections and drops towards zero over time. The average biomarker dynamics were modeled by logistic link function and the variation between individuals was modeled by the beta distribution as in Eqs (2–3). The best fit of the model for the average GSI dynamics (solid red curve) and its 95% confidence intervals (CI) (dashed red curves) are presented. The maximum likelihood estimates of the model parameters are M = 495.8 [415.1–575.6], S = 176.8 [124.3–239.7], V = 0.96 [0.86–1.12] and c = 0.95 [0.94–0.96]. Each parameter’s 95% CI was obtained by resampling incident specimens’ biomarker data 10,000 times. The average biomarker’s 95% CI (dashed red curves) is the 95% CI of 10,000 fitted biomarker dynamics curves for each time point. (B) The density plot of the estimated GSI distribution over time. The GSI probability density function peaked (red) close to 1 during early infection and at 0 around two years post infection. However, around one year the density function peaked in both high and low GSI regions. These profiles collectively reflect the sequence data trends at the population level. The model estimate of the probability of being recent, defined in Eq. (4), is presented by a blue line and the proportion of subjects with GSI greater than the threshold in each one year bin is presented by black circles. The 95% CIs are presented by blue dashed curves and black lines, respectively. The beta distribution model was consistent with the one year bin evaluation. (D) The MDRI estimated by the model (blue), 420 [361–467] days, was compared with that from the bin-method (black), 378 [304–460] days.
