Mathematical Biology

Reproducible Stochastic Simulation Stochastic simulations are commonly used to quantitatively or semi-quantitatively describe the dynamics of biological systems. At various scales and in multiple applications, stochastic simulation better reflects observed biological processes and robustness. Various methods are widely used to incorporate stochasticity into biological simulation, such as the Gillespie stochastic simulation algorithm for systems biology …

Uncertainty Quantification in Complex Models of Complicated Biology Validated mathematical models of complex biological phenomena are increasingly recognized as invaluable for elucidating mechanisms that underlie real-world (experimental or clinical) observations. Agent-based models (ABMs) have emerged as a natural formulation of choice in such models, providing a logical structure for capturing the multiple time and spatial …

Including human behavior in infectious disease models The COVID-19 pandemic has revealed the good and the bad of infectious disease models. While a well-developed model provides invaluable insights needed to understand and combat the pandemic, many models suffer from imperfect or simplistic assumptions that result in inaccurate or even completely wrong predictions. In this talk, …

A multi-scale approach for modeling cell dynamics The characterization of biological phenomena related to cell evolution and their interactions with the microenvironment often involves processes occurring across a range of spatial and temporal scales. As a result, mathematical models designed to describe cell dynamics must capture this inherent multi-scale complexity. In this seminar, we introduce …

How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum …