Mathematical Models of Structured Populations in Biology

主要研究者研究由个人行为构成的流行病数学模型。这些模型适用于三个层次的人群流行病学：（1）微生物的宿主发病机制，（2）医院获得性流行病，（3）社会大规模流行病。该研究适用于（1）由原纤维长度构成的单个朊病毒聚合物的朊病毒复制模型，（2）医院环境中由感染耐药菌株后的年龄构成的个体患者的抗生素耐药性模型，以及（3）由感染后的年龄构成的个体感染者的病毒呼吸道流行病模型。该模型由非线性微分方程组成，研究方法利用微分方程理论，算子理论，泛函分析，数值分析和计算机模拟。模型的参数输入是根据与科学合作者协商的实验和流行病学数据。本研究的目的是（1）评价朊病毒增殖在牛海绵状脑病等疾病发展中的假设机制（疯牛病）和预测治疗干预的功效，（2）了解医院中耐多药抗生素菌株的演变，并评估预防或减少其流行的医院政策，（3）分析2003年SARS疫情和1918年流感大流行等疫情中检疫隔离措施的效果。本研究的意义在于为控制流行病的公共卫生政策做出贡献。

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.