[PAST EVENT] CSUMS Lecture/Mathematics Colloquium: Hongying Shu (University of New Brunswick, Canada)

September 2, 2011
3pm - 4pm
Jones Hall, Room 301
200 Ukrop Way
Williamsburg, VA 23185Map this location
Abstract: The dynamics of an in-host model with general form of target-cell dynamics, nonlinear incidence and distributed delay are investigated. The model can describe in vivo infections of HIV-I, HCV, HBV and HTLV-I infection. We derive the basic reproduction number R0 for the viral infection, and establish that the global dynamics are completely determined by the values of R0. An implication is that intracellular delays will lead to periodic oscillations in in-host models only with the right kind of target-cell dynamics. To understand joint e ffects of target cells dynamics and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis. The bifurcation parameters are the mitosis rate r of the target cells and an intracellular delay tau in the incidence of viral infection. We describe the stability region of the chronic-infection equilibrium E* in the two-dimensional (r,tau) parameter space, as well as the global Hopf bifurcation curves as each of  tau and r varies. Our analysis shows that, while both tau and r can destabilize E* and cause Hopf bifurcations, they do behave differently. The intracellular delay  can cause Hopf bifurcations only when r is positive and sufficiently large, while r can cause Hopf bifurcations even when tau=0. Intracellular delay tau can cause stability switches in E* while r does not. This is a joint work with Michael Y. Li, University of Alberta.