On October 3, 2011, three scientists (Bruce A. Beutler, Jules A. Hoffmann and Ralph M. Steinman) won Nobel Prizes in Medicine or Physiology for their discoveries on how the innate and adaptive phases of the immune response are activated and thereby provide novel insights into disease mechanisms. Their work has opened up new avenues for the development of prevention and therapy against infections, cancer, and inflammatory diseases. In this talk I’ll use malaria as an example to explain how both innate immunity and adaptive immunity fight against malaria infection and to model the within-host dynamics of malaria infection with immune response. For the ODE model consisted of healthy red blood cells, infected red blood cells, malaria parasitemia, and immune effectors, conditions on the existence and stability of both infection equilibria are given and it is shown that the model can exhibit periodic oscillations. Using the Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille-Yosida operator, it is shown that the age-structured malaria model of infected red blood cells (Rouzine and McKenzie, Proc Natl Acad Sci USA, 2003) undergoes Hopf bifurcation when the replication rate is used as the bifurcation parameter. Both mathematical analysis and numerical simulations confirm the observation of Kwiatkowski and Nowak (Proc Natl Acad Sci USA,1991) that synchronization with regular periodic oscillations (of period 48 h) occurs in malaria infection with modest replication rates.

报告人简介: 阮士贵教授于1992年于加拿大University of Alberta获得博士学位，现为University of Miami数学系教授。研究领域为生物数学、动力系统以及微分方程，近年来在流行病数学建模以及分析中取得重要成果。已经在PNAS，Trans AMS，Memoris AMS,JDE，JMB等重要刊物发表学术论文一百余篇，并受聘为Mathematical Biosciences、DCDS-B等重要刊物编委。此外，作为组委会主席，曾在法国等地组织过多次重要国际会议。详细研究工作见：http://www.math.miami.edu/~ruan/.