Research

My work involves optimal decision theory, uncertainty quantification, fluid mechanics, optimization, and image analysis, among other topics, and I collaborate with immunologists, 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 IISER Tirupati (formerly at BITS Pilani-Hyderabad) and A. Kearsley at NIST, and with experimental collaborators L. Muehling and G. Canderan at UVA and P. Pannaraj, Y. Lee, and W. Cheng at UCSD), and (3) modeling and agent-based simulation of biofilm matrix breakoff and enzymatic disruption (joint work with S. Olsen at WPI, J. Kreig at LANL, Y. Yu at IUI, and Z. Wang at UK). A pre-print of our biofilm cluster detachment work is available on arXiv.

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.

Contact lens drug delivery

In an invited paper published in a special collection of La Matematica, we describe models for drug release by a contact lens during wear over 24 hours of blinking. The model considers pathways of drug release to the pre- and post-lens tear films, and loss from those regions by absorption into the eyelid, sweep out due to blinking, and slide or squeeze out by the motion of the lens. Using physically realistic parameter values, we find good agreement between our solutions and experimental data from an in vitro eye model.

Schematic that describes the mechanisms/processes between and during blinks. Red and blue ink denote processes affecting tear film thickness and drug concentration, respectively

This work has been presented at several conferences including the Association for Research in Vision and Ophthalmology (ARVO) Annual Meeting in Seattle, WA in May 2024 and the American Physical Society Division of Fluid Dynamics (APS DFD) Annual Meeting in Washington, D.C. in November 2023.

Work on a related project modeling drug delivery from a composite lens was recently presented at the 2026 ARVO Annual Meeting in Denver, CO; see poster below.

ARVO_2026_poster_updated.pdf

Poster presented at the 2026 ARVO Annual Meeting in Denver, CO.

We also mention this work in a SIAM News blog post on parameter estimation for tear film thinning and breakup, a cause of dry eye disease.

Antibody kinetics of infection and vaccination

In a paper published in the Bulletin of Mathematical Biology, we designed the first known system to capture immune state transitions and track antibody response over time simultaneously, via a coupled probabilistic and Markov chain model. We also developed an unbiased prevalence estimation scheme to track the fraction of the population that is infected or vaccinated across time. A continuation of the project is funded in part by a collaborative research grant from 4-VA (see below for more).

This work has been presented at several conferences, including at the SIAM Conference on Computational Science and Engineering in Ft. Worth, TX in March 2025, as a keynote address at the SIAM DMV Conference on Applied Mathematics in Baltimore, MD in April 2025, and as a colloqiuium speaker at Swarthmore College in February 2026.

Prevalence estimates for infection (top) and vaccination (bottom) over time for various sample sizes with confidence interval bands. True prevalence (pink) is related to true incidence rate (insets). Estimates generated using synthetic data assuming a wave of infections and a constant rate of vaccination.

An important extension of this work is available as a pre-print on arXiv. The GIFs show visualizations of our new models.

Several potential PhD student projects related to this work are available.

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