Mathematical Sciences: Mathematical Models of Cell Population Dynamics

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This project will make theoretical and numerical investigations of the nonlinear partial differential equations that describe structured models of cell population dynamics. Individual cells are distinguished by structure variables corresponding to size, age, or other physical characteristics. The populations are divided into population subclasses that interact through nonlinear transition rates. The main objective will be to understand the qualitative behavior of the populations, the on- set of oscillatory phenomena, and the response to external periodic loss functions. The main methods will apply the theory of semigroups of positive linear and nonlinear operators in Banach lattices. The main applications will be to tumor cell populations with proliferating and quiescent classes and to multi-level blood cell production systems. The goal in the tumor cell population studies will be to understand the role of quiescence in tumor growth and tumor therapy. The goal in the blood cell population studies will be to understand the regulation processes in normal and abnormal systems.