Research Interests
My research career is focused on development and calibration of mathematical models of biological systems using systems of ordinary differential equations, biologically informed neural networks (BINNs), and more recently, agent-based models. My primary interest is within host viral/immune system modeling, with a secondary interest in models of complex antibody-antigen binding kinetics.
My background is a bit unique: I have a Masters’ degree in Biochemistry and a PhD in pure Mathematics. As a graduate student in Biochemistry, I developed methodology to simulate protein folding in-silico. This required extensive scientific programming experience in addition to understanding the physics of molecular dynamics and statistical mechanics. My training also involved work at the lab bench, following experimental protocols and designing experiments. This provides a background for understanding biological mechanism, and how to construct efficient computational simulations of mechanistic models. As a mathematician, I have deep understanding of the features of non-linear dynamic modeling, such as sensitivity of model outputs to initial conditions and changes in parameters, and structural and practical identifiability. After joining the Department of Biostatistics and Bioinformatics, I initially conducted research in statistical genetics before gravitating to mathematical modeling of immune system and pathogen dynamics. As part of my responsibilities, I have taught Introduction to Statistical Theory and Methods I in our Masters of Biostatistics program and I designed and taught R for Data Science in the data science track of the program. Teaching these courses, I have learned how to model and quantify uncertainty, and developed an appreciation of the complex issues with the statistical calibration of dynamical systems models.
With regard to with-in host modeling, I have co-authored several works modeling SHIV infection in Rhesus Macaques. A simple model for viral decay dynamics and the distribution of infected cell life spans in SHIV-infected infant rhesus macaques, and Assessing the impact of autologous virus neutralizing antibodies on viral rebound time in postnatally SHIV-infected ART-treated infant rhesus macaques.
I was awarded an R21, Mathematical modeling for optimal control of BK virus infection in kidney transplant recipients, where we are developing a model to determine the optimal level of immune suppression for kidney transplant recipients infected with the opportunistic pathogen BK virus. We have our first publication, Modeling Immune Response to BK Virus Infection in Renal Transplant Recipients was published in Viruses in early 2025. A second paper, Interpretable Discovery of Hidden Dynamics in BK Virus Infection Dynamics Modeling in Renal Transplant Recipients is in draft and submission is planned for September 2025.
With regard to antibody-antigen binding kinetics, I have been particularly interested in high-throughput SPR without regeneration of surface and interactions that are multi-valent in nature. These models are similar in that they involve systems of non-linear ordinary differential equations, unobserved compartments, identifiability issues and local minima. In this area, I have worked closely with biophysicists in the lab of Dr. Georgia Tomaras, founder of Duke’s CHSI. A manuscript describing our work on a bivalent analyte model that uses simulation to determine the optimal experimental design to determine rate parameters has been published in Analytical Biochemistry. Additionally, I have developed an open source R package for SPR kinetic analysis that includes options to automate dissociation window choice and to choose an optimal range of concentrations. This package will be expanded to include multivalent binding models in the context of a non-regenerated surface – something that does not exist in currently available software. The package is available on Comprehensive R Archive Network (CRAN).
Finally, I believe strongly that the future direction of biomedical research is in team science. To that end, I have and continue to work in close collaboration with biological researchers, including biophysicists in the Tomaras lab and nephrologists at the Duke Transplant Center. I have also initiated a collaboration with the Center for Research in Scientific Computation at North Carolina State University (NCSU), who have expertise in optimal control and machine learning that we are applying to optimal control of immune suppression in BKV-infected kidney transplant recipients. My inter-disciplinary training has provided me with the skills to communicate effectively with both biologists and mathematicians, creating a bridge that helps to unite the team and move projects forward.