Age-structured multiscale models have been developed to study viral kinetics. However, they are notoriously difficult to solve and when utilizing this type of models parameter estimation presents a challenge. Here, we investigate the numerical solutions of a multiscale model of hepatitis C virus (HCV) dynamics during antiviral treatment and compare them with analytical approximations. First, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. We compare between several numerical schemes that are suitable and show the benefit of using the Rosenbrock method, an implicit adaptive stepsize method that is both efficient and stable. Second, we address parameter estimation by constrained optimization and show that derivative-free methods such as Powell's constrained optimization by linear approximation (COBYLA) provides an efficient procedure for this task. For simulating trajectories of viral hepatitis progression or decline in patients who are treated with antiviral drugs, we developed a simulator with a graphical user interface. Machine learning of data from patients will be incorporated in the next phase.
Danny Barash received his PhD degree in 1999 from the University of California at Davis. From 1999 to 2001, he was employed at Hewlett Packard Laboratories at the Technion, Israel, pursuing research on image processing and computer vision. From 2001 to 2003, he was a Howard Hughes Medical Institute postdoctoral fellow at New York University and a research fellow at the Institute of Evolution at the University of Haifa, Israel, where he made a transition to computational biology and later on to mathematical biology. Since 2004, he has been with the department of computer science at Ben-Gurion University. His research interests include computational & mathematical biology, viral dynamics, RNA structure prediction, computational imaging, scientific computing and applied numerical analysis for data science.