Mathematical Models of Structured Populations in Biology

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Webb0190148 The investigator studies differential equation models ofstructured populations. The structured models arise inconsidering four applications: (1) models of tumor cordsstructured by the cell cycle, (2) models of blood cell productionsystems with proliferating and quiescent compartments structuredby cell maturity, (3) models of replicating prion populationsstructured by polymer length, and (4) models ofvancomycin-resistant enterococci epidemics in dialysis clinicsstructured by the time since patient admission. This project applies theoretical mathematics to biologicaland medical research involving population interactions. Thespecific goals are to identify the behavior of proliferating andquiescent cell populations in the micro-architecture ofvascularized tumors, to differentiate, qualitatively andquantitatively, the development of normal and abnormal blood cellpopulation lines, to evaluate hypothetical mechanisms involved inthe polymerization processes of prion population growth intransmissible spongiform encephalopathies (mad cow disease), andto predict the epidemiological effects in dialysis clinics ofhealth care worker hygiene, patient-health care worker ratios,and screening of temporarily absent patients. Benefits tosociety are the project's contributions to the fundamentalknowledge of biological and health sciences.