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

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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