Callibration in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation or fitting (callibration) that solves all cases of data points available presents a formidable challenge, as efficiency considerations need to be employed in order for the method to become practical. In the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derviative approximations. These steps that were successful in significantly speeding up a highly non-efficient approach, rendering it practical, can also be adapted to multiscale models of other viruses and other sophisticated differential equation models. The newly efficient methods that were developed as a result of the above approach are described. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for multiscale models. We provide a simulator called HCVMulti-scaleFit with a Graphical User Interface that applies these methods and is useful to perform parameter estimation for simulating viral dynamics during antiviral treatment.

1.
J.
Guedj
,
H.
Dahari
,
L.
Rong
,
N. D.
Sansone
,
R. E.
Nettles
,
S. J.
Cotler
,
T. J.
Layden
,
S. L.
Uprichard
, and
A. S.
Perelson
,
Proc Natl Acad Sci USA
110
,
3991
3996
(
2013
).
2.
L.
Rong
,
J.
Guedj
,
H.
Dahari
,
D. J. J.
Coffield
,
M.
Levi
,
P.
Smith
, and
A. S.
Perelson
,
PLOS Comput. Biol.
9
, p.
e1002959
(
2013
).
3.
L.
Rong
and
A. S.
Perelson
,
Math Biosci.
245
,
22
30
(
2013
).
4.
B. M.
Quintela
,
J. M.
Conway
,
J. M.
Hyman
,
J.
Guedj
,
R. W. dos
Santos
,
M.
Lobosco
, and
A. S.
Perelson
,
Front. Microbiol.
9
, p.
601
(
2018
).
5.
World Health Organization
,
Global hepatitis report
(
World Health Organization
,
2017
).
6.
H.
Dahari
,
B.
Sainz
,
A. S.
Perelson
, and
S. L.
Uprichard
,
Journal of Virology
83
,
6383
6390
(
2009
).
7.
H.
Dahari
,
R. M.
Ribeiro
,
C. M.
Rice
, and
A. S.
Perelson
,
Journal of Virology
81
,
750
760
(
2007
).
8.
H.
Dahari
,
E.
Shudo
,
R. M.
Ribeiro
, and
A. S.
Perelson
,
Hepatitis C: Methods and Protocols
439
453
(
2009
).
9.
H.
Dahari
,
J.
Guedj
,
A. S.
Perelson
, and
T. J.
Layden
,
Current Hepatitis Reports
10
,
214
227
(
2011
).
10.
L.
Sandmann
,
M. P.
Manns
, and
B.
Maasoumy
,
Liver Int.
39
,
815
817
(
2019
).
11.
A. U.
Neumann
,
N. P.
Lam
,
H.
Dahari
,
D. R.
Gretch
,
T. E.
Wiley
,
T. J.
Layden
, and
A. S.
Perelson
,
Science
282
,
103
107
(
1998
).
12.
J.
Guedj
and
A. U.
Neumann
,
J. Theor. Biol.
267
,
330
340
(
2010
).
13.
J.
Weickert
,
B. ter Haar
Romeny
, and
M.
Viergever
,
IEEE Trans. Imag. Proc.
7
,
398
410
(
1998
).
14.
D.
Barash
,
M.
Israeli
, and
R.
Kimmel
, “
An accurate operator splitting scheme for nonlinear diffusion fil-tering
,” in
Proceedings of the 3rd International Conference on ScaleSpace and Morphology
(
LNCS Series, Springer-Verlag
,
2001
), pp.
281
289
.
15.
D.
Barash
,
Appl. Num. Math.
52
,
1
11
(
2005
).
16.
V.
Reinharz
,
A.
Churkin
,
H.
Dahari
, and
D.
Barash
,
Front. Appl. Math. Stat.
3
, p.
20
(
2017
).
17.
V.
Reinharz
,
H.
Dahari
, and
D.
Barash
,
Math Biosci.
300
,
1
13
(
2018
).
18.
K.
Levenberg
,
Quarterly of applied mathematics
2
,
164
168
(
1944
).
19.
D. W.
Marquardt
,
Journal of the society for Industrial and Applied Mathematics
11
,
431
441
(
1963
).
20.
K.
Kitagawa
,
S.
Nakaoka
,
Y.
Asai
,
K.
Watashi
, and
S.
Iwami
,
J. Theor. Biol.
267
,
330
340
(
2018
).
21.
M. J. D.
Powell
,
Cambridge University Technical Report DAMTP 2007
(
2007
).
22.
E.
Gorstein
,
M.
Martinello
,
A.
Churkin
,
S.
Dasgupta
,
K.
Walsh
,
T.
Applegate
,
D.
Yardeni
,
O.
Etzion
,
S. L.
Uprichard
,
D.
Barash
, et al.,
Antiviral Research
(
2020), 10.1016/j.antiviral.2020.104862
.
23.
S.
Dasgupta
,
M.
Imamura
,
E.
Gorstein
,
T.
Nakahara
,
M.
Tsuge
,
A.
Churkin
,
D.
Yardeni
,
O.
Etzion
,
S. L.
Uprichard
,
D.
Barash
,
S. J.
Cotler
,
H.
Dahari
, and
K.
Chayama
,
The Journal of Infectious Diseases
(
2020), 10.1093/infdis/jiaa219,jiaa219
.
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