Bacterial communities play an important role in many aspects of life, both good and bad from a human perspective. In medicine they cause a variety of infection diseases, hinder wound healing, compromise prosthetics and medical implants, whilst the microbial flora in the gut perform a vital part of the healthy digestive tract. In food industry, bacterial contamination affects food safety, quality and shelf life. In other industrial systems, bacterial depositions can lead to microbially induced corrosion and biofouling of materials.  On the other hand, in environmental engineering, biological wastewater treatment technologies and soil decontamination strategies are developed based on microbial processes. Such microbial systems and processes can be highly complex. They often involve direct and indirect interaction of several (up  to hundreds) species, complex biochemical reactions and pathways, and often depend on the physical conditions in their environment and on physical  processes such as fluid dynamics, mass transport, shear fields, etc. In many instances bacterial populations are spatially structured, e.g. in form of bacterial biofilms, which are dominated by diffusion gradients and may allow the development of ecological microniches, and in which they are protected against mechanical washout by a self-produced polymeric layer.

Despite there being relatively few active researchers involved in the mathematical modeling of microbial populations, in comparison to some other  areas of mathematical biology, it is a long-standing and successful field and  has had a strong impact in biology and bioengineering. For example, the  results of the mathematical theory of the chemostat are routinely (but often  unbeknownst) used by biologists to design microbial population experiments  in continuous flow systems; mathematical models, often as simulation tools,  are routinely used by environmental engineers, e.g. to design wastewater treatment plants; food microbiologists routinely use relatively simple mathematical models to analyse bacterial growth data; several very different mathematical models showing the same qualitative results suggested that environmental conditions are responsible for the irregular spatially morphologies of many biofilms, a hypothesis which has since been verified experimentally and is now commonly accepted.

Some of the current high level challenges in microbiology and microbial process engineering are:

- The success and ease of accessibility of antibiotics both in hospital settings and in agriculture have lead to their overuse and the emergence of widespread antimicrobial resistance. To combat this requires the development and testing of alternative antimicrobial agents and treatment  strategies to destroy or manage infecting microbial systems.

- Efficient production of sustainable and renewable energy, e.g. in form of transportation fuels (e.g. cellulosic ethanol; biogas) or electric energy (microbial fuel cells) requires a good understanding of the interplay of physical reactor conditions and microbial processes.

- The importance of gut health and its implication for many diseases has been increasingly recognized in recent years. To study complex gut community structures and processes in laboratory reactors requires an understanding of the interplay of physical conditions with the complex microbial ecology and biochemistry.

Considering the enormity of these tasks it can be expected that mathematical modeling will have a strong role to play in tackling these. This will require an extension and rethinking of current modeling concepts, and an application of existing techniques to problems of ever  increasing complexity.  In particular, the interplay between physical and microbial processes will become more and more important, which implies an emerging emphasis on multi-scale/multi-science modeling approaches. Workshop topics include:

- microbial processes involving several species and applications in disease,  environmental/industrial systems, etc.

- quorum sensing (QS) within and between colonies

- control of microbial populations: antibiotics, phages, signalling based strategies and related concepts, etc.

- biofilm mechanics, hydrodynamics, detachment, etc.

- biofilm process models on the engineering scale

- multi-scale modeling (cell-colony-reactor, fast/slow processes)

- evolution of antimicrobial resistance

The bulk of mathematical models arising in these areas is based on ordinary or partial differential equations, but some aspects are better modeled  by discrete concepts such individual based models or cellular automata with  stochastic components. In many cases one has hybrid models that bridge  various length and/or time scales, including PDE-ODE coupled systems of  various types, differential-algebraic problems, mixed hyperbolic-elliptic free  boundary value problems with non-local effects, degenerate parabolic systems, hybrid discrete-continuous descriptions, etc. This raises mathematical questions of fundamental nature, such as well-posedness, stability and long term behavior, and of practical nature, such as numerical treatment and accurate analytical and semi-analytical approximations, bifurcation problems, etc.

The workshop will bring together researchers with expertise in mathematical modeling (microbial population dynamics, biochemical reactions  and pathways, biofluid dynamics, uid/soft structure interactions, multiscale modeling), nonlinear analysis (dynamical systems, partial differential  equations, control theory, homogenization theory), and computational mathematics (numerical PDEs and ODEs, Computational Fluid Dynamics, agent based modeling, multi-scale and multi-physics simulation, scientific computing and software).

A major objective of the workshop is to map out current and future challenges in biofilm modeling and to be a platform to establish collaborations between researchers with different mathematical expertise to tackle those in a multi-pronged approach.

Participants of this event might also be interested in the Workshop on the Role of Mathematics in Combatting Antibiotic Resistance and Developing Novel Antibacterials on May 14: http://www.fields.utoronto.ca/activities/17-18/antibacterials .