Biomathematics

Mathematical modeling of spatial evolution with applications to cancer Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in life sciences. In this talk I will discuss how spatial interactions may change the laws of …

Geometric Mechanisms of Temporal Variability and Precision in Transient Biological Dynamics Understanding transient temporal effects—when events occur and how variable their timing is—represents a central challenge across biological systems. While traditional analyses often focus on steady-state behaviors and average frequencies, the response variability and timing precision observed in real biological systems demand a deeper understanding …

Mechanistic Models as Hypotheses: Integrating Structure and Data from Sickle Cell Disease to Bacterial Infection Mechanistic models gain scientific value when treated as testable hypotheses rather than fixed descriptions of biology. I illustrate this idea through two modeling studies that differ sharply in how biology and data shape mechanistic structure. I begin with my work …

A Data-Driven Computational Framework for Identifiability and Nonlinear Dynamics Discovery in Complex Systems Data-driven modeling is essential for deciphering complex biological systems, yet its utility is often constrained by two fundamental hurdles: the inability to guarantee parameter identifiability and the high computational cost of learning nonlinear dynamics. This talk introduces a unified computational framework designed …

One equation helps solve three paradoxes in the spatial ecology of predators and prey In this talk I will introduce three paradoxes in the spatial ecology of predators and prey (1) Buffer Zone Paradox: Why do wolves maintain stable buffer zones for prey, even though they may be only saving prey for the neighboring packs? …

Integrated Mathematical Modeling of Cancer - Modeling the ecology and evolution of cancer and treatment resistance We present a suite of hybrid agent-based models (ABMs) that integrate discrete cell-level dynamics with continuous microenvironmental signaling to study eco-evolutionary processes in cancer. Our 2D on-lattice framework couples agent behaviors—proliferation, mutation, and selection—with reaction-diffusion equations governing cytokine fields …

Modeling GLP-1 Treatments in Ovulatory Dysfunction GLP-1 receptor agonists (GLP-1 RAs) have gained widespread attention for their effectiveness in treating metabolic abnormalities such as type 2 diabetes and obesity. Central to their success is the regulation of glucose-insulin metabolism and improvement of insulin resistance. In reproductive endocrinology, GLP-1 RAs have also shown promise as off-label …

Pertussis transmission models and demographic shifts under evolving vaccination programs Pertussis, a highly contagious infection of the respiratory tract, was one of the main causes of child morbidity and mortality in developed countries, in the pre-vaccine era. Following the scale-up and roll-out of childhood vaccination programs in the 1940s–1960s, the incidence and severity of pertussis …

To be rescheduled next semester. Biologically grounded mechanistic modelling from single-cell transcriptomics: case studies in neuroblastoma developmental dynamics and tubular injury in kidney rejection Ordinary differential equation models are ubiquitous in mathematical biology due to their interpretability and tractability. At the same time, their construction relies on substantial a priori assumptions about the relevant variables …