Contributions to mathematical modelling and numerical simulation of biofilms

Abstract

The main goal of this PhD work is the development and numerical resolution of mathematical models that simulate the dynamics of bacterial biofilm systems, paying special attention to those biofilms formed by the Listeria monocytogenes, a pathogen of special relevance in food safety. A biofihn is a layer of microorganisms attached to a surface and protected by a matrix of exopolysaccharides. Biofilm structures difficult the removal of microorganisms, thus the study of the type of structures formed throughout a biofilm life cycle is key to design elimination techniques. In the present work, we develop different models that simulate the dynamics of biofilms formed by different strains of L. monocytogenes. We start with a 1D model that can be used to describe the formation of flat biofilms. Afterwards, we apply the acquired knowledge to develop a 2D model capable of describing more complex structures. All this models are solved with efficient numerical methods and robust numerical techniques, such as the Level Set method, that guarantees the good behaviour of the obtained solutions. Finally, the numerical results are compared with the experimental measurements obtained in the Instituto de Investigaciones Marinas, CSIC (Vigo, Spain), and the Micalis Institute, INRA (Massy, France).