`Discrete Dynamics in Nature and SocietyVolume 2013 (2013), Article ID 712829, 9 pageshttp://dx.doi.org/10.1155/2013/712829`
Research Article

## Hepatitis B Virus Dynamics: Modeling, Analysis, and Optimal Treatment Scheduling

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University (Assiut Branch), Assiut 71511, Egypt
3Department of Mathematics, Faculty of Science, King Khalid University, Abha 9004, Saudi Arabia

Received 8 December 2012; Revised 11 March 2013; Accepted 13 March 2013

Academic Editor: Manuel De la Sen

Copyright © 2013 A. M. Elaiw et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Modeling, analysis, and control of hepatitis B virus (HBV) infection have attracted the interests of mathematicians during the recent years. Several mathematical models exist and adequately explain the HBV dynamics as well as the effect of antiviral drug therapies. However, none of these models can completely exhibit all that is observed clinically and account the full course of infection. Besides model inaccuracies that HBV dynamics models suffer from, some disturbances/uncertainties from different sources may arise in the modeling. In this paper, the HBV dynamics is described by a system of nonlinear ordinary differential equations. The disturbances or uncertainties are modeled in the HBV dynamics model as additive bounded disturbances. The model is incorporated with two types of drug therapies which are used to inhibit viral production and prevent new infections. The model can be considered as nonlinear control system with control input is defined to be dependent on the drug dose and drug efficiency. We developed treatment schedules for HBV infected patients by using multirate model predictive control (MPC). The MPC is applied to the stabilization of the uninfected steady state of the HBV dynamics model. The inherent robustness properties of the MPC against additive disturbances are also shown.