@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_banks_stark_2005, title={Population dynamics models in plant-insect herbivore-pesticide interactions}, volume={196}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2004.09.001}, abstractNote={We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus non-autonomous model dynamics. We conclude with a brief discussion of some not-so-subtle pitfalls that can arise when using quantitative measures of model fit-to-data to make biological inferences as well as offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to suggest synergisms.}, number={1}, journal={MATHEMATICAL BIOSCIENCES}, author={Adams, BM and Banks, HT and Banks, JE and Stark, JD}, year={2005}, month={Jul}, pages={39–64} }
 @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} }