Administration
Department of Mathematics
College of Science and Mathematics
Department of Mathematics
Medical College of Georgia
Department of Population Health Science
Medical College of Georgia
Department of Population Health Science: Biostats & Data Science
I view teaching as akin to nurturing a garden; students thrive when they are cared for and supported. In such an environment, they develop confidence, self-esteem, and a sense of assurance. My awareness that students come from diverse cultural and educational backgrounds drives me to simplify complex topics and tailor my instruction to ensure every student, regardless of their starting point, can understand and engage with the material.
I emphasize active learning by consistently involving students in problem-solving activities and encouraging open dialogue through questions and discussion during lectures. In every class, I provide students with printouts of classwork problems aligned with each section covered. These problems are attempted collaboratively during class, with guidance and input from me, fostering a participatory learning environment where students learn by doing and reflecting in real-time.
In my teaching, I adopt a step-by-step problem-solving approach, pausing regularly to ensure students are following along. I supplement instruction with similar in-class exercises to reinforce concepts and verify understanding. To help students stay engaged during lectures, I provide PowerPoint slides and supplementary materials in advance through our online learning platform. This allows students to focus on the lecture itself rather than transcribing notes and ensures they have structured resources readily available for review and self-study.
I regularly incorporate real-world projects that require students to apply their mathematical knowledge to practical scenarios in certain classes. These projects culminate in student presentations, which not only reinforce their understanding but also highlight the relevance of mathematics across various disciplines, including biology, chemistry, physics, engineering, finance, medicine, and the social sciences. To bridge the gap between abstract concepts and tangible understanding, I integrate hands-on demonstrations and visual tools that promote discovery-based learning. For instance, when introducing the topic of series and power series in my calculus classes, I create custom animations using MATLAB and Mathematica codes to visually illustrate how the partial sums of a power series converge within their interval of convergence. These dynamic representations help students build intuitive insight into convergence behavior and deepen their conceptual grasp of infinite series.
I believe in employing diverse assessment strategies to gauge student comprehension across varied learning styles. From my classroom experience, I’ve found that combining conceptual explanations with illustrative examples and practice exercises significantly enhances knowledge retention. Regular homework assignments provide additional practice and reinforce learning, while my open-door policy during office hours ensures students have access to help when needed.
I am confident that my teaching approach makes mathematics both accessible and enjoyable. Through clear presentation, engaging problem-solving, and enthusiastic delivery, I aim to instill in my students a genuine appreciation for the subject and a lasting enthusiasm for learning.
My research lies at the intersection of stochastic modeling, dynamical systems, and statistical analysis, with a focus on applications in biological, medical, and public health contexts. A core theme of my work is developing and applying mathematical models to understand the dynamics of infectious diseases, tumor growth, and population health, especially under uncertainty. I incorporate time-dependent stochastic processes, differential equations, and statistical estimation frameworks to analyze complex, high-dimensional data from real-world systems.
A key contribution is the development of the Local Lagged Adapted Generalized Method of Moments (LLGMM), a patented (U.S. Patent No. 10,719,578) nonparametric estimation framework designed to infer time-varying parameters and hidden states in stochastic differential equations. This method has been applied to influenza and COVID-19 data in the United States, producing accurate temporal estimates of transmission rates, reproduction numbers, recovery rates, and other key epidemiological quantities. LLGMM has demonstrated strong performance in both state estimation and forecasting, as published in the Journal of Mathematical Biology and Results in Physics.
In collaboration with students, I extended this framework to study COVID-19 using a detailed SEIRS model. We accounted for public health interventions and modeled population heterogeneity across all U.S. states and territories. I also developed short-term forecasting models for COVID-19 deaths and applied first-passage-time (FPT) analysis to understand rare oncological events and spontaneous cancer remission. In particular, I derived explicit FPT distributions under dynamic tumor barriers, validated with experimental tumor volume data from mouse models. This work was presented at the 2025 Joint Mathematical Meetings (JMM) and published in Scientific Reports.
My research on tumor growth in toxicant-stressed environments, using stochastic models with treatment effects, was published in the Journal of Mathematical Biology (2024). Graduate student Selassie Hatekah later extended the model to include CAR-T therapy and immune cell interactions. The model describes how random environmental stress, treatment intensity, and shape parameters influence tumor dynamics.
In another collaborative project, I worked with undergraduate student Alexandra Yu, during the 2023 CURS SSP Summer Research Program, to analyze vaccine breakthrough and rebound infections in COVID-19 across the ten U.S. Health and Human Services (HHS) regions. We developed a novel multi-strain SVEAIR model and estimated parameters across several SARS-CoV-2 variants. This work was presented at JMM (2023) and BAMM (2022), and later published in the Journal of Infectious Disease Modelling.
Other studies include modeling HIV/TB co-infection under random perturbations, revealing how treatments and noise affect long-term dynamics and disease eradication thresholds. Additional work involves the derivation of time-dependent probability distributions using Fokker–Planck equations for SIS epidemic and logistic growth models. These results, published in Chaos, Solitons & Fractals, and Physica A, respectively, provide analytical insight into stochastic population behavior and optimal control strategies.
My research program fosters student involvement through independent research, conference presentations, and co-authored publications. These collaborations not only advance theoretical and applied science but also support student development and success in mathematical biology and public health modeling.
