Date of Award
2011
Degree Type
Thesis
Degree Name
Master of Science
Program
Applied Mathematics
Supervisor
Dr. Pei Yu
Abstract
We propose a mathematical model for HIV-1 infection with two time delays, one for the average latent period of cell infection and the other for the average time needed for the virus production after a virion enters a cell. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. When only the intracellular delay is enrolled into model (1.13), the basic reproduction numbers Rq and Rd are identified and their threshold properties are discussed. When Rq < 1, the infection-free equilibrium Eq is globally asymptotically stable. When Rq > 1, Eq becomes unstable and there occurs the single-infection equilibrium Es. If Rq > 1 and Rd < 1, Es is asymptotically stable, while for Rd > 1, Es loses its stability to the double-infection equilibrium. For the double-infection equilibrium Ed, we show how to determine its stability and existence of Hopf bifurcation. Some simulations are presented to demonstrate the theoretical results.
Further investigation is carried over by introducing the second time lag into model (2.1). We have identified the new basic reproduction numbers Rqand Rd, and proved that for Rq < 1 the infection-free equilibrium Eq is globally asymptotically stable. If Rq > 1 and Rd < 1, the single-infection equilibrium Es is asymptotically stable. For
the double-infection equilibrium Ed, it has been found that there exist both Hopf and N
double Hopf bifurcations. These theoretical predictions are verified by using some numerical examples. Evidences indicate that the viral-therapy, of recombining HIV-1 virus with a genetically modified virus may be effective in reducing the HIV-1 load, and larger delays may be able to help eradicate the virus.
Recommended Citation
Bai, Yu, "Study of an HIV-1 Model with Time Delays" (2011). Digitized Theses. 3517.
https://ir.lib.uwo.ca/digitizedtheses/3517