Figure 1.
Example of a biphasic decline of HCV, following a short delay, after initiation of interferon- therapy at
.
Fit of Neumann et al. model (solid line) to data for Patient 1E (dots) from [3].
Figure 2.
HCV viral load undergoes biphasic decay upon initiation of silibinin treatment at time .
The transition time between the first and second phases, , is calculated by maximizing the curvature
in equation (14), and is marked by a vertical dashed line. VE model fit of Canini et al. [19] (solid line) and HCV viral load data (dots) for (a) Patient 46, with transition time
days, and for (b) Patient 48, with transition time
days.
Table 1.
Model parameter estimates obtained for different drug treatments of chronic HCV.
Figure 3.
Approximate and analytic solution of VE model.
(a) Comparison of analytic solution (equation (11)) and the approximation (equation (16)) assuming sibilinin treatment (see Table 1 for parameters) and initial viral load of . (b) Relative error in
of approximation.
Figure 4.
Different exponential terms in approximate solution (16) compared with the exact solution and for silibinin treatment parameters, for which (see Table 1).
(a) Exponential terms from (16) plotted separately. (b) Exponential terms from (16) plotted in combined form.
Figure 5.
Approximate and analytic solution of the VE model under danoprevir () or telaprevir (
) treatment with patient data.
(a,c) Approximate solution (16) compared to the analytic solution (11) for (a) danoprevir or (c) telaprevir treatment. (b,d) Different exponential terms in approximate solution compared with the exact solution, with decay phases indicated, for (b) danoprevir or (d) telaprevir treatment. Danoprevir treatment: data from patient 04-94XD (dosing 200 mg tid) in [25] with associated parameter estimates for VE model ,
,
,
,
,
, and
[unpublished]. Telaprevir treatment: data from patient 6 in [6] with associated parameter estimates
,
,
,
,
,
, and
[6].
Figure 6.
Approximation to viral dynamics compared to exact dynamics under mericitabine treatment, 750 mg qd, .
(a) For patient 92102 from [16], characterized as “flat”. (b) For patient 92103 from [16], characterized as “non-flat”. (c) Different exponential terms in approximate solution (16) compared with the exact solution for patient 92103, characterized as “non-flat”. Parameter estimates from [16]: For patient 92102, ,
,
,
,
,
, and
; for patient 92103,
,
,
,
,
,
, and
.
Table 2.
Goodness of approximation, Eq. (16), for ranges in the parameter .
Figure 7.
Truncated series solutions for the VE model compared with the exact solution (11) under silibinin treatment (; see Table 1 for parameters).
Legend: (i) Series terms with exponents ,
,
, and
terms, included in the approximation (16), from the series solution (19); (ii) Series terms with exponents from (i) and also the
and
terms missing from the approximation.