Speaker: Prof. Shigui Ruan, Department of Mathematics, University of Miami
Abstract: 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.