Mathematical Sciences: Biological Models with Time Delays and Spatial Dependence

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This investigation will continue the study of cellular control models. There are three main areas of study in this project. First, the principal investigator will extend his analysis of compartmental models which include both time delays and spatial effects. These models are studied to show the stability of the differential equations describing the biological system. The second area of study details a model for the initiation of replication at OriC in E. coli. The model, which is based on biochemical kinetics, is being developed in conjunction with ongoing experiments. The final problem is to examine a linear delay differential equation with two time delays. For fixed delays the bifurcation surface is examined with respect to the coefficient parameters. For all three problems the project will be applicable to broad classes of equations that occur in modeling certain biological and physical phenomena.