This paper describes a model of the immunologic response of latent viruses and a donor kidney in a renal transplant recipient. An optimal control problem with state variable inequality constraints is considered to maintain the balance between over-suppression where latent viruses are reactivated and under-suppression where the transplanted kidney is rejected. A feedback methodology based on the model predictive control (MPC) method is proposed to design (sub)optimal treatment regimes. In addition, the problem of implementing the MPC methodology and nonlinear Kalman filter with inaccurate or incomplete observation data and long measurement periods is addressed. The results of numerical simulations show that a (sub)optimal dynamic immunosuppression therapy method can help strike a balance between the over-suppression and under-suppression of the immune system.
Bibliographical noteFunding Information:
The work of Hee-Dae Kwon was supported by the NRF Grant funded by the Korean government ( NRF-2012R1A1 A2005605 ) and by Inha University Research Grant. The work of Jeehyun Lee was supported by Basic Science Research Program through the NRF funded by the Ministry of Education ( 2013R1A1A2058848 ). The work of Myoungho Yoon was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2009-0093827 ).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics