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

DMS奖摘要奖#：0137687PI：Martcheva，Maia研究所：纽约理工大学项目：基础设施项目经理：Catherine Mavriplis标题：高级研究员奖：宿主年龄结构对传染病发展和进化的影响本项目的研究部分侧重于通过使用偏微分方程和动力系统理论来研究疾病调节和宿主-寄生虫系统在有结构的种群中的共同进化的作用。对这一中心目标的研究是通过三个具体系统进行的。第一个模型阐明了疾病进展(感染年龄)和重复感染在产生复杂的动力学和具有交替稳定性的多重平衡中的作用。第二部分考察了宿主异质性对同一宿主的传染性演化和多重感染的影响。第三个应用涉及寄主异质性在疾病病原体遗传多样性中的作用。研究了年龄结构对同一病原竞争菌株共存的影响，以及复杂动力学对微寄生虫毒力和寄主异质性的协同进化的影响。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及其在生命科学中的应用相结合。作为该项目的一部分，研究人员将通过开发适当的教学材料，努力将MatLab纳入微积分课程。这位研究人员还将在康奈尔大学的REU计算、数学和理论生物学项目中讲课和指导学生研究项目。Maia Martcheva建议开展活动，以发展数学生物学的学术生涯。该研究计划的重点是通过使用数学模型来研究寄主-寄生虫系统在具有结构的种群中的疾病调节和协同进化的作用。从历史上看，疾病控制战略依赖于阈值条件，其中最广为人知的条件要求疾病的繁殖数量(由一名感染者在易感人群中造成的二次感染的平均数量)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，特别是在死亡率较高的疾病的情况下。另一种阈值要求将繁殖次数减少到另一个值(小于1)以下，该值称为传输阈值。传播阈值可能很难计算，但可以计算出低估值，这给出了导致根除疾病的阈值条件。Martcheva的教育活动包括课程开发和指导本科生的数学生物学。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