דן ברש

Multiscale mathematical models that incorporate both intracellular and extracellular hepatitis C virus (HCV) dynamics have been developed in recent years to study HCV-host dynamics and antivirals mode of action and efficacy. They were built upon the standard HCV dynamic model that keeps track of uninfected hepatocytes, HCV-infected hepatocytes, and free virus in blood (for each there is a differential equation), along with a fourth equation that considers the intracellular viral RNA (vRNA) dynamics in an infected cell. A multiscale model with vRNA dynamics consideration is substantially more difficult to solve and the governing differential equations are stiff. In one of the derived differential equations there is also an integral involving the vRNA that is more accurately computed by considering previous iterations, impeding the use of canned solvers. To solve this problem we have chosen to implement a stable and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, the Rosenbrock method. We provide a user friendly simulator called HCVMultiscaleDyn with a Graphical User Interface that applies this method and is useful to simulate viral dynamics during antiviral treatment.