Mathematical Models of Structured Populations in Biology

Vanderbilt University, Nashville TN

Investigators

Abstract

Webb 0190148 The investigator studies differential equation models of structured populations. The structured models arise in considering four applications: (1) models of tumor cords structured by the cell cycle, (2) models of blood cell production systems with proliferating and quiescent compartments structured by cell maturity, (3) models of replicating prion populations structured by polymer length, and (4) models of vancomycin-resistant enterococci epidemics in dialysis clinics structured by the time since patient admission. This project applies theoretical mathematics to biological and medical research involving population interactions. The specific goals are to identify the behavior of proliferating and quiescent cell populations in the micro-architecture of vascularized tumors, to differentiate, qualitatively and quantitatively, the development of normal and abnormal blood cell population lines, to evaluate hypothetical mechanisms involved in the polymerization processes of prion population growth in transmissible spongiform encephalopathies (mad cow disease), and to predict the epidemiological effects in dialysis clinics of health care worker hygiene, patient-health care worker ratios, and screening of temporarily absent patients. Benefits to society are the project's contributions to the fundamental knowledge of biological and health sciences.