Mathematical Sciences: Mathematical Models in Microbial Ecology

点击翻译按钮获取中文摘要

In this project research will be focused on differential equation models studying the effects of spatial heterogeneity and indirect nutrient consumption on microbial growth. The model equations for two competing species generate a strongly monotone dynamical system, and steady state coexistence has been shown to be possible. Using various techniques in nonlinear analysis and numerical simulations, the investigator will study the choice of parameters for coexistence, the effect of microbial mobility on coexistence, and the maximum number of coexisting species. Research on indirect nutrient consumption will focus on models of both extracellular and intracellular conversion of the nutrient to an intermediate product which is assimilated for growth. The goal is to compare the efficiency of the different consumption processes, and to study the possibility of coexistence of species with different mechanisms of nutrient assimilation. This project is concerned with the study of mathematical models of microbial growth and competition in continuous culture, a commonly used laboratory technique in microbiology. Microorganisms play very important roles in natural ecological systems, and their activities have numerous industrial applications, e.g., waste water treatment, production of food, drugs and various other chemicals, bacterial control, etc. Competition between different species is an important feature in many ecological systems, and the design of many industrial processes, e.g., use of biological agents in bacterial control or waste disposal, is based on the competitiveness of different species. Experimental study of microbial activities in laboratory environments are especially amenable to mathe matical modeling by differential equations. Analysis of the model equations gives better understanding of the underlying principles of microbial behaviors, and often leads to new experimental designs.