This was part of Mathematical Modeling of Biological Interfacial Phenomena

kinetic model for bacteria moving in confined environments

Min Tang, Shanghai Jiaotong University

Friday, December 13, 2024



Slides
Abstract: The motile micro-organisms such as Escherichia coli, sperm, or some seaweed are usually modeled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation phenomenon at the boundary, which is an active research field that has attracted a lot of biologists and biophysicists. Self-propelled particles at the microscale have complex behaviors, while characteristics at the population level are more important for practical applications but rely on individual behaviors. Kinetic PDE models that describe the time evolution of the probability density distribution of the motile micro-organisms are widely used. However, how to impose the appropriate boundary conditions that take into account the boundary aggregation phenomena is rarely studied. In this talk, we propose the boundary conditions for a confined run-and-tumble model (CRTM) for self-propelled particle populations, study its long time behavior. We establish the relation between CRTM and the confined Fokker–Planck model and confined diffusion model. Then discuss their possible clinical applications.