Controllability of Efficiency of Antiviral Therapy in Hepatitis B Virus Infections

Authors: Shyam S.N. Perera

Abstract:

An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.

Keywords: Virus infection model, Optimal control, Adjoint system, Steepest descent

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070109

References:

[1] S. M. Ciupe R. M. Ribeiro, P. W. Nelson, A. S. Perelson, Modeling the mechanisms of acute hepatitis B virus Infection, J. Theor Biol., 247(1):23-35, 2007.
[2] K. Ito K, S. S. Ravindran, Optimal control of thermaly convected fluid flows, SIAM J. Sci. Comput. 19(6):1847-1869, 1998.
[3] C. T. Kelley, Iterative methods for optimization, SIAM, 1999.
[4] G. Lau, M. Tsiang, J. Hou, S. Yuen, w. Carman, L. Zhang, C. Gibbs, S. Lam, Combination therapy with lamivudine and famciclovir for chronic hepatitis B infected Chinese patient: a viral dynamics study, Hepatology, 32:394-399, 2000.
[5] D. Lavanchy, Worldwide epidomology of HBV infections, disease burden and vaccine prevention, J. Clin. Virol., 34:1-5, 2005.
[6] S. Lewin, R. Ribeiro, T. Walters, G. Lau, S. Bowden, S. Locarnini, A. Perelson, Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed, Hepatology, 34:1012-1020, 2001.
[7] M. A. Nowak MA, S. B. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas, H. Mcdade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93:4398-4404, 1996.
[8] R. Ribeiro, A. Lo, A. Perelson, Dynamics of hepatitis B virus iinfection, Microbes and Infection, 4:829-835, 2002.
[9] L. F. Shampine, and M. W. reichelt, The MATLAB ode suite, SIAM J. Sci. Comput., 18:1-22, 1997.
[10] M. Tsiang, J. Rooney, J. Toole, C. Gibbs, Biphasic clearence kinetics of hepatitis B virus form patients during adefovir dipivoxil therapy, Hepatology, 29: 1863-1869, 1999.