In this paper, we derive efficient drug treatment strategies for hepatitis B virus (HBV) infection by formulating a feedback control problem. We introduce and analyze a dynamic mathematical model that describes the HBV infection during antiviral therapy. We determine the reproduction number and then conduct a qualitative analysis of the model using the number. A control problem is considered to minimize the viral load with consideration for the treatment costs. In order to reflect the status of patients at both the initial time and the follow-up visits, we consider the feedback control problem based on the ensemble Kalman filter (EnKF) and differential evolution (DE). EnKF is employed to estimate full information of the state from incomplete observation data. We derive a piecewise constant drug schedule by applying DE algorithm. Numerical simulations are performed using various weights in the objective functional to suggest optimal treatment strategies in different situations.
Bibliographical noteFunding Information:
The work of Hee-Dae Kwon was supported by a NRF Grant funded by the Korean government (NRF-2014R1A1A2056498). The work of Jeehyun Lee was supported by NRF grant 2015 R1A5A1009350 and NRF-2016R1A2B4014178.
2010 Mathematics Subject Classification. Primary: 92B05; Secondary: 49K15. Key words and phrases. Feedback control, HBV, model predictive control, ensemble Kalman filter, differential evolution. The work of Hee-Dae Kwon was supported by a NRF Grant funded by the Korean government (NRF-2014R1A1A2056498). The work of Jeehyun Lee was supported by NRF grant 2015 R1A5A1009350 and NRF-2016R1A2B4014178. ∗ Corresponding author: Hee-Dae Kwon.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Agricultural and Biological Sciences(all)
- Computational Mathematics
- Applied Mathematics