In this seminar, we will explore the mathematical modeling of biological processes, focusing on population and resource dynamics within biofilms. The model formulation is based on differential equations that describe the biofilm's response to external and self-produced substances, leading to highly non-linear diffusion-reaction systems. We will examine the existence of solutions, considering experiments that establish a saturation threshold for biomass and conditions for spatial spreading.

The seminar will also delve into the kinetics of biofilm metabolism, drawing parallels with chemical reactions, and addressing key processes such as nutrient consumption, biofilm growth, and transport mechanisms like diffusion and convection. Additionally, we will discuss modeling challenges, including pattern formation under nutrient limitations and the protective mechanisms employed by organisms within biofilms, such as slower diffusion in the matrix, altered growth modes, and the role of persister cells in cell-to-cell communication. Finally, we will present computer simulations and numerical experiments, providing an ecological interpretation of the results and offering insights into the qualitative properties of the solutions.

Short Bio: Messoud Efendiev is a Professor at the Helmholtz Zentrum in Germany and serves as the Rector's Distinguished Visiting Professor at Mamaru University in Turkey. His distinguished academic career includes appointments as the Dean's Distinguished Visiting Professor at the University of Toronto and the James D. Murray Distinguished Visiting Professor at the University of Waterloo. Among his many accolades, Dr. Efendiev is a Humboldt Fellow and an elected Fellow of the Fields Institute, reflecting his significant contributions to the field.