My research interests lie in the field of mathematical modeling of biological processes, specifically using partial differential equations and analysis and numerical simulation of these models. Integrating mathematical modeling, analysis and numerical simulations, my research aims to gain insights into the spatial and temporal dynamics of biological processes.
In recent years, I have mainly been interested in population dynamics, especially in mathematical models of cancer cell therapy. My goal is to better understand the spatial and temporal dynamics of resistance development to therapies, using selection-mutation-models adapted from population dynamics. More details can be found here.
In the case of lung cancer, treatment approaches include the use of aerosols (air/particle mixtures). This motivated my recent work on a model and numerics for aerosols. The underlying model consists of a fluid equation for the air flow, coupled with a Vlasov equation for the particle transport. More details can be found here.
A model coupling the fluid with chemotaxis, instead of particles, brings us directly to coupled chemotaxis-fluid models, where my research continues to have a remarkable impact. More details can be found here.