@article{banks_hu_jang_kwon_2012, title={Modelling and optimal control of immune response of renal transplant recipients}, volume={6}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2012.655328}, abstractNote={We consider the increasingly important and highly complex immunological control problem: control of the dynamics of immunosuppression for organ transplant recipients. The goal in this problem is to maintain the delicate balance between over-suppression (where opportunistic latent viruses threaten the patient) and under-suppression (where rejection of the transplanted organ is probable). First, a mathematical model is formulated to describe the immune response to both viral infection and introduction of a donor kidney in a renal transplant recipient. Some numerical results are given to qualitatively validate and demonstrate that this initial model exhibits appropriate characteristics of primary infection and reactivation for immunosuppressed transplant recipients. In addition, we develop a computational framework for designing adaptive optimal treatment regimes with partial observations and low-frequency sampling, where the state estimates are obtained by solving a second deterministic optimal tracking problem. Numerical results are given to illustrate the feasibility of this method in obtaining optimal treatment regimes with a balance between under-suppression and over-suppression of the immune system.}, number={2}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Hu, Shuhua and Jang, Taesoo and Kwon, Hee-Dae}, year={2012}, pages={539–567} }
 @article{adams_banks_davidian_kwon_tran_wynne_rosenberg_2005, title={HIV dynamics: Modeling, data analysis, and optimal treatment protocols}, volume={184}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2005.02.004}, abstractNote={We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented.}, number={1}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Adams, BM and Banks, HT and Davidian, M and Kwon, HD and Tran, HT and Wynne, SN and Rosenberg, ES}, year={2005}, month={Dec}, pages={10–49} }
 @article{adams_banks_kwon_tran_2004, title={Dynamic multidrug therapies for HIV: Optimal and STI control approaches}, volume={1}, DOI={10.3934/mbe.2004.1.223}, abstractNote={We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug "cocktail " therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) in hibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI)in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.}, number={2}, journal={Mathematical Biosciences and Engineering}, author={Adams, B. M. and Banks, H. T. and Kwon, H. D. and Tran, Hien}, year={2004}, pages={223–241} }