Table 1.
Model parameters and their corresponding prior distributions.
Figure 1.
Survival curves for Wolb− (A) and Wolb+ (B) groups of D. melanogaster.
Dots represent experimental data. Dark blue curves show the model fit to the survival of control flies. Shaded areas represents 95% CI (credible intervals).
Figure 2.
Dose-response curves and susceptibility distributions inferred from mortality measurements 30 and 50 days post-challenge.
Dose-responses models adopted here are the standard formulations (1–3). A,D, Curves represent the fitted dose-response model to mortality on selected day post-challenge (dots), for Wolb− (black) and Wolb+ (blue). Shaded areas represent the 95% CI. B,E, Distribution of susceptibility to infection in Wolb+. The posterior median distribution is the curve and the shaded area is the 95% CI. C,F, Posterior samples of the Beta-distribution shape parameters describing Wolb+ susceptibility in blue. Red dot mark the median of the respective distributions. The homogeneous model was adopted for Wolb−.
Figure 3.
Schematic illustration of the proposed experimental design and inference procedure.
Table 2.
Estimated parameters by applying dose-response models to selected day mortality.
Table 3.
Estimated parameters governing time to death from causes other than DCV infection.
Figure 4.
Fit of time-dependent dose-response model to survival curves.
Black and blue dots are the observed proportions surviving over time for Wolb− and Wolb+ groups, respectively. The curve is the fitted mean posterior survival over time and the shaded area is the 95% CI. Fifty flies per group were pricked with: A, buffer solution (shown for comparison but not used on this analysis); and B, ; C,
; D,
; E,
; F,
; G,
; H,
TCID50 DCV.
Table 4.
Parameters governing estimated number infected per dose of DCV challenge and time to death from infection using time-dependent dose-response models described in Methods.
Figure 5.
Dose-response curves and susceptibility distributions inferred from survival curves.
A, Curves represent the estimated dose-response relationships from fitting the model described in Methods to survival over time, for Wolb− (black) and Wolb+ (blue). Shaded areas represent the 95% CI. B, Distribution of susceptibility to infection in Wolb+. The posterior median distribution is the curve and the shaded area is the 95% CI. C, Posterior samples of the Beta-distribution shape parameters describing Wolb+ susceptibility in blue. Red dot marks the median of distribution.
Figure 6.
Selection of optimal days to collect mortality measurements for traditional dose-response models.
The red line traces a score for how well mortality at any given day represents infection estimated by the time-dependent model (refer to axis on the right). The score is given by , where Δ denotes the number of doses in the dataset,
(
) represents the proportion infected in the Wolb− (Wolb+) group subject to DCV dose j, and
(
) the observed mortality proportion over time in the Wolb− (Wolb+) group subject to DCV dose j. Gray vertical lines mark the optimal day to measure mortality for dose-response models (day 30, dash-dotted line) and the limits of the acceptable range (days 17 and 46). Dashed lines represent the Gamma distributions that describe old-age mortality, and black (blue) full curves refer to the Gamma distributions that describe infection-induced mortality in Wolb− (Wolb+) (refer to axis on the left). Curves are the mean posterior probabilities and shaded areas represent the 95% CI.