Mathematical Models of Biofilm in Various Environments
Abstract
Microbial biofilms are defined as clusters of microbial cells living in self-produced extracellular polymeric substances (EPS), which always attached to various kinds of surfaces. In this thesis, we studied several mathematical models of biofilm in the human body and marble environment. Some related background of biofilm growth and some basic existing numerical models were introduced in the first chapter. In the first project, we introduced how biofilm affects the local oxygen concentration near the neutrophil cells in the human body with three one-dimensional reaction-diffusion models from different geometries. In nature, microbial biofilm development can be observed on almost all kinds of stone monuments and can also be associated with the problem of monument conservation. In the second part of my research, we built the deliquescence models for biofilm growth environment in the first model and added biomass into consideration in the second one. Also, we analyzed the stability of the equilibria. In the third part, we applied the weather data collected from the weather station on the roof of the Jefferson Memorial to the deliquescence model with biofilm. Furthermore, compared the simulation result for biofilm growth in cold and warm weathers. In the last part of this thesis, we analyzed the biofilm activity with support vector regression. The machine learning model we obtained can be used to find the growth trends of biofilm for any pair of temperature and relative humidity…
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