Mathematical Models of Structured Populations in Biology

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The Principal Investigator studies mathematical models of epidemics structured by individual behavior. The models are applicable to three levels of population epidemiology: (1) in-host pathogenesis of microorganisms, (2) noscocomial (hospital acquired) epidemics, and (3) large-scale epidemics in society. The research is applicable to (1) models of prion replication with individual prion polymers structured by fibril length, (2) models of antibiotic resistance in hospital settings with individual patients structured by age since becoming infected with drug resistant bacterial strains, and (3) models of viral respiratory epidemics with individual infectives structured by age since becoming infected. The models consist of nonlinear differential equations and the methods of research utilize differential equations theory, operator theory, functional analysis, numerical analysis, and computer simulations. The parametric input of the models is based on experimental and epidemiological data in consultation with scientific collaborators. The goals of the research are (1) to evaluate hypothesized mechanisms of prion proliferation in the development of diseases such as bovine spongiform encephalopathy (mad cow disease) and to predict the efficacy of therapeutic intervention, (2) to understand the evolution of multi-drug antibiotic resistant bacterial strains in hospitals and to evaluate hospital policies that prevent or reduce their endemicity, and (3) to analyze the effects of quarantine and isolation measures in epidemics such as the 2003 SARS epidemic and the influenza pandemic of 1918. The significance of the research is its contribution to public health policy in control of epidemic diseases.