Strategies to overcome DAA failure.

<p>The best-fit (solid line) and 95% CIs (dashed lines) of Eq (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.e185" target="_blank">18</a>) (Methods) to data (symbols) of SVR rates in treatment-naïve versus treatment-experienced patients <b>(A)</b> without liver cirrhosis and <b>(B)</b> with liver cirrhosis, treated with DAAs with (filled) or without (open) PR. The list of clinical trials from which data has been collated is presented in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s005" target="_blank">S2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s006" target="_blank">S3</a> Tables, respectively. The fits yielded and 33±14% in the two subpopulations, respectively, and using which, we estimated the corresponding <i>ϕ</i>_<i>null</i> = 0.07 and 0.12. <b>(C)</b> Regions in the phase diagram (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.g002" target="_blank">Fig 2A</a>) where addition of PR to the DAA would elicit cure in otherwise failing patients with (orange) or without (orange and red) liver cirrhosis. SVR would be elicited in the dark blue region of the phase diagram. <b>(D)</b> The yellow box in (C) zoomed to demonstrate the influence of adding PR to an individual with a cirrhotic (small white arrow) or a non-cirrhotic (large white arrow) liver, adding a new DAA or increasing DAA dosage (yellow arrow), or adding PR and a new DAA (green arrow). <b>(E-H)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for the different conditions marked in (D). <b>(I)</b> The duration of treatment in weeks required to achieve SVR for a range of values of IFN-responsiveness, , and the relative fitness of the RAV, <i>γ</i>_<i>t</i>. <b>(J)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for the different conditions marked in (I), corresponding to daclatasvir treatment (Methods). <i>Inset</i>: The percentage of patients predicted to achieve SVR as a function of the duration of treatment with daclatasvir. The percentages corresponding to the conditions marked in (I) are indicated. Thus, 19.2%, 46% and 60.6% SVR rates are expected in 8, 10, and 12 weeks of treatment, respectively.</p

Response to PR+DAA treatment.

<p><b>(A)</b> Phase diagram indicating regimes of IFN-responsiveness pre- and during treatment, and , leading to SVR (dark blue) and treatment failure due to virological breakthrough by the RAV (light blue) for a fixed relative fitness of the RAV during treatment, <i>γ</i>_<i>t</i>. <b>(B)</b> Dynamics of wild-type (solid) and RAV (dashed) viral populations following treatment initiation for parameter combinations numbered in (A). <b>(C)</b> Phase diagram on a plot for fixed . <b>(D)</b> Dynamics for the points numbered in (C). In (A)-(D), the DAA efficacy against the wild-type, . Also, <i>γ</i> = 0.4. <b>(E)-(H)</b> Corresponding predictions with . In (E) and (G), treatment failure occurred due to the RAV (light blue), wild-type (green), or both (brown). Here, <i>γ</i> = 0.2. Other parameter values employed are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s008" target="_blank">S5 Table</a>. Phase diagrams for other values of are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s003" target="_blank">S3 Fig</a>.</p

Pre-treatment frequencies and populations of virions.

<p>Model predictions (lines) and analytical approximations (symbols) (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s009" target="_blank">S1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s011" target="_blank">S3 Texts</a>) of the mutant frequencies (left) and viral populations (right) in the pre-treatment steady state as a function of the level of IFN-responsiveness, , for different combinations of the mutation rate, <i>μ</i>, and the relative fitness of the RAV, <i>γ</i>: (<i>μ</i>,<i>γ</i>) = (3×10⁻⁴,0.9) (blue), (3×10⁻⁴,0.8) (red), (3×10⁻⁴,0.7) (green) and (3×10⁻⁵,0.8) (black). Here, <i>γ</i> = <i>p</i>₁/<i>p</i>₀, the ratio of the viral production rates, or equivalently the replicative abilities, of the mutant and wild-type strains; without loss of generality, the RAV was assumed not to compromise viral infectivity (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s009" target="_blank">S1</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s011" target="_blank">S3 Texts</a>). Single mutant frequencies (<b>A)</b> and the populations of wild-type <b>(B)</b> and single mutant <b>(C)</b> virions when the genetic barrier is 1. Double mutant frequencies <b>(D)</b> and the populations of wild-type <b>(E)</b>, single mutant <b>(F)</b>, and double mutant <b>(G)</b> virions when the genetic barrier is 2. In the latter case, the two single mutants have the same relative fitness, <i>γ</i>, and the double mutant, <i>γ</i>². In (B) and (E), the different lines and symbols are indistinguishable. Parameter values employed are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s008" target="_blank">S5 Table</a>. The parameters to which these predictions are sensitive are as expected from the analytical approximations (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s001" target="_blank">S1 Fig</a>).</p

Response to DAA-based treatments.

<p>SVR rates elicited by various IFN-free and IFN-containing DAA combinations in treatment-naïve and prior null responders to PR from recent clinical trials. The treated population size is indicated in brackets. The significance of the difference in the SVR rates in the two populations is computed using the χ² test. The HCV genotype and whether the patients had liver cirrhosis is indicated. The details of the treatment regimens along with the sources of the data are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006335#pcbi.1006335.s004" target="_blank">S1 Table</a>.</p