ENG 
ESP Session S12 - Delay and functional differential equations and applications
Wednesday, July 21, 19:45 ~ 20:20 UTC-3
A Delay Model for Persistent Viral Infections in Replicating Cells
Gail Wolkowicz
McMaster University, Canada - This email address is being protected from spambots. You need JavaScript enabled to view it.
Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating \textit{transcritical (backward and forward), saddle-node, and Hopf} bifurcations, and provide evidence of {\it homoclinic bifurcations} and a \textit{Bogdanov-Takens bifurcation}. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of \textit{robust uniform persistence}. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.
Joint work with Hayriye Gulbudak (University of Louisiana at Lafayette) and Paul L. Salceanu (University of Louisiana at Lafayette).