# How bacterial infections might give you mathematics

Bacteria tend to form biofilms. These are microbial depositions on immersed surfaces that one can find virtually everywhere where the environmental conditions can sustain microbial life. Depending on the context, such biofilms can be beneficial, for example in environmental engineering technologies, or detrimental, for example when they cause infections in the body. The mathematical modeling of such microbial communities is one of the research areas of Dr Eberl's Computational Biomathematics group.

Biofilms can be characterised both, as spatially structured populations, and as complex mechanical objects. Accordingly, the mathematical modeling of biofilm communities brings several areas of applied mathematics together, such as Mathematical Biology, Ordinary and Partial Differential Equations, and Numerical Methods.

The questions for which Dr Eberl and his students develop mathematical models are manifold. They can be concerned with understanding and improving biofilm process performance, for example in wastewater treatment or soil remediation. But they can also be concerned with the response of bacterial communities to antibiotics, or how one can support antibiotic therapies by interfering with bacterial communication processes. Or with the question how bacterial processes can be harnessed for the production of energy. The biological and physical complexity of biofilms is rendered by the mathematical complexity of the equations that describe them. Often this will require the development of new mathematical and computational methods to deal with such multi-faceted models.

High school students interested in developing the mathematical and statistical skills to tackle a real world problem such as this should consider our Mathematical Science Major, with an Area of Emphasis in Biology, Biomathematical Modelling, Computer Science, Food Science, Energy and Mass Transfer, Microbiology, or Physics.

Prospective graduate students interested in working with Dr. Eberl should visit his website, or read more about Graduate Studies at Guelph.