In this talk, we suggest a guideline for efficient drug treatment strategies for hepatitis B virus (HBV) infection. We introduce and analyze a dynamic mathematical model that describes the HBV infection during antiviral therapy. We determine the reproduction number $R_0$ and investigate the local/global stability of virus-free steady state. A control problem is considered to minimize the viral load while being mindful of treatment costs. In order to reflect the status of patients not only at the initial time but also at the follow-up visits, we consider the feedback control problem based on ensemble Kalman filter and differential evolution. The ensemble Kalman filter is employed to estimate full information of the state from incomplete observation data. We derive piecewise constant drug schedule applying techniques of differential evolution algorithm. Numerical simulations are performed using various weights in the objective functional to suggest optimal treatment strategies in different situations.

Professor Hee-Dae Kwon (http://math.inha.ac.kr/~hdkwon/), department of Mathematics Inha University. He had his Ph.D in Iowa State University in 2003, and then did his postdoc at Center for Research in Scientific Computation, NCSU, Raleigh from 2003 to 2004. His now an associated professor at Inha University. His research interests centering around: mathematical biology, optimal control problems, numerical analysis  and computational methods for partial differential equations.