ADVANCE Fellows: Effects of Host Age-Structure on the Development and Evolution of Infectious Diseases

DMS Award AbstractAward #： 0137687 PI： Martcheva，马亚机构： 纽约理工大学课程： 组织结构项目经理：Catherine Mavriplis职务：ADVANCE Fellows奖：本项目的研究内容是利用偏微分方程和动力系统理论，研究具有结构的种群中宿主-寄生虫系统的疾病调控和协同进化作用。对这一中心目标的研究通过三个具体系统进行。第一个模型阐明了疾病进展（感染年龄）和超级感染在产生复杂的动态和多重平衡交替稳定的作用。第二部分研究了宿主异质性对同一宿主的感染性和多重感染的影响。第三个应用是关于宿主异质性在病原体遗传多样性中的作用。年龄结构的影响共存的竞争菌株相同的病原体的影响进行了研究，所以是复杂的动力学的共同进化的微寄生虫的毒力和宿主异质性的影响。该项目的教育部分涉及在中学后教育和培训的早期和后期阶段将数学和科学计算结合起来，并将其应用于生命科学。作为该项目的一部分，调查员将致力于通过开发适当的教学材料将MATLAB纳入微积分课程。研究员还将在康奈尔大学的计算，数学和理论生物学REU项目中进行讲座和指导学生研究项目。马亚Martcheva提出的活动，以发展学术生涯中的数学生物学。该研究计划的重点是通过使用数学建模研究疾病调节的作用和宿主-寄生虫系统在具有结构的种群中的共同进化。从历史上看，疾病控制策略依赖于阈值条件，其中最著名的是要求疾病的繁殖数（由一种传染性物质在易感人群中引起的继发感染的平均数给出）小于1。本项目中考虑的模型表明，这一阈值条件可能不足以根除疾病，特别是在死亡率高的疾病中。另一个阈值要求再生数降低到另一个值（小于1）以下，称为传输阈值。传播阈值可能难以计算，但可以计算出一个低估值，这给出了导致疾病根除的阈值条件。Martcheva的教育活动包括课程开发和指导数学生物学的本科生。 日期：2002年1月28日

DMS Award AbstractAward #: 0137687PI: Martcheva, Maia Institution: Polytechnic University of New YorkProgram: InfrastructureProgram Manager: Catherine MavriplisTitle: ADVANCE Fellows Award: Effects of Host Age-Structure on the Development and Evolution on Infectious DiseasesThe research component of this project focuses on the study of the role of disease regulation and coevolution of host-parasite systems in populations with structure through the use of partial differential equations and dynamical systems theory. Research on this central objective is carried out through three specific systems. The first model elucidates the role of disease progression (age of infection) and super-infection in generating complex dynamics and multiple equilibria with alternating stability. The second investigates the impact of host heterogeneity on the evolution of infectivity and multiple infections of the same host. The third application is concerned with the role of host heterogeneity in the genetic diversity of a disease pathogen. The impact of age-structure on coexistence of competing strains of the same causative agent is investigated and so are the effects of complex dynamics on the coevolution of microparasite virulence and host heterogeneity. The educational component of this project is concerned with the integration of mathematics and scientific computing, and their application to life sciences, in the early and later stages of postsecondary education and training. As part of the project the investigator will work for the incorporation of MATLAB into the calculus curriculum through development of appropriate instructional materials. The investigator will also give lectures and mentor student research projects in a REU program in computational, mathematical and theoretical biology at Cornell University. Maia Martcheva proposes activities to develop an academic career in Mathematical Biology. The research plan focuses on the study of the role of disease regulation and coevolution of host-parasite systems in populations with structure through the use of mathematical modeling. Historically strategies for disease control have relied on threshold conditions, the most well-known of which requires that the reproductive number of the disease (given by the average number of secondary infections caused by one infective in a population of susceptibles) be smaller than one. The models considered in this project demonstrate that this threshold condition may not be sufficient for the eradication of the disease, particularly in case of diseases with high mortality. An alternative threshold requires that the reproductive number is reduced below another value (smaller than one), called transmission threshold. The transmission threshold may be difficult to calculate but an underestimate can be computed which gives a threshold condition leading to the eradication of the disease. Martcheva's educational activities include curriculum development and mentoring undergraduates in mathematical biology. Date: January 28, 2002