Hal Smith

• 
  Modeling Microbial Populations in the Chemostat
  Hal Smith
  Modeling Microbial Populations in the Chemostat by Hal Smith
• 
  The Freter Model of Biofilm Formation
  Hal Smith
  Driven by recent advances in noninvasive microscopy, staining techniques, and genetic probes, there has been enormous increase in our understanding of biofilms. Along with this increase in understanding, has been increasing interest in mathematical models of biofilms to get at important mechanisms. Most recent modeling in the field has been directed towards understanding the mechanisms underlying the remarkable spatial structure of biofilms which has become evident through the use of modern imaging techniques. Most of these models are so complex that they can be investigated only using sophisticated numerical simulations.
  
  On the other hand, there are relatively few simple, conceptual biofilm models which are amenable to mathematical analysis yet which yield significant and useful results. Here, we speak of models which do not attempt to provide much detail on the spatial structure of biofilms but which provide information on conditions suitable for biofilm formation and maintenance and which model the formation of biofilms directly, starting from an inoculum of planktonic bacteria. Freter et al. formulated a mathematical model to understand the phenomena of colonization resistance in the mammalian gut (stability of resident microflora to colonization). Essentially, their model can be viewed as a crude biofilm model. In contrast to state of the art biofilm models, the Freter model completely ignores the three-dimensional spatial structure of the biofilm. Yet it can give useful results. The model and its implications will be surveyed.