Research
My work involves optimal decision theory, uncertainty quantification, fluid mechanics, optimization, and image analysis, among other topics, and I have collaborated with epidemiologists and optometrists.
Current research topics include (but are not limited to): (1) contact lens drug delivery modeling and comparison to experimental data (joint work with D. Anderson at GMU), (2) probabilistic and Markov chain modeling of time-dependent antibody kinetics (joint work with P. Bedekar at JHU/NIST and A. Kearsley at NIST), and (3) modeling and data science approaches to defining and predicting Long COVID (joint work with A. Mollalo at MUSC, G. Shaw at UNC Charlotte, and G. Clarke at U Minnesota).
I am passionate about science communication. I value presenting my work in an understandable format to stakeholders (immunologists, eye doctors, etc.) and I enjoy attending both mathematics and non-mathematics conferences.
4-VA funded collaborative research
From July 2024 -- June 2025, I will lead a team including immunologists (L. Muehling and G. Canderan at UVA), a graduate student, and undergraduate students on a project entitled "Data-Driven Modeling of the Time-Dependent Immune Response to Infection and Vaccination." Interested undergraduates can find more information and apply by contacting me.
Top: A plot showing the decrease in variance of prevalence estimates from their true values as the number of samples is increased.
Bottom: A GIF from our paper: Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 assays.
Recent Work
Our paper on modeling in higher dimensions to improve diagnostic testing accuracy was published this spring and highlighted on Kudos.
In a 2023 paper, we solve the multiclass diagnostic classification problem and provide a prevalence estimation framework for settings with more than two classes.
This work has been presented at several conferences including the Seronet Investigators Meeting that gathered researchers studying immune and vaccine responses to SARS-CoV-2, the Joint Mathematics Meetings in Boston, MA, and ECMTB (European Conference on Mathematical and Theoretical Biology) in Heidelberg, Germany that was jointly organized with SMB (Society for Mathematical Biology).
Top: Presenting a talk in a minisymposium at ECMTB in Heidelberg, Germany in September 2022.
Bottom: Presenting a poster at the AWM Research Symposium in Minneapolis, MN in June 2022.
Attending the 2019 Association for Research in Vision and Ophthalmology (ARVO) Annual Meeting in Vancouver, BC. I presented a poster.
PhD Thesis
My dissertation research focused on fitting models for extreme thinning of the tear film (TBU) to patient data under the advisement of Dr. Richard Braun and in collaboration with Dr. Carolyn Begley and Deborah Antwi (School of Optometry, Indiana University). I extracted meaningful parameters and analyzed quantities that cannot be measured in vivo.
In the final year of my dissertation, I won the Wenbo Li Scholarship for Graduate Research that recognizes an outstanding research paper in the mathematical sciences. The paper is #8 below in Recent Publications.
My PhD thesis was entitled Parameter Identification for Tear Film Thinning and Breakup.
Pitching a poster at the High Performance Computing Symposium in Newark, DE in 2020.
Recent Publications
Luke RA, Kelly N, Stoner M, Esplin O’Brien J, Ellwein Fix L, Lubkin S (in press) Towards a mathematical understanding of ventilator-induced lung injury in preterm rat pups. Mathematical Modeling for Women’s Health: a Collaborative Workshop for Women in Mathematical Biology.
Driscoll TA, Braun RJ, Luke RA, Sinopoli S, Phatak A, Dorsch J, Begley CG, Awisi-Gyau D (to appear) Fitting ODE models of tear film breakup. Modeling and Artificial Intelligence in Ophthalmology 5(1):1-36. https://www.maio-journal.com/index.php/MAIO/article/view/128
Luke RA, Kearsley AJ, Pisanic N, Manabe YC, Thomas DL, Heaney C, Patrone PN (2023) Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 assays. PLoS ONE 18(3): e0280823. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0280823
Access the supplemental figures HERE
Luke RA, Kearsley AJ, Patrone PN (2023) Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes. Mathematical Biosciences 358:108982. https://www.sciencedirect.com/science/article/pii/S0025556423000238
Luke RA, Braun RJ, Begley CG (2021) Mechanistic determination of tear film thinning via fitting simplified models to tear breakup. Modeling and Artificial Intelligence in Ophthalmology, 3(1):71-100. https://doi.org/10.35119/maio.v3i1.114
Braun RJ, Luke RA, Driscoll TA, Begley CG (2021) Dynamics and mechanisms for tear breakup (TBU) on the ocular surface. Mathematical Biosciences and Engineering, 18(5):5146-5175. http://aimspress.com/article/doi/10.3934/mbe.2021262
Luke RA, Braun RJ, Driscoll TA, Awisi-Gyau D, Begley CG (2021) Parameter estimation for mixed- mechanism tear film thinning. Bulletin of Mathematical Biology, 83(56). https://link.springer.com/article/10.1007/s11538-021-00871-x
Luke RA, Braun RJ, Driscoll TA, Begley CG, Awisi-Gyau D (2020) Parameter estimation for evaporation-driven tear film thinning. Bulletin of Mathematical Biology, 82(71). https://link.springer.com/article/10.1007/s11538-020-00745-8
For more detailed information, see Dr. Luke's CV and Google Scholar.