Fig 1.
Schematic of the utilized viral dynamics model.
V, T1, T2 denote virus, early infected T-cells and productively infected T-cells respectively. Each reaction is denoted by its reaction propensity a1 − a6. Briefly, a free virus can either be cleared (with reaction propensity a1), or infect a susceptible T cell with rate a4 to yield an early infected cell T1. These cells denote a state where the virus has penetrated the host cell, but has not yet integrated its proviral DNA into the host cell’s genome, thus not yet producing viral offspring. Early infected cells T1 can either be cleared with rate a2 or the proviral DNA irreversibly becomes integrated into the host cells DNA with rate a5 to yield a productively infected T-cell T2. T2 cells start producing infectious progeny virus with rate a6, or they may get cleared by the immune system with rate a3.
Table 1.
Parameters for viral dynamics model.
Table 2.
Prophylactic efficacy in case of multiple viral challenges.
Fig 2.
Model simulations in the absence of drugs.
A. Probability density function of the extinction event in absence of drug, for one initial virus and 10 initial viruses respectively. B. Relation between the expected inoculum size and the corresponding average infection probability per exposure, in the absence of drugs. The distribution of inoculum sizes is described in [24]. Average infection probabilities for homosexual vs. heterosexual transmission [16], are marked by dots.
Fig 3.
Prophylactic efficacy for 3-days once daily short-course oral 50mg DTG.
The extinction probabilities were computed by PGS, for a representative individual with pharmacokinetic parameters ka = 2.24h−1, Vp/Fbio = 0.73 L, Q/Fbio = 0.0082 L/h, CL/Fbio = 0.85 L/h and Vc/Fbio = 17.7 L. Observation began from two days before the first dose (the drug-doses are marked by arrows), until the 10th day after the first dose of DTG. The X-axis denotes the timing of viral exposure relative to the first dose, i.e. negative values represent a viral exposure before the first dose of DTG (post-exposure prophylaxis, PEP), whereas positive values represent pre-exposure prophylaxis (PrEP) scenarios. A. DTG plasma concentration (dashed brown line) and the extinction probability profiles, with regards to one virus , one T1-cell
and one T2-cell
are shown by solid red, green and blue lines. B. DTG plasma concentration (dashed brown line) and the corresponding prophylactic efficacies for one virus
, one T1-cell
and one T2-cell
are shown by solid red, green and blue lines.
Fig 4.
Prophylactic efficacy for PrEP and PEP computed by EXTRANDE and the new methods.
2 mg (lines below) and 50 mg (lines above) DTG were ingested for three days, respectively. The extinction probabilities were computed by EXTRANDE and PGS, for a representative individual with pharmacokinetic parameters ka = 2.24h−1, Vp/Fbio = 0.73 L, Q/Fbio = 0.0082 L/h, CL/Fbio = 0.85 L/h and Vc/Fbio = 17.7 L. The prophylactic efficacy was computed using Eq (1) for initial state Y0 = [1, 0, 0]T (exposure to a single virus particle). The X-axis represents the timing of the first DTG dose relative to the virus challenge, which is marked by the arrow. EXTRANDE was run 10 000 times for each condition. The error bars denote the 95% confidence bounds for the ensemble estimate, computed using the Greenwood’s formula [42].
Fig 5.
Profiles of prophylactic efficacy for different inoculum sizes.
The experimental setup was chosen identical to Fig 3. To calculate the prophylactic efficacy profiles, an exponential scaling is applied to the solutions of the PGS (Eq (3)). The solutions are plugged into Eq (1).
Fig 6.
Long-term prophylactic profile with different levels of adherence.
N = 1000 virtual patients were sampled from the pharmacokinetic parameter distributions defined in Table 2 of [11]. 50 mg dose of DTG / day was ingested in this six-month-long regimen with adherence level of 0.75, 0.5, 0.33 and 0.25. The red line depicts the median predicted prophylactic efficacy, whereas the dark- and light grey areas present the quartile range and the 2.5%–97.5% range respectively. The prophylactic efficacy was computed for Y0 = [1, 0, 0]T.
Fig 7.
Cumulative probability and probability density function of extinction event.
N = 1000 virtual patients were sampled from the pharmacokinetic parameter distributions defined in Table 2 of [11]. 50 mg dose of DTG / day was ingested for three days, first dose was taken at t0 = 0, coinciding with viral exposure. A. Cumulative extinction probability for one initial virus. B. Probability density function of extinction for one initial virus. C. Cumulative extinction probability for 20 initial viruses. D. Probability density function of extinction for 20 initial viruses. The red and green lines depict the respective median values, whereas the dark- and light grey areas present the quartile range and 2.5%–97.5% confidence range, taking inter-individual pharmacokinetic differences into account.