Mathematical Models of Structured Populations in Biology

首席调查员研究由个人行为构成的流行病的数学模型。该模型适用于人群流行病学的三个层次：(1)微生物在宿主内的发病；(2)医院内(医院获得性)流行病；(3)大规模的社会流行病。这项研究适用于(1)由纤毛长度构成的单个Prion聚合体的Prion复制模型，(2)医院环境中单个患者自感染耐药细菌菌株以来按年龄结构的抗生素耐药性模型，以及(3)自感染以来按年龄结构的病毒呼吸道流行病模型。模型由非线性微分方程组组成，研究方法运用了微分方程组理论、算子理论、泛函分析、数值分析和计算机模拟。模型的参数输入是基于与科学合作者协商的实验和流行病学数据。这项研究的目标是(1)评估在牛海绵状脑病(疯牛病)等疾病的发展过程中Pron增殖的假设机制，并预测治疗干预的效果；(2)了解医院中耐多药抗生素细菌菌株的演变，并评估医院防止或减少其地方性的政策；(3)分析检疫和隔离措施在2003年SARS疫情和1918年流感大流行等流行病中的效果。这项研究的意义在于它对控制传染病的公共卫生政策做出了贡献。

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.